The document discusses Mathew Joseph's PhD defense presentation on query answering over contextualized RDF/OWL knowledge with bridge rules. The presentation covers quad-systems, which represent contextualized RDF data and bridge rules between contexts. It introduces the distributed chase algorithm for query answering over quad-systems and identifies decidability challenges due to potential non-termination of the chase. The presentation also outlines decidable classes of quad-systems where the chase is guaranteed to terminate.
A Signature Scheme as Secure as the Diffie Hellman Problemvsubhashini
This document summarizes a theory seminar on cryptography that covered digital signature schemes. It began with an introduction to hard assumptions like the discrete log problem and computational Diffie-Hellman problem. It then described the ElGamal digital signature scheme, including its key generation, signing, and verification algorithms. It discussed the security of signature schemes in the chosen message attack model and how the ElGamal scheme's unforgeability relies on the hardness of computing discrete logs. It analyzed the probability of an adversary using oracle queries to forge a signature or solve the computational Diffie-Hellman problem. References for the original ElGamal and related signature scheme papers were also provided.
Processing Reachability Queries with Realistic Constraints on Massive Network...BigMine
Massive graphs are ubiquitous in various application domains, such as social networks, road networks, communication networks, biological networks, RDF graphs, and so on. Such graphs are massive (for example, with hundreds of millions of nodes and edges or even more) and contain rich information (for example, node/edge weights, labels and textual contents). In such massive graphs, an important class of problems is to process various graph structure related queries. Graph reachability, as an example, asks whether a node can reach another in a graph. However, the large graph scale presents new challenges for efficient query processing.
In this talk, I will introduce two new yet important types of graph reachability queries: weight constraint reachability that imposes edge weight constraint on the answer path, and k-hop reachability that imposes a length constraint on the answer path. With such realistic constraints, we can find more meaningful and practically feasible answers. These two reachablity queries have wide applications in many real-world problems, such as QoS routing and trip planning.
Lattice-Based Cryptography: CRYPTANALYSIS OF COMPACT-LWEPriyanka Aash
Destructive and constructive methods in lattice-based cryptography will be discussed. Topic 1: Cryptanalysis of Compact-LWE Authors: Jonathan Bootle; Mehdi Tibouchi; Keita Xagawa Topic 2: Two-message Key Exchange with Strong Security from Ideal Lattices Authors: Zheng Yang; Yu Chen; Song Luo
(Source: RSA Conference USA 2018)
This document summarizes a research paper on identifying micro-architectures in evolving object-oriented software systems. The paper presents an approach called SGFinder that models class diagrams as labeled graphs and defines micro-architectures as connected induced subgraphs. SGFinder efficiently enumerates all micro-architectures up to a given size. The paper applies SGFinder to two open-source systems and analyzes the identified micro-architectures to find those that are particularly fault-prone, fault-free, stable or change-prone. The results provide insights into common micro-architecture patterns and their relationships to quality attributes.
In this paper we study of the MOR cryptosystem using camina group. We show that using the automorphism of the camina group one can build a secure MOR cryptosystem.
NIPS2017 Few-shot Learning and Graph ConvolutionKazuki Fujikawa
The document discusses meta-learning and prototypical networks for few-shot learning. It introduces prototypical networks, which learn a metric space such that classification can be performed by finding the nearest class prototype to a query example in embedding space. The document summarizes results on few-shot image classification benchmarks like Omniglot and miniImageNet, finding that prototypical networks achieve state-of-the-art performance.
Sensors and Samples: A Homological ApproachDon Sheehy
In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that its possible to certify the coverage of a coordinate free sensor network even with very minimal knowledge of the space to be covered. We give a new, simpler proof of the de Silva-Ghrist Topological Coverage Criterion that eliminates any assumptions about the smoothness of the boundary of the underlying space, allowing the results to be applied to much more general problems. The new proof factors the geometric, topological, and combinatorial aspects of this approach. This factoring reveals an interesting new connection between the topological coverage condition and the notion of weak feature size in geometric sampling theory. We then apply this connection to the problem of showing that for a given scale, if one knows the number of connected components and the distance to the boundary, one can also infer the higher betti numbers or provide strong evidence that more samples are needed. This is in contrast to previous work which merely assumed a good sample and gives no guarantees if the sampling condition is not met.
A Signature Scheme as Secure as the Diffie Hellman Problemvsubhashini
This document summarizes a theory seminar on cryptography that covered digital signature schemes. It began with an introduction to hard assumptions like the discrete log problem and computational Diffie-Hellman problem. It then described the ElGamal digital signature scheme, including its key generation, signing, and verification algorithms. It discussed the security of signature schemes in the chosen message attack model and how the ElGamal scheme's unforgeability relies on the hardness of computing discrete logs. It analyzed the probability of an adversary using oracle queries to forge a signature or solve the computational Diffie-Hellman problem. References for the original ElGamal and related signature scheme papers were also provided.
Processing Reachability Queries with Realistic Constraints on Massive Network...BigMine
Massive graphs are ubiquitous in various application domains, such as social networks, road networks, communication networks, biological networks, RDF graphs, and so on. Such graphs are massive (for example, with hundreds of millions of nodes and edges or even more) and contain rich information (for example, node/edge weights, labels and textual contents). In such massive graphs, an important class of problems is to process various graph structure related queries. Graph reachability, as an example, asks whether a node can reach another in a graph. However, the large graph scale presents new challenges for efficient query processing.
In this talk, I will introduce two new yet important types of graph reachability queries: weight constraint reachability that imposes edge weight constraint on the answer path, and k-hop reachability that imposes a length constraint on the answer path. With such realistic constraints, we can find more meaningful and practically feasible answers. These two reachablity queries have wide applications in many real-world problems, such as QoS routing and trip planning.
Lattice-Based Cryptography: CRYPTANALYSIS OF COMPACT-LWEPriyanka Aash
Destructive and constructive methods in lattice-based cryptography will be discussed. Topic 1: Cryptanalysis of Compact-LWE Authors: Jonathan Bootle; Mehdi Tibouchi; Keita Xagawa Topic 2: Two-message Key Exchange with Strong Security from Ideal Lattices Authors: Zheng Yang; Yu Chen; Song Luo
(Source: RSA Conference USA 2018)
This document summarizes a research paper on identifying micro-architectures in evolving object-oriented software systems. The paper presents an approach called SGFinder that models class diagrams as labeled graphs and defines micro-architectures as connected induced subgraphs. SGFinder efficiently enumerates all micro-architectures up to a given size. The paper applies SGFinder to two open-source systems and analyzes the identified micro-architectures to find those that are particularly fault-prone, fault-free, stable or change-prone. The results provide insights into common micro-architecture patterns and their relationships to quality attributes.
In this paper we study of the MOR cryptosystem using camina group. We show that using the automorphism of the camina group one can build a secure MOR cryptosystem.
NIPS2017 Few-shot Learning and Graph ConvolutionKazuki Fujikawa
The document discusses meta-learning and prototypical networks for few-shot learning. It introduces prototypical networks, which learn a metric space such that classification can be performed by finding the nearest class prototype to a query example in embedding space. The document summarizes results on few-shot image classification benchmarks like Omniglot and miniImageNet, finding that prototypical networks achieve state-of-the-art performance.
Sensors and Samples: A Homological ApproachDon Sheehy
In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that its possible to certify the coverage of a coordinate free sensor network even with very minimal knowledge of the space to be covered. We give a new, simpler proof of the de Silva-Ghrist Topological Coverage Criterion that eliminates any assumptions about the smoothness of the boundary of the underlying space, allowing the results to be applied to much more general problems. The new proof factors the geometric, topological, and combinatorial aspects of this approach. This factoring reveals an interesting new connection between the topological coverage condition and the notion of weak feature size in geometric sampling theory. We then apply this connection to the problem of showing that for a given scale, if one knows the number of connected components and the distance to the boundary, one can also infer the higher betti numbers or provide strong evidence that more samples are needed. This is in contrast to previous work which merely assumed a good sample and gives no guarantees if the sampling condition is not met.
The Art Gallery problem is a fundamental visibility problem in Computational Geometry, introduced by Klee in 1973. The input consists of a simple polygon P, (possibly infinite) sets X and Y of points within P, and an integer k, and the objective is to decide whether at most k guards can be placed on points in X so that every point in Y is visible to at least one guard. In the classic formulation of Art Gallery, X and Y consist of all the points within P. Other well-known variants restrict X and Y to consist either of all the points on the boundary of P or of all the vertices of P. The above mentioned variants of Art Gallery are all W[1]-hard with respect to k [Bonnet and Miltzow, ESA'16]. Given the above result, the following question was posed by Giannopoulos [Lorentz Center Workshop, 2016].
``Is Art Gallery FPT with respect to the number of reflex vertices?''
In this talk, we will obtain a positive answer to the above question, for some variants of the Art Gallery problem. By utilising the structural properties of ``almost convex polygons'', we design a two-stage reduction from (Vertex,Vertex)-Art Gallery to a new CSP problem where constraints have arity two and involve monotone functions. For the above special version of CSP, we obtain a polynomial time algorithm. Sieving these results, we obtain an FPT algorithm for (Vertex,Vertex)-Art Gallery, when parameterized by the number of reflex vertices. We note that our approach also extends to (Vertex,Boundary)-Art Gallery and (Boundary,Vertex)-Art Gallery.
This slides are from a talk that I gave at the Algorithms Seminar at Tel-Aviv University.
This document provides a summary of various cheat sheets for AI topics including neural networks, machine learning, deep learning, and big data. It includes sections on neural network basics and graphs, machine learning basics and algorithms, and data science tools and libraries like TensorFlow, PyTorch, NumPy, Pandas, and Matplotlib. The document aims to be a complete list of the best AI cheat sheets for readers to learn key concepts in a concise manner.
My 2hr+ survey talk at the Vector Institute, on our deep learning theorems.Anirbit Mukherjee
This document provides an overview of several results from papers related to analyzing neural networks. It discusses questions about what functions neural networks can represent and the properties of their loss landscapes. Key results presented include showing neural networks can perform exact empirical risk minimization in polynomial time for 1D networks, proving networks can represent continuous piecewise linear functions, and demonstrating depth separations where shallower networks require much larger size to represent certain functions. Open problems are also discussed, such as fully characterizing the function space of neural networks.
The document discusses doing research on formally defining the operational semantics of the Java programming language. It aims to better understand Java's behavior and features like inheritance, modifiers, constructors through developing a semantic extension. The project would breakdown Java and represent features like access modifiers, final/abstract modifiers, and static modifiers through a new formal syntax.
Polylogarithmic approximation algorithm for weighted F-deletion problemsAkankshaAgrawal55
The document presents an approximation algorithm for weighted graph modification problems where the goal is to find a minimum weight set of vertices to delete such that the resulting graph has a certain property. Specifically, it provides a polylogarithmic approximation algorithm for weighted planar H-minor-free deletion, weighted chordal vertex deletion, and weighted distance hereditary deletion. The algorithm works by finding a well-structured set of vertices whose removal leaves a graph with bounded treewidth, then solving the problem on this subgraph using dynamic programming on a tree decomposition.
Do we need a logic of quantum computation?Matthew Leifer
1) The document discusses whether quantum computing needs a formal logic in the same way that classical computing is understood through classical logic. It examines previous proposals for "quantum logics" and focuses on Sequential Quantum Logic (SQL).
2) SQL models sequences of quantum measurements and operations through projection operators and sequential conjunction. The document proposes testing SQL propositions through a quantum algorithm that prepares an encoded "history state" and applies renormalization operations.
3) The proposed algorithm could test SQL propositions with exponentially small probability of success. Several open questions are raised about generalizing and improving SQL as a logic for quantum computing.
1) The document discusses problems related to complexity classes P and NP. It shows that several problems are NP-complete, including the Hamiltonian cycle problem, subgraph isomorphism problem, 0-1 integer programming problem, and Hamiltonian path problem.
2) It provides algorithms and reductions to prove several problems are NP-complete, such as reducing Hamiltonian cycle to the subgraph isomorphism problem and reducing 3-SAT to the 0-1 integer programming problem.
3) It also discusses properties of complexity classes P and NP, such as showing P is closed under certain operations and contained within NP intersect co-NP.
Probabilistic Abductive Logic Programming using Possible WorldsFulvio Rotella
Reasoning in very complex contexts often requires purely deductive reasoning to be supported by a variety of techniques that can cope with incomplete data. Abductive inference allows to guess information that has not been explicitly observed. Since there are many explanations for such guesses, there is the need for assigning a probability to each one. This work exploits logical abduction to produce multiple explanations consistent with a given background knowledge and defines a strategy to prioritize them using their chance of being true. Another novelty is the introduction of probabilistic integrity constraints rather than hard ones. Then we propose a strategy that learns model and parameters from data and exploits our Probabilistic Abductive Proof Procedure to classify never-seen instances. This approach has been tested on some standard datasets showing that it improves accuracy in presence of corruptions and missing data.
Predicting organic reaction outcomes with weisfeiler lehman networkKazuki Fujikawa
This document discusses neural message passing networks for modeling quantum chemistry. It defines message passing networks as having message functions that update node states based on neighboring node states, vertex update functions that update node states based to accumulated messages, and a readout function that produces an output for the full graph. It provides examples of specific message, update, and readout functions used in existing message passing models like interaction networks and molecular graph convolutions.
Constructing Distributed Doubly Linked Lists without Distributed LockingKota Abe
Explains a novel distributed algorithm for constructing distributed doubly linked lists (or bidirectional ring), which are common in structured P2P networks.
This presentation is used at the 2015 IEEE International Conference on Peer-to-Peer Computing (P2P2015).
The paper is available at
<http://www.media.osaka-cu.ac.jp/~k-abe/research/Constructing_Distributed_Doubly_Linked_Lists_without_Distributed_Locking.html>
Author: Kota Abe (Osaka City University/NICT), Mikio Yoshida (BBR Inc.)
Abstract:
A distributed doubly linked list (or bidirectional ring) is a fundamental distributed data structure commonly used in structured peer-to-peer networks. This paper presents DDLL, a novel decentralized algorithm for constructing distributed doubly linked lists. In the absence of failure, DDLL maintains consistency with regard to lookups of nodes, even while multiple nodes are simultaneously being inserted or deleted. Unlike existing algorithms, DDLL adopts a novel strategy based on conflict detection and sequence numbers. A formal description and correctness proofs are given. Simulation results show that DDLL outperforms conventional algorithms in terms of both time and number of messages.
This document discusses graph kernels, which are positive definite kernels defined on graphs that allow applying machine learning algorithms to graph-structured data like molecules. It covers different types of graph kernels like subgraph kernels, path kernels, and walk kernels. Walk kernels count the number of walks between two graphs and can be computed efficiently in polynomial time, unlike subgraph and path kernels. The document also discusses using product graphs to compute walk kernels and presents results on classifying mutagenicity using random walk kernels. It concludes by proposing using graph kernels and product graphs to define data depth measures for labeled graph ensembles.
An improved spfa algorithm for single source shortest path problem using forw...IJMIT JOURNAL
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph,
the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network.
SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed.
In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically
analyse the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient.
International Journal of Managing Information Technology (IJMIT)IJMIT JOURNAL
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph, the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network. SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed. In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically analyse the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient
An improved spfa algorithm for single source shortest path problem using forw...IJMIT JOURNAL
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph,
the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network.
SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed.
In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically
analyse the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient.
The document describes an algebraic attack on the KeeLoq block cipher. KeeLoq is used in car keyless entry systems and has 528 rounds with a 64-bit key. The attack sets up a system of equations modeling the encryption rounds using a SAT solver to recover the key from known plaintext-ciphertext pairs. It converts the algebraic normal form equations to conjunctive normal form required by the SAT solver to solve for the key.
This document provides an overview of clustering techniques, including supervised vs. unsupervised learning, clustering concepts, non-hierarchical clustering like k-means, and hierarchical clustering like hierarchical agglomerative clustering. It discusses clustering applications, algorithms like k-means and hierarchical agglomerative clustering, and evaluation metrics like cluster silhouettes. Key clustering goals are to partition unlabeled data into clusters such that examples within a cluster are similar and different between clusters.
This document summarizes a presentation about variational autoencoders (VAEs) presented at the ICLR 2016 conference. The document discusses 5 VAE-related papers presented at ICLR 2016, including Importance Weighted Autoencoders, The Variational Fair Autoencoder, Generating Images from Captions with Attention, Variational Gaussian Process, and Variationally Auto-Encoded Deep Gaussian Processes. It also provides background on variational inference and VAEs, explaining how VAEs use neural networks to model probability distributions and maximize a lower bound on the log likelihood.
The document discusses constraint-based problem solving, including modeling problems as constraints on acceptable solutions, defining variables and domains, and defining constraints; solving models by defining search spaces and algorithms like backtracking search and stochastic search; and verifying and analyzing solutions. It also provides examples of constraint satisfaction problems and how they can be modeled and solved using different constraint languages and representations.
The document discusses using machine learning techniques like Gaussian processes (GPs) to optimize the configuration of software systems. It notes that software performance landscapes are often complex, with non-linear interactions between parameters and non-convex response surfaces. Measurements are also subject to noise. The document introduces an approach called TL4CO that uses multi-task Gaussian processes to model software performance across different versions/deployments, allowing it to leverage data from other versions to improve optimization. This helps address challenges in DevOps where new versions are continuously delivered.
The Art Gallery problem is a fundamental visibility problem in Computational Geometry, introduced by Klee in 1973. The input consists of a simple polygon P, (possibly infinite) sets X and Y of points within P, and an integer k, and the objective is to decide whether at most k guards can be placed on points in X so that every point in Y is visible to at least one guard. In the classic formulation of Art Gallery, X and Y consist of all the points within P. Other well-known variants restrict X and Y to consist either of all the points on the boundary of P or of all the vertices of P. The above mentioned variants of Art Gallery are all W[1]-hard with respect to k [Bonnet and Miltzow, ESA'16]. Given the above result, the following question was posed by Giannopoulos [Lorentz Center Workshop, 2016].
``Is Art Gallery FPT with respect to the number of reflex vertices?''
In this talk, we will obtain a positive answer to the above question, for some variants of the Art Gallery problem. By utilising the structural properties of ``almost convex polygons'', we design a two-stage reduction from (Vertex,Vertex)-Art Gallery to a new CSP problem where constraints have arity two and involve monotone functions. For the above special version of CSP, we obtain a polynomial time algorithm. Sieving these results, we obtain an FPT algorithm for (Vertex,Vertex)-Art Gallery, when parameterized by the number of reflex vertices. We note that our approach also extends to (Vertex,Boundary)-Art Gallery and (Boundary,Vertex)-Art Gallery.
This slides are from a talk that I gave at the Algorithms Seminar at Tel-Aviv University.
This document provides a summary of various cheat sheets for AI topics including neural networks, machine learning, deep learning, and big data. It includes sections on neural network basics and graphs, machine learning basics and algorithms, and data science tools and libraries like TensorFlow, PyTorch, NumPy, Pandas, and Matplotlib. The document aims to be a complete list of the best AI cheat sheets for readers to learn key concepts in a concise manner.
My 2hr+ survey talk at the Vector Institute, on our deep learning theorems.Anirbit Mukherjee
This document provides an overview of several results from papers related to analyzing neural networks. It discusses questions about what functions neural networks can represent and the properties of their loss landscapes. Key results presented include showing neural networks can perform exact empirical risk minimization in polynomial time for 1D networks, proving networks can represent continuous piecewise linear functions, and demonstrating depth separations where shallower networks require much larger size to represent certain functions. Open problems are also discussed, such as fully characterizing the function space of neural networks.
The document discusses doing research on formally defining the operational semantics of the Java programming language. It aims to better understand Java's behavior and features like inheritance, modifiers, constructors through developing a semantic extension. The project would breakdown Java and represent features like access modifiers, final/abstract modifiers, and static modifiers through a new formal syntax.
Polylogarithmic approximation algorithm for weighted F-deletion problemsAkankshaAgrawal55
The document presents an approximation algorithm for weighted graph modification problems where the goal is to find a minimum weight set of vertices to delete such that the resulting graph has a certain property. Specifically, it provides a polylogarithmic approximation algorithm for weighted planar H-minor-free deletion, weighted chordal vertex deletion, and weighted distance hereditary deletion. The algorithm works by finding a well-structured set of vertices whose removal leaves a graph with bounded treewidth, then solving the problem on this subgraph using dynamic programming on a tree decomposition.
Do we need a logic of quantum computation?Matthew Leifer
1) The document discusses whether quantum computing needs a formal logic in the same way that classical computing is understood through classical logic. It examines previous proposals for "quantum logics" and focuses on Sequential Quantum Logic (SQL).
2) SQL models sequences of quantum measurements and operations through projection operators and sequential conjunction. The document proposes testing SQL propositions through a quantum algorithm that prepares an encoded "history state" and applies renormalization operations.
3) The proposed algorithm could test SQL propositions with exponentially small probability of success. Several open questions are raised about generalizing and improving SQL as a logic for quantum computing.
1) The document discusses problems related to complexity classes P and NP. It shows that several problems are NP-complete, including the Hamiltonian cycle problem, subgraph isomorphism problem, 0-1 integer programming problem, and Hamiltonian path problem.
2) It provides algorithms and reductions to prove several problems are NP-complete, such as reducing Hamiltonian cycle to the subgraph isomorphism problem and reducing 3-SAT to the 0-1 integer programming problem.
3) It also discusses properties of complexity classes P and NP, such as showing P is closed under certain operations and contained within NP intersect co-NP.
Probabilistic Abductive Logic Programming using Possible WorldsFulvio Rotella
Reasoning in very complex contexts often requires purely deductive reasoning to be supported by a variety of techniques that can cope with incomplete data. Abductive inference allows to guess information that has not been explicitly observed. Since there are many explanations for such guesses, there is the need for assigning a probability to each one. This work exploits logical abduction to produce multiple explanations consistent with a given background knowledge and defines a strategy to prioritize them using their chance of being true. Another novelty is the introduction of probabilistic integrity constraints rather than hard ones. Then we propose a strategy that learns model and parameters from data and exploits our Probabilistic Abductive Proof Procedure to classify never-seen instances. This approach has been tested on some standard datasets showing that it improves accuracy in presence of corruptions and missing data.
Predicting organic reaction outcomes with weisfeiler lehman networkKazuki Fujikawa
This document discusses neural message passing networks for modeling quantum chemistry. It defines message passing networks as having message functions that update node states based on neighboring node states, vertex update functions that update node states based to accumulated messages, and a readout function that produces an output for the full graph. It provides examples of specific message, update, and readout functions used in existing message passing models like interaction networks and molecular graph convolutions.
Constructing Distributed Doubly Linked Lists without Distributed LockingKota Abe
Explains a novel distributed algorithm for constructing distributed doubly linked lists (or bidirectional ring), which are common in structured P2P networks.
This presentation is used at the 2015 IEEE International Conference on Peer-to-Peer Computing (P2P2015).
The paper is available at
<http://www.media.osaka-cu.ac.jp/~k-abe/research/Constructing_Distributed_Doubly_Linked_Lists_without_Distributed_Locking.html>
Author: Kota Abe (Osaka City University/NICT), Mikio Yoshida (BBR Inc.)
Abstract:
A distributed doubly linked list (or bidirectional ring) is a fundamental distributed data structure commonly used in structured peer-to-peer networks. This paper presents DDLL, a novel decentralized algorithm for constructing distributed doubly linked lists. In the absence of failure, DDLL maintains consistency with regard to lookups of nodes, even while multiple nodes are simultaneously being inserted or deleted. Unlike existing algorithms, DDLL adopts a novel strategy based on conflict detection and sequence numbers. A formal description and correctness proofs are given. Simulation results show that DDLL outperforms conventional algorithms in terms of both time and number of messages.
This document discusses graph kernels, which are positive definite kernels defined on graphs that allow applying machine learning algorithms to graph-structured data like molecules. It covers different types of graph kernels like subgraph kernels, path kernels, and walk kernels. Walk kernels count the number of walks between two graphs and can be computed efficiently in polynomial time, unlike subgraph and path kernels. The document also discusses using product graphs to compute walk kernels and presents results on classifying mutagenicity using random walk kernels. It concludes by proposing using graph kernels and product graphs to define data depth measures for labeled graph ensembles.
An improved spfa algorithm for single source shortest path problem using forw...IJMIT JOURNAL
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph,
the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network.
SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed.
In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically
analyse the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient.
International Journal of Managing Information Technology (IJMIT)IJMIT JOURNAL
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph, the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network. SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed. In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically analyse the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient
An improved spfa algorithm for single source shortest path problem using forw...IJMIT JOURNAL
We present an improved SPFA algorithm for the single source shortest path problem. For a random graph,
the empirical average time complexity is O(|E|), where |E| is the number of edges of the input network.
SPFA maintains a queue of candidate vertices and add a vertex to the queue only if that vertex is relaxed.
In the improved SPFA, MinPoP principle is employed to improve the quality of the queue. We theoretically
analyse the advantage of this new algorithm and experimentally demonstrate that the algorithm is efficient.
The document describes an algebraic attack on the KeeLoq block cipher. KeeLoq is used in car keyless entry systems and has 528 rounds with a 64-bit key. The attack sets up a system of equations modeling the encryption rounds using a SAT solver to recover the key from known plaintext-ciphertext pairs. It converts the algebraic normal form equations to conjunctive normal form required by the SAT solver to solve for the key.
This document provides an overview of clustering techniques, including supervised vs. unsupervised learning, clustering concepts, non-hierarchical clustering like k-means, and hierarchical clustering like hierarchical agglomerative clustering. It discusses clustering applications, algorithms like k-means and hierarchical agglomerative clustering, and evaluation metrics like cluster silhouettes. Key clustering goals are to partition unlabeled data into clusters such that examples within a cluster are similar and different between clusters.
This document summarizes a presentation about variational autoencoders (VAEs) presented at the ICLR 2016 conference. The document discusses 5 VAE-related papers presented at ICLR 2016, including Importance Weighted Autoencoders, The Variational Fair Autoencoder, Generating Images from Captions with Attention, Variational Gaussian Process, and Variationally Auto-Encoded Deep Gaussian Processes. It also provides background on variational inference and VAEs, explaining how VAEs use neural networks to model probability distributions and maximize a lower bound on the log likelihood.
The document discusses constraint-based problem solving, including modeling problems as constraints on acceptable solutions, defining variables and domains, and defining constraints; solving models by defining search spaces and algorithms like backtracking search and stochastic search; and verifying and analyzing solutions. It also provides examples of constraint satisfaction problems and how they can be modeled and solved using different constraint languages and representations.
The document discusses using machine learning techniques like Gaussian processes (GPs) to optimize the configuration of software systems. It notes that software performance landscapes are often complex, with non-linear interactions between parameters and non-convex response surfaces. Measurements are also subject to noise. The document introduces an approach called TL4CO that uses multi-task Gaussian processes to model software performance across different versions/deployments, allowing it to leverage data from other versions to improve optimization. This helps address challenges in DevOps where new versions are continuously delivered.
This document discusses approximate query processing using sampling to enable interactive queries over large datasets. It describes BlinkDB, a framework that creates and maintains samples from underlying data to return fast, approximate query answers with error bars. BlinkDB verifies the correctness of the error bars it returns by periodically replacing samples and using diagnostics to check the accuracy without running many queries. The document discusses challenges like selecting appropriate samples, estimating errors, and verifying results to balance speed, accuracy and correctness for interactive analysis of big data.
The document describes Dedalo, a system that automatically explains clusters of data by traversing linked data to find explanations. It evaluates different heuristics for guiding the traversal, finding that entropy and conditional entropy outperform other measures by reducing redundancy and search time. Experiments on authorship clusters, publication clusters, and library book borrowings demonstrate Dedalo's ability to discover explanatory linked data patterns within a limited domain. Future work includes extending Dedalo to handle more complex datasets by addressing issues such as sameAs linking and use of literals.
Parallel Computing 2007: Bring your own parallel applicationGeoffrey Fox
This document discusses parallelizing several algorithms and applications including k-means clustering, frequent itemset mining, integer programming, computer chess, and support vector machines (SVM). For k-means and frequent itemset mining, the algorithms can be parallelized by partitioning the data across processors and performing partial computations locally before combining results with an allreduce operation. Computer chess can be parallelized by exploring different game tree branches simultaneously on different processors. SVM problems involve large dense matrices that are difficult to solve in parallel directly due to their size exceeding memory; alternative approaches include solving smaller subproblems independently.
RedisConf18 - CRDTs and Redis - From sequential to concurrent executionsRedis Labs
The document discusses conflict-free replicated data types (CRDTs) and how they allow for concurrent executions while preserving sequential semantics. It explains that CRDTs can be implemented by tracking a log of operations and defining semantics based on happens-before relationships between operations. It provides examples of how counters, registers, and sets can be implemented as CRDTs by defining their semantics under both sequential and concurrent executions. Redis uses these principles to provide replicated data types like counters, registers, and sets that can support concurrent updates across replicas.
An Uncertainty-Aware Approach to Optimal Configuration of Stream Processing S...Pooyan Jamshidi
https://arxiv.org/abs/1606.06543
Finding optimal configurations for Stream Processing Systems (SPS) is a challenging problem due to the large number of parameters that can influence their performance and the lack of analytical models to anticipate the effect of a change. To tackle this issue, we consider tuning methods where an experimenter is given a limited budget of experiments and needs to carefully allocate this budget to find optimal configurations. We propose in this setting Bayesian Optimization for Configuration Optimization (BO4CO), an auto-tuning algorithm that leverages Gaussian Processes (GPs) to iteratively capture posterior distributions of the configuration spaces and sequentially drive the experimentation. Validation based on Apache Storm demonstrates that our approach locates optimal configurations within a limited experimental budget, with an improvement of SPS performance typically of at least an order of magnitude compared to existing configuration algorithms.
Continuous Architecting of Stream-Based SystemsCHOOSE
Pooyan Jamshidi CHOOSE Talk 2016-11-01
Big data architectures have been gaining momentum in recent years. For instance, Twitter uses stream processing frameworks like Storm to analyse billions of tweets per minute and learn the trending topics. However, architectures that process big data involve many different components interconnected via semantically different connectors making it a difficult task for software architects to refactor the initial designs. As an aid to designers and developers, we developed OSTIA (On-the-fly Static Topology Inference Analysis) that allows: (a) visualizing big data architectures for the purpose of design-time refactoring while maintaining constraints that would only be evaluated at later stages such as deployment and run-time; (b) detecting the occurrence of common anti-patterns across big data architectures; (c) exploiting software verification techniques on the elicited architectural models. In the lecture, OSTIA will be shown on three industrial-scale case studies.
See: http://www.choose.s-i.ch/events/jamshidi-2016/
Parallel iterative solution of the hermite collocation equations on gpusManolis Vavalis
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Ontology mapping requires context, background knowledge, and approximation. Using background knowledge from multiple large ontologies can improve ontology mapping results between two target ontologies by discovering more matches. Exploiting the hierarchical structure in background ontologies through indirect subsumption reasoning can significantly increase the number of matches found. Allowing for approximate matches by introducing a "sloppiness" threshold based on the semantic distance between concepts can further improve results by discovering desirable matches while avoiding undesirable ones except at high sloppiness levels.
This document provides an overview of clustering techniques including k-means clustering, expectation maximization algorithms, and spectral clustering. It discusses how k-means clustering works by initializing random cluster centers, assigning data points to the closest centers, and adjusting the centers iteratively. Expectation maximization is presented as a way to learn the parameters of a Gaussian mixture model to cluster data. Finally, applications of clustering like document clustering using mixture models are briefly described.
TMPA-2015: Implementing the MetaVCG Approach in the C-light SystemIosif Itkin
Alexei Promsky, Dmitry Kondtratyev, A.P. Ershov Institute of Informatics Systems, Novosibirsk
12 - 14 November 2015
Tools and Methods of Program Analysis in St. Petersburg
Shape Safety in Tensor Programming is Easy for a Theorem Prover -SBTB 2021Peng Cheng
This document discusses the Shapesafe project, which uses dependent types in Scala to enable type-safe linear algebra operations. It aims to push type safety to the extreme by exploring symbolic reasoning and weird operands. The author maintains Shapesafe uses the Curry-Howard isomorphism to translate proofs to functional programs. Moving forward, Shapesafe could benefit from Scala 3's improved type inference and implicit resolution, though some Shapeless features may need to be reimplemented. The end goal is to integrate Shapesafe into machine learning libraries to catch errors at compile-time.
This document discusses kernel methods and radial basis function (RBF) networks. It begins with an introduction and overview of Cover's theory of separability of patterns. It then revisits the XOR problem and shows how it can be solved using Gaussian hidden functions. The interpolation problem is explained and how RBF networks can perform strict interpolation through a set of training data points. Radial basis functions that satisfy Micchelli's theorem allowing for a nonsingular interpolation matrix are presented. Finally, the structure and training of RBF networks using k-means clustering and recursive least squares estimation is covered.
Ineluctable modality of the distributed systems knowledge in distributed systems. Uncertainty is what makes reasoning about distributed systems difficult. Protocols are just mechanisms to ensure that a group has shared knowledge of a fact by climbing the hierarchy from someone knowing to common knowledge. Common knowledge of initially undetermined facts is not attainable in any distributed system where communication is not guaranteed.
This document discusses using particle swarm optimization based on variable neighborhood search (PSO-VNS) to attack classical cryptography ciphers. PSO is a population-based optimization algorithm inspired by bird flocking behavior. VNS is a metaheuristic algorithm that explores neighborhoods of solutions to escape local optima. The paper proposes improving PSO with VNS to find better solutions. It evaluates PSO-VNS on substitution and transposition ciphers, finding it recovers keys better than standard PSO and other variants.
This document introduces Julia and provides an overview of its key features. It begins with introductions and background on why Julia was created. It then covers basic Julia concepts like variables, arithmetic operators, control flow, arrays, functions, and parallelization capabilities. The document also discusses Julia's built-in package ecosystem and provides examples of packages like DataFrames. It aims to provide attendees with foundational knowledge of the Julia programming language.
Computational Techniques for the Statistical Analysis of Big Data in Rherbps10
The document describes techniques for improving the computational performance of statistical analysis of big data in R. It uses as a case study the rlme package for rank-based regression of nested effects models. The workflow involves identifying bottlenecks, rewriting algorithms, benchmarking versions, and testing. Examples include replacing sorting with a faster C++ selection algorithm for the Wilcoxon Tau estimator, vectorizing a pairwise function, and preallocating memory for a covariance matrix calculation. The document suggests future directions like parallelization using MPI and GPUs to further optimize R for big data applications.
Computational Techniques for the Statistical Analysis of Big Data in R
presentation
1. Query Answering over Contextualized
RDF/OWL Knowledge with Forall-Existential
Bridge Rules: Decidable Classes
Mathew Joseph1,2
1DKM, FBK-IRST, Trento, Italy
2DISI, University of Trento, Trento, Italy
PhD Defence Presentation
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
2. Outline of the talk
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
3. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
4. Contextualized Knowledge
The fact “I am giving this presentation” is only true in a
certain context.
Contextualized RDF knowledge is proliferating:
Recent releases of Billion Triples Challenge Datasets,
DBPedia datasets are all in NQuads format.
Triple stores are more and more moving to quad-stores -
4store, Openlink Virtuoso, Sesame.
RDF 1.1 introduced NQuads as official W3C
recommendation in 2014.
The focus of the thesis work is query answering over
contextualized RDF Knowledge/Quads.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
5. Contextualized Knowledge
The fact “I am giving this presentation” is only true in a
certain context.
Contextualized RDF knowledge is proliferating:
Recent releases of Billion Triples Challenge Datasets,
DBPedia datasets are all in NQuads format.
Triple stores are more and more moving to quad-stores -
4store, Openlink Virtuoso, Sesame.
RDF 1.1 introduced NQuads as official W3C
recommendation in 2014.
The focus of the thesis work is query answering over
contextualized RDF Knowledge/Quads.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
6. Contexts: Literature review
John McCarthy 1987 - Proposed contexts as a solution to
Generality problem in AI.
Multi-context Systems (MCS) - contexts are propositional
theories and propositional bridge rules enable interoperability.
Distributed Description Logics (DDL) - contexts are description
logic KBs and bridge rules are of the form:
c : φ(x) → c : φ (x),
where φ(x), φ (x) are either both concept (role) atoms.
Contextualized Knowledge Repository (CKR) - a framework
developed at DKM group. Its aims are to design and implement
effective algorithms for reasoning and query answering over
contextual knowledge.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
7. Thesis Novelty/Advancement
Key Difference
BRs, we consider, are more expressive than the BRs in the
above works and contain ∧s and ∃ operators
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
8. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
9. Quads and Quad-graphs
Let C be a distinguished set of URIs called context identifiers.
A quad is an expression of the form c : (s, p, o), where c ∈ C,
(s, p, o) is a triple.
A quad graph is a set of quads.
Notation:
QC is the quad-graph whose set of context identifiers is C.
For any c ∈ C, graphQC
(c) = {(s, p, o) | c : (s, p, o) ∈ QC}
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
10. Example: Quad-graph
Example
Let C = {cWC2014, cUEFA2014, cSerieA2014}
cWC2014 - context about World cup football 2014.
cUEFA2014 - context about UEFA cup football 2014.
cSerieA2014 - context about Italian Serie A football 2014.
Quad-graph
QC =
cWC2014 : (Buffon, playsFor, Italy)
cWC2014 : (Buffon, captains, Italy)
. . .
cUEFA2014 : (Buffon, playsFor, Juventus)
. . .
cSerieA2014 : (Buffon, playsFor, Juventus)
. . .
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
11. Quad-graph: Visualization
QC can be viewed as a family of RDF graphs
Buffon
Italy
graphQC
(cWC2014)
playsFor Buffon
Agnelli
Juventus
graphQC
(cUEFA2014)
owns
playsFor
superMario
InterMilan
graphQC
(cSerieA2014)
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
12. Bridge Rules (BRs)
Eg: cUEFA2014 : (x, a, GoodPlayer), cSerieA : (x, a, GoodPlayer )
→ cWC2014 : (x, playsFor, Italy)
A BR is an expression of the form:
∀x∀z [
body
c1: t1(x, z) ∧ ... ∧ cn: tn(x, z) →
∃y c1: t1(x, y) ∧ ... ∧ cm: tm(x, y)
head
]
c1 : t1(x, z), ..., cn : tn(x, z) are quad patterns over variable
sets {x} or {z}.
c1 : t1(x, y), ..., cm : tm(x, y) are quad patterns over variable
sets {x} or {y},
where a quad-pattern is a quad that allows variables at s, p, o.
Variables in x are called frontier variables.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
13. Quad-Systems
Definition (Quad-System)
A quad-system QSC is defined as a pair QC, R , where QC is a
quad-graph, and R is a set of bridge rules.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
14. Quad-System Semantics
Semantics of a quad-system QSC is defined on top of a
distributed interpretation structure IC = {Ic}c∈C, where
Ic = ∆c, ·c , for each c ∈ C, is a local interpretation structure.
local ∈ { rdf, rdfs, owl-horst, . . .}
Ic |=local graphQ(c), when Ic is a local model of the triples in
context c.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
15. Model of a Quad-system
Definition (Model of a Quad-system (|=))
A distributed interpretation structure IC = {Ic}c∈C satisfies a
quad-system QSC = QC, R , in symbols IC |= QSC iff all the
following are satisfied:
1 For every c ∈ C, Ic |=local graphQC
(c);
2 For every BR r ∈ R, for every σ ∈ {x} ∪ {z} → ∆C, where
∆C = c∈C ∆c, if
Ic1
|=local t1(x, z)[σ], ..., Icn
|=local tn(x, z)[σ],
then there exists function σ ⊇ σ, s.t.
Ic1 |=local t1(x, y)[σ ], ..., Icm |=local tm(x, y)[σ ].
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
16. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
17. Contextualized Conjunctive Queries
A Contextualized Conjunctive Query (CCQ) is an expression of
the form:
∃y c1 : t1(x, y) ∧ ... ∧ cp : tp(x, y)
where qi, for i = 1, ..., p are quad patterns over vectors of free
variables x and quantified variables y.
Example
If context c1 is about Football World Cup 2014 and context c2
about Football Euro Cup 2012. Then the CCQ
c1: (x, beat, Italy) ∧ c2: (x, beat, Italy), where x is a variable.
intuitively means “Who beat Italy in both Euro Cup 2012 and
World Cup 2014”.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
18. Query Answering Decision Problem over QS
CCQ evaluation problem
Decision problem of determining, for any vector of constants a,
a CCQ CQ(x) over a quad-system QSC, if QSC |= CQ(a).
Distributed chase (dChase) of a quad-system
We extend the standard chase algorithm [Meir et al. 79] to
our setting, call its output the distributed chase,
abbreviated dChase.
The algorithm runs iteratively, for iterations i = 0, . . . ,
producing outputs dChase0(QSC), . . . ,, respectively.
dChase(QSC) = i∈N dChasei(QSC)
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
23. Distributed chase of a quad-system
Termination condition: If ∃i s.t. dChasei(QSC) =
dChasei+1, then dChase(QSC) = dChasei(QSC).
It might be the case that the termination condition is never
satisfied and dChase is infinite, which leads to
non-termination of dChase algorithm.
So what? Same problem occurs in DLs DL-Lite, EL etc.,
but QA algorithms based on rewriting
techniques [Calvanese et al. 2007] and combined
approaches [Lutz et al., 2009] exists.
Is there an algorithm for deciding CCQ evaluation problem
for quad-systems?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
24. Distributed chase of a quad-system
Termination condition: If ∃i s.t. dChasei(QSC) =
dChasei+1, then dChase(QSC) = dChasei(QSC).
It might be the case that the termination condition is never
satisfied and dChase is infinite, which leads to
non-termination of dChase algorithm.
So what? Same problem occurs in DLs DL-Lite, EL etc.,
but QA algorithms based on rewriting
techniques [Calvanese et al. 2007] and combined
approaches [Lutz et al., 2009] exists.
Is there an algorithm for deciding CCQ evaluation problem
for quad-systems?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
25. Distributed chase of a quad-system
Termination condition: If ∃i s.t. dChasei(QSC) =
dChasei+1, then dChase(QSC) = dChasei(QSC).
It might be the case that the termination condition is never
satisfied and dChase is infinite, which leads to
non-termination of dChase algorithm.
So what? Same problem occurs in DLs DL-Lite, EL etc.,
but QA algorithms based on rewriting
techniques [Calvanese et al. 2007] and combined
approaches [Lutz et al., 2009] exists.
Is there an algorithm for deciding CCQ evaluation problem
for quad-systems?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
26. Distributed chase of a quad-system
Termination condition: If ∃i s.t. dChasei(QSC) =
dChasei+1, then dChase(QSC) = dChasei(QSC).
It might be the case that the termination condition is never
satisfied and dChase is infinite, which leads to
non-termination of dChase algorithm.
So what? Same problem occurs in DLs DL-Lite, EL etc.,
but QA algorithms based on rewriting
techniques [Calvanese et al. 2007] and combined
approaches [Lutz et al., 2009] exists.
Is there an algorithm for deciding CCQ evaluation problem
for quad-systems? Ans: NO
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
27. Undecidability of Query Answering for QS
Theorem
CCQ evaluation problem is undecidable
Non emptyness checking of intersection of languages
generated by two CFGs in undecidable.
Reduction: Each PR of the form S → S1S2 . . . Sn can be
encoded as a BR of the form:
c : (x1, S1, x2), c : (x2, S2, x3), . . . , c : (xn, Sn, xn+1) →
c : (x1, S, xn+1)
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
28. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
29. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
30. Triple generating context
For any quad-system QSC = QC, R , a context c ∈ C is called a
triple generating context (TGC), if there exists a BR r ∈ R, with
c : (s, p, o) ∈ head(r) and s or p or o is an existential variable.
Definition (Context dependency graph)
of a quad-system QSC = QC, R is a directed graph V, E ,
V = context identifiers in C s.t. TGCs are marked with a ∗, and
E are s.t.:
for each BR r ∈ R {
for each context ci occurring in the body of r {
for each context cj occurring in the head of r {
exists edge from ci to cj;
}}}
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
31. Example
Consider a quad-system, whose set of BRs R are:
c1 : (x1, x2, U1) → ∃y1 c2 : (x1, x2, y1),
c3 : (x2, a, rdf:Property)
c2 : (x1, x2, z1) → c1 : (x1, x2, U1)
c3 : (x1, x2, x3) → c1 : (x1, x2, x3)
c1
c2
∗
c3
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
32. Example
Consider a quad-system, whose set of BRs R are:
c1 : (x1, x2, U1) → ∃y1 c2 : (x1, x2, y1),
c3 : (x2, a, rdf:Property)
c2 : (x1, x2, z1) → c1 : (x1, x2, U1)
c3 : (x1, x2, x3) → c1 : (x1, x2, x3)
c1
c2
∗
c3
A quad-system is said to be context acyclic (cAcyclic), iff its
context dependency graph does not contain cycles involving
TGCs.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
33. Example
Consider a quad-system, whose set of BRs R are:
c1 : (x1, x2, U1) → ∃y1 c2 : (x1, x2, y1),
c3 : (x2, a, rdf:Property)
c2 : (x1, x2, z1) → c1 : (x1, x2, U1)
c3 : (x1, x2, x3) → c1 : (x1, x2, x3)
c1
c2
∗
c3
A quad-system is said to be context acyclic (cAcyclic), iff its
context dependency graph does not contain cycles involving
TGCs.
Since the cycle (c1, c2, c1) in the quad-system contains c2
which is a TGC, the quad-system is not cAcyclic.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
34. Context Acyclic Quad-Systems: Complexity Results
Theorem
(i) Combined Complexity of CCQ evaluation is
2EXPTIME-complete.
(ii) Data complexity of CCQ evaluation is PTIME-complete
(ii) PTIME-hardness established by the reduction of 3HornSat,
i.e. satisfiability of Propositional Horn clauses with at most 3
literals.
(i) 2EXPTIME-hardness established by reduction of word
problem of double exponentially time bounded Deterministic
Turing Machine.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
35. 2EXPTIME-Hardness of CCQ Evaluation
0 0 1 1 · · ·
qI
Figure : Deterministic Turing Machine (DTM)
A 2EXPTIME DTM is a DTM that decides acceptance in
atmost double exponential number of transitions w.r.t. input
size.
Computation also uses atmost double exponential number
of cells
Reduction of the word problem of 2EXPTIME DTM to CCQ
evaluation problem of context acyclic quad-systems.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
36. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
37. C(dChase(QSC)) = U(dChase(QSC) ∪ L(dChase(QSC)) ∪
B(dChase(QSC)) can be potentially infinite.
U(dChase(QSC) ⊆ U(QSC), and L(dChase(QSC)) ⊆ L(QSC)
are finite sets.
Hence, the real reason of non-finiteness is B(dChase(QSC))
and, specifically, the set of Skolem blank nodes.
Intuitively, csafe, msafe, and safe classes restricts the structure
of the Skolem blank nodes in the dChase to be DAGs of
bounded depth.
Assumption: Every BR has a unique identifier.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
38. Origin ruleId, Origin vector, Descendants of Skolem
blank nodes
Consider the application of an assignment µ on the following
BR ri = body(ri)(x, z) → head(ri)(x, y)
body(ri)
x1
. . .
xp z1
. . .
zq
head(ri)
x1
. . .
xp y1
. . .
yr
a1 . . . ap c1 . . . cq
µ
ri
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
39. Origin ruleId, Origin vector, Descendants of Skolem
blank nodes
body(ri)
x1
. . .
xp z1
. . .
zq
head(ri)
x1
. . .
xp y1
. . .
yr
a1 . . . ap c1 . . . cq
µ
apply
ri
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
40. Origin ruleId, Origin vector, Descendants of Skolem
blank nodes
body(ri)
x1
. . .
xp z1
. . .
zq
head(ri)
x1
. . .
xp y1
. . .
yr
a1 . . . ap _: b1
. . .a1 . . . ap c1 . . . cq
µ
apply
ri
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
41. Origin ruleId, Origin vector, Descendants of Skolem
blank nodes
originRuleId(_: b1) = i
body(ri)
x1
. . .
xp z1
. . .
zq
head(ri)
x1
. . .
xp y1
. . .
yr
a1 . . . ap _: b1
. . .a1 . . . ap c1 . . . cq
µ
apply
ri
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
42. Origin ruleId, Origin vector, Descendants of Skolem
blank nodes
originVector(_: b1) = a1, . . . , ap
body(ri)
x1
. . .
xp z1
. . .
zq
head(ri)
x1
. . .
xp y1
. . .
yr
a1 . . . ap _: b1
. . .a1 . . . ap c1 . . . cq
µ
apply
ri
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
43. Origin ruleId, Origin vector, Descendants of Skolem
blank nodes
hasChild(_: b1, a1), . . . , hasChild(_: b1, ap)
body(ri)
x1
. . .
xp z1
. . .
zq
head(ri)
x1
. . .
xp y1
. . .
yr
a1 . . . ap _: b1
. . .a1 . . . ap c1 . . . cq
µ
apply
ri
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
44. Origin ruleId, Origin vector of Skolem blank nodes
For any Skolem blank node _: b generated in the dChase by
the application of the BR ri = body(ri)(x, z) → head(ri)(x, y)
using assignment µ,
we say that
originRuleId(_: b) = i
Also, we say
originVector(_: b) = a = x[µ]
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
45. Origin Contexts/Descendants of Skolem blank nodes
Origin contexts
of _: b is the set of contexts in which triples containing _: b are
first generated, during the dChase construction. Formally
originContexts(_: b) = {c | c : (s, p, o) ∈ dChasei(QSC),
s = _: b or p = _: b or o = _: b, and
∃j < i with c : (s , p , o ) ∈ dChasej(QSC),
s = _: b or p = _: b or o = _: b}
Descendants
We call a c = µ(xi), for any xi ∈ x, as the childOf _: b, in
symbols hasChild(_: b, c).
hasDescendant=hasChild+ (transitive closure)
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
46. Origin Contexts/Descendants of Skolem blank nodes
Origin contexts
of _: b is the set of contexts in which triples containing _: b are
first generated, during the dChase construction. Formally
originContexts(_: b) = {c | c : (s, p, o) ∈ dChasei(QSC),
s = _: b or p = _: b or o = _: b, and
∃j < i with c : (s , p , o ) ∈ dChasej(QSC),
s = _: b or p = _: b or o = _: b}
Descendants
We call a c = µ(xi), for any xi ∈ x, as the childOf _: b, in
symbols hasChild(_: b, c).
hasDescendant=hasChild+ (transitive closure)
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
55. Example Contd.
Consider the quad-system QC, R , where QC = {c1 : (a, b, c)}.
Suppose R is the following set:
R =
c1 : (x11, x12, z1) → c2 : (x11, x12, y1) (r1)
c2 : (z21, z22, x2) → c3 : (y21, y22, x2) (r2)
c3 : (z3, x31, x32) → c2 : (y3, x31, x32) (r3)
dChase3(QSC) = {c1:(a, b, c),
c2 : (a, b, _: b1), c3 : (_: b2, _: b3,
_: b1), c2 : (_: b4, _: b3, _: b1) }
dChase4(QSC) = dChase3(QSC)
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
56. Descendance Graph
Descendance graph for _ :b4 of example above is:
_:b4
3, _:b3, _:b1 , {c2}
_:b3
2, _:b1 ,
{c3}
_:b1
1, a, b ,
{c2}
a b
Figure : Nodes labelled with tuple:Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
57. Safe, Msafe, and Csafe Quad-systems
Definition (safe, msafe, csafe quad-systems)
A quad-system QSC is said to be:
unsafe iff ∃ Skolem blank nodes _: b = _: b in
dChase(QSC) s.t. _: b is a descendant of _: b ,
with originRuleId(_: b) = originRuleId(_: b ) and
originVector(_: b) ∼= originVector(_: b ),
unmsafe iff ∃ Skolem blank nodes _: b = _: b in
dChase(QSC) s.t. _: b is a descendant of _: b ,
with originRuleId(_: b) = originRuleId(_: b ),
uncsafe iff ∃ Skolem blank nodes _: b = _: b in
dChase(QSC) s.t. _: b is a descendant of _: b ,
with originContexts(_: b) = originContexts(_: b ).
A quad-system is safe (resp. msafe, resp. csafe) iff it is not
unsafe (resp. unmsafe, resp. uncsafe).
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
58. Safe, Msafe, and Csafe Quad-systems: Properties
Theorem
Let CACYCLIC, SAFE, MSAFE, and CSAFE denote the class of
context acyclic, safe, msafe, and csafe quad-systems,
respectively, then the following holds:
CACYCLIC ⊂ CSAFE ⊂ MSAFE ⊂ SAFE
Lemma (DAG property)
For a safe (csafe, msafe) quad-system QSC, and for any blank
node b ∈ Bsk (dChase(QSC)), its descendance graph is a DAG
with bounded depth.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
59. Safe quad-systems: Properties
Theorem
For any safe/msafe/csafe quad-system, the following holds:
(i) size of the dChase is double exponential,
(ii) dChase can be computed in 2EXPTIME,
(iii) when the size of bridge rules are assumed to be a constant,
dChase can be computed in PTIME
Theorem
For any safe/msafe/csafe quad-system, the following holds: (i)
The data complexity of CCQ evaluation is PTIME-complete (ii)
The combined complexity of CCQ evaluation is
2EXPTIME-complete.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
60. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
61. Range Restricted (RR) Quad-Systems
Suppose if we disallow the occurrence of existentially quantified
variable from our bridge rules, then the resulting BRs are of the
form:
∀x∀z[c1 : t1(x, z) ∧ . . . ∧ cn : tn(x, z)
→ c1 : t1(x) ∧ . . . ∧ cm : tm(x)]
Any such BR can be replaced with the following equivalent set
of BRs each of which has exactly one quad-pattern in its head:
∀x∀z[c1 : t1(x, z) ∧ . . . ∧ cn : tn(x, z) → c1 : t1(x)]
...
∀x∀z[c1 : t1(x, z) ∧ . . . ∧ cn : tn(x, z) → cm : tm(x)]
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
62. RR quad-systems: Computational Properties
Theorem
For any RR quad-system QSC = QC, R , the following holds:
Size of dChase(QSC) is a polynomial sized,
dChase(QSC) can be computed in EXPTIME,
When R is assumed to be constant sized, then
dChase(QSC) can be computed in PTIME.
Theorem
For RR quad-systems, the following holds:
(i) Combined complexity of CCQ evaluation problem is in
EXPTIME,
(ii) Data complexity of CCQ evaluation problem is
PTIME-complete. P-hardness by reduction of 3HornSat.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
63. RR quad-systems: Computational Properties
Theorem
For any RR quad-system QSC = QC, R , the following holds:
Size of dChase(QSC) is a polynomial sized,
dChase(QSC) can be computed in EXPTIME,
When R is assumed to be constant sized, then
dChase(QSC) can be computed in PTIME.
Theorem
For RR quad-systems, the following holds:
(i) Combined complexity of CCQ evaluation problem is in
EXPTIME,
(ii) Data complexity of CCQ evaluation problem is
PTIME-complete. P-hardness by reduction of 3HornSat.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
64. Restricted RR quad-systems
Restricted RR quad-system
is an RR quad-system in which the number of quad-patterns in
the body of each bridge rule is less than or equal to a constant
n. For instance,
n = 1, we get linear quad-systems,
n = 2, we get quadratic quad-systems, etc.
Theorem
For restricted RR quad-systems, the following holds:
(i) Data complexity of CCQ evaluation problem is
PTIME-complete. P-hardness by reduction of 3HornSat.
(ii) Combined complexity of CCQ evaluation problem is
NP-complete. NP-hardness by reduction of the graph coloring
problem.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
65. Restricted RR quad-systems
Restricted RR quad-system
is an RR quad-system in which the number of quad-patterns in
the body of each bridge rule is less than or equal to a constant
n. For instance,
n = 1, we get linear quad-systems,
n = 2, we get quadratic quad-systems, etc.
Theorem
For restricted RR quad-systems, the following holds:
(i) Data complexity of CCQ evaluation problem is
PTIME-complete. P-hardness by reduction of 3HornSat.
(ii) Combined complexity of CCQ evaluation problem is
NP-complete. NP-hardness by reduction of the graph coloring
problem.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
66. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
67. Quad-systems and Forall-Existential (∀∃) rules
A ternary ∀∃ rule is an expression of the form:
∀x∀z[P1(x, z) ∧ . . . ∧ Pn(x, z) → ∃y P1(x, y) ∧ . . . ∧ Pm(x, y)],
where
Pi(x, z), 1 ≤ i ≤ n, are atoms over variables {x} or {z},
Pj(x, y), 1 ≤ j ≤ n, are atoms over variables {x} or {y},
ar(Pi) ≤ 3 and ar(Pj ) ≤ 3.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
68. Translation from Quad-systems to ∀∃ rules
Let τq be the translation s.t. for any quad (pattern) c : (s, p, o),
τq(c : (s, p, o)) = c(s, p, o);
For any quad-graph QC with bnodes _: b1, . . ., _: bn
τ(QC) =→ ∃y1, . . . , yn qi ∈QC
τq(qi)[µB]
where µB = {_: bi → yi}i=1...n;
For any BR r for the form seen before,
τ(r) = ∀x∀z τq(q1(x, z)) ∧ . . . τq(qn(x, z)) → ∃y τq(q1(x, z))
∧ . . . ∧ τq(qm(x, z));
For any quad-system QSC = QC, R ,
τ(QSC) = τ(QC) ∪ r∈R τ(r).
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
69. Quad-system and ∀∃ rules
Theorem
Given the translation τ as defined above, for any quad-system
QSC and boolean CCQ CQ(a), QSC |= CQ(a) iff
τ(QSC) |=fol τ(CQ(a)).
Note that τ(QSC) is a ∀∃ rule set, τ(CQ(a)) is a standard
conjunctive query, and τ is a PTIME translation.
Inverse translation τ−1
Similarly, PTIME inverse translation τ−1 exists from ternary ∀∃
rules (resp. CQs) to quad-systems (resp. CCQs) s.t. for any ∀∃
ruleset P and a boolean CQ Q(), P |=fol Q() iff τ−1(P) |=
τ−1(Q()).
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
70. Quad-systems and Ternary ∀∃ rules
Corollary
CCQ evaluation problem of quad-systems is polynomially
equivalent to CQ evaluation problem over ternary ∀∃ rules.
This means that the well known techniques for decidability
guarantees such as Weak acyclicity (WA) [Fagin et al. 2005],
Joint acyclicity (JA) [Krötzsch et al. 2011], and Model faithful
acyclicity (MFA) [Cuenca Grau et al. 2013] from the discipline
of ∀∃ rules are also applicable in our settings, and vice versa.
The following relations holds [Cuenca Grau et al. 2013]:
WA ⊂ JA ⊂ MFA,
what are the relations with our decidability approaches to these
existing notions?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
71. Quad-systems and Ternary ∀∃ rules
Corollary
CCQ evaluation problem of quad-systems is polynomially
equivalent to CQ evaluation problem over ternary ∀∃ rules.
This means that the well known techniques for decidability
guarantees such as Weak acyclicity (WA) [Fagin et al. 2005],
Joint acyclicity (JA) [Krötzsch et al. 2011], and Model faithful
acyclicity (MFA) [Cuenca Grau et al. 2013] from the discipline
of ∀∃ rules are also applicable in our settings, and vice versa.
The following relations holds [Cuenca Grau et al. 2013]:
WA ⊂ JA ⊂ MFA,
what are the relations with our decidability approaches to these
existing notions?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
72. Quad-systems and Ternary ∀∃ rules
Corollary
CCQ evaluation problem of quad-systems is polynomially
equivalent to CQ evaluation problem over ternary ∀∃ rules.
This means that the well known techniques for decidability
guarantees such as Weak acyclicity (WA) [Fagin et al. 2005],
Joint acyclicity (JA) [Krötzsch et al. 2011], and Model faithful
acyclicity (MFA) [Cuenca Grau et al. 2013] from the discipline
of ∀∃ rules are also applicable in our settings, and vice versa.
The following relations holds [Cuenca Grau et al. 2013]:
WA ⊂ JA ⊂ MFA,
what are the relations with our decidability approaches to these
existing notions?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
73. Quad-systems and ∀∃ rules
Theorem
1 CACYCLIC ⊂ WA,
2 If local semantics of contexts is OWL-Horst or its derivative,
then QSC is context acyclic iff τ(QSC) is weakly acyclic.
3 WA ⊆ CSAFE and CSAFE ⊆ WA,
4 JA ⊆ CSAFE and CSAFE ⊆ JA,
5 MFA ≡ MSAFE,
6 MFA ⊂ SAFE. Important! because MFA was the most
expressive of the known classes with finite chase property,
so far
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
74. Quad-systems and ∀∃ rules
Theorem
1 CACYCLIC ⊂ WA,
2 If local semantics of contexts is OWL-Horst or its derivative,
then QSC is context acyclic iff τ(QSC) is weakly acyclic.
3 WA ⊆ CSAFE and CSAFE ⊆ WA,
4 JA ⊆ CSAFE and CSAFE ⊆ JA,
5 MFA ≡ MSAFE,
6 MFA ⊂ SAFE. Important! because MFA was the most
expressive of the known classes with finite chase property,
so far
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
75. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
76. Related Work
∀∃, Datalog+- rules, Tgds
Beeri and Vardi, 1981 Proved that reasoning with Tgds is
undecidable.
Deutch et al., Fagin et al., 2003 Weakly acyclic Tgds: A
decidable class for query answering. Tgds are analyzed using
a dependency graph. Difference: nodes in the dependency
graph contain predicate positions, in place of context identifiers
in our approach.
(Weakly) (Frontier) Guarded Rules Ensures decidability using
bounded tree width property of underlying models (Courcelle’s
theorem)
Linear TGDs, Sticky Tgds Ensures decidability using query
rewriting approach.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
77. Outline
1 Introduction
2 Quad-Systems
3 Query Answering over Quad-Systems
4 Decidable Classes of Quad-Systems
Context Acyclic Quad-Systems
Csafe, Msafe, and Safe Quad-systems
Range Restricted Quad-Systems
5 Quad-systems and Forall-Existential rules
6 Related Work
7 Conclusion
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
78. Complexity of
CCQ Entailment
Expressivity Landscape dChase size
UNRESTRICTEDUNDECIDABLE INFINITE
TERNARY
∀∃ RULES
SAFE
MSAFE MFA [Cuenca Grau et al. 2013]
CSAFE JA [Krötzsch et al. 2011]
WA [Fagin et al. 2005]
CACYCLIC
2EXPTIME-
COMPLETE
DOUBLE
EXPONENTIAL
RREXPTIME
POLYNOMIAL
REST. RRNP-COMPLETE
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
79. Data Complexity & Complexity of Recognition
Quad-System Complexity Data Complexity of
Fragment of Recognition CCQ evaluation
Unrestricted PTIME Undecidable
Safe 2EXPTIME PTIME-complete
MSafe 2EXPTIME PTIME-complete
CSafe 2EXPTIME PTIME-complete
Context Acyclic PTIME PTIME-complete
RR PTIME PTIME-complete
Restricted RR PTIME PTIME-complete
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
80. Conclusion
We know ways to code bridge rules over quads s.t. query
answering can be done with termination guarantees and
reasonably efficiently.
Since SAFE ⊃ MFA, we also have new ways of writing
ternary ∀∃ rules that allows for termination guaranteed
query answering.
The technique of safety can also be ported to general ∀∃
rules setting by keeping track of origin ruleId/vector and
descendants.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
81. Articles and Conference Experiences
M.Joseph, G.Kuper, T. Mossakowski, L.Serafini. Query
Answering over Contextualized RDF/OWL Knowledge with
Forall-Existential Bridge Rules: Decidable Finite Extension
Classes. Semantic Web Journal (Accepted for
Publications, To Appear). IOS Press. 2015
M.Joseph, G.Kuper, L.Serafini. Query Answering over
Contextualized RDF/OWL Knowledge with
Forall-Existential Bridge Rules: Attaining Decidability using
Acyclicity. In Proceedings of International Conference in
Web Reasoning and Rule Systems (RR-2014). 2014
M.Joseph, G.Kuper, L.Serafini. Query Answering over
Contextualized RDF Knowledge with Forall-Existential
Bridge Rules: Attaining Decidability using Acyclicity. In
Proceedings of Italian Conference in Computational Logic
(CILC-2014). 2014
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
82. Articles and Conference Experiences: Contd
M.Joseph, L.Serafini. Simple Reasoning for Contextualized
RDF Knowledge. In Proceedings of Workshop on Modular
Ontologies (WOMO-2011). Ljubljana, Slovenia. 2011
A. Tamilin, B. Magnini, L. Serafini, C. Girardi, M. Joseph, R.
Zanoli. Context-driven Semantic Enrichment of Italian
News Archive. In proceedings of Extended Semantic Web
Conference (ESWC-2010). In use track. 364-378 crete,
greece. 2010
M. Joseph. A Contextualized Knowledge Framework for
Semantic Web. In proceedings of Extended Semantic Web
Conference (ESWC-2010). PhD symposium track. crete,
greece. 2010
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
83. THANKS
Thanks for your attention
Questions?
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
89. [Borgida, Serafini. 2003]
Borgida, A., Serafini, L.: Distributed Description Logics:
Assimilating Information from Peer Sources. J. Data
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[Giunchiglia and Ghidini, 2001]
Giunchiglia, F., Ghidini, C.: Local models semantics, or
contextual reasoning = locality + compatibility. Artificial
Intelligence 127 (2001)
[Fagin et al. 2005]
Fagin, R., Kolaitis, P.G., Miller, R.J., Popa, L.: Data
Exchange: Semantics and Query Answering. In:
Theoretical Computer Science. pp. 28(1):89–124 (2005)
[Deutsch et al. 2008]
Deutsch, A., Nash, A., Remmel, J.: The chase revisited. In:
Proceedings of the twenty-seventh ACM
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
90. SIGMOD-SIGACT-SIGART symposium on Principles of
database systems. pp. 149–158. PODS ’08 (2008)
[Johnson and Klug, 84]
Johnson, D.S., Klug, A.C.: Testing containment of
conjunctive queries under functional and inclusion
dependencies. Computer and System Sciences 28,
167–189 (1984)
[Lutz et al., 2009]
C. Lutz, D. Toman, F. Wolter, Conjunctive query answering
in the description logic EL using a relational database
system twenty-first International Joint Conference on
Artificial Intelligence. 2009 (IJCAI 09).
[Calvanese et al. 2007]
D. Calvanese, G. Giacomo, D. Lembo, M. Lenzerini, and
R. Rosati, “Tractable reasoning and efficient query
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge
91. answering in description logics: The dl-lite family,” J. Autom.
Reason., vol. 39, pp. 385–429, Oct. 2007.
[Cuenca Grau et al. 2013]
B. Cuenca Grau„ I. Horrocks, M. Krötzsch, C. Kupke,
D. Magka, B. Motik, and Z. Wang, “Acyclicity Notions for
Existential Rules and Their Application to Query Answering
in Ontologies,” in Journal of Artificial Intelligence Research
(JAIR), vol. 47, pp. 741–808, AI Access Foundation, 2013.
[Krötzsch et al. 2011]
M. Krötzsch and S. Rudolph, “Extending decidable
existential rules by joining acyclicity and guardedness,” in
Proceedings of the 22nd International Joint Conference on
Artificial Intelligence (IJCAI’11) (T. Walsh, ed.),
pp. 963–968, AAAI Press/IJCAI, 2011.
Mathew Joseph Query Answering over Contextualized RDF/OWL Knowledge