1. The document proposes a dynamical model of formal logic where logic emerges from the interaction between a system and its internal agent over time.
2. In the model, formal logic is represented as a directed graph that is autonomously transformed through the interaction between the system and its internal agent.
3. This interaction works to increase the transitivity rate of the graph by successively applying the transitive law to add arrows, aiming to generate a graph that fully represents formal logic.
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Parameter Estimation for Semiparametric Models with CMARS and Its ApplicationsSSA KPI
AACIMP 2010 Summer School lecture by Gerhard Wilhelm Weber. "Applied Mathematics" stream. "Modern Operational Research and Its Mathematical Methods with a Focus on Financial Mathematics" course. Part 11.
More info at http://summerschool.ssa.org.ua
Label propagation - Semisupervised Learning with Applications to NLPDavid Przybilla
Label propagation is a semi-supervised learning algorithm that propagates labels from a small set of labeled data points to unlabeled data points. The algorithm constructs a graph with nodes for each data point and weighted edges representing similarity between points. It then iteratively propagates the labels across the graph from labeled to unlabeled points until convergence, resulting in "soft" probabilistic labels for all points. The algorithm aims to minimize an energy function that encourages points connected by strong edges to receive similar labels. It performs well with limited labeled data by leveraging the graph structure to make predictions for unlabeled points.
Generative Adversarial Networks : Basic architecture and variantsananth
In this presentation we review the fundamentals behind GANs and look at different variants. We quickly review the theory such as the cost functions, training procedure, challenges and go on to look at variants such as CycleGAN, SAGAN etc.
El documento describe el modelo de negocios de Nespresso. Nespresso ofrece cápsulas de café y máquinas de café a clientes minoristas. Mantiene una relación personal con los clientes a través de tiendas minoristas y su sitio web. Genera ingresos a través de las ventas recurrentes de cápsulas y accesorios de café. Sus principales recursos son su marca reconocida y su red de distribución minorista.
This document discusses various sources of funding for startups in Chile and abroad, including incubators, seed funds, angels, angel networks, CORFO programs, venture capitalists, and funds in the United States. It provides information on typical funding ranges from these sources, and evaluates them based on factors such as their focus on developing a pitch deck, executive summary, business plan, assessing user traction, growth hacking capabilities, letters of intent, revenue, and social proof.
This presentation by Sue Austin discusses her experience with deep sea diving in a wheelchair. It highlights quotes about creativity, taking risks, and defying limitations. The presentation explains how Austin worked to create an underwater wheelchair and dive despite being told by engineers it would not work. It concludes by thanking the audience.
esta presentacion habla acerca de los fines que tiene este sistema educativo en mexico y el mundo para saciar de empleados a las empresas que intervinieron para llevar a cabo este modelo
Fuzzy logic can be applied in geology to deal with imprecise concepts. Fuzzy set theory involves membership functions to indicate the degree to which objects belong to sets, unlike classical set theory which involves sharp boundaries. A case study applied formal concept analysis to 9 fossils characterized by attributes like spine size and body shape. This generated a fuzzy concept lattice that revealed natural concepts and hierarchies in the data. Fuzzy similarity relations were also useful for analyzing relationships between fossils. Fuzzy logic has also been applied to problems like stratigraphic modeling, paleobiological taxonomy, and earthquake research.
This document provides an introduction to homotopy type theory, including:
- Types represent objects, propositions, functions, and proofs.
- Equalities are represented as paths between types, with properties like reflexivity and transitivity.
- Dependent types allow the output of a function to depend on the input.
- Identity types represent proofs of equality between elements of a type.
- Function extensionality and univalence are axioms in homotopy type theory.
This document discusses fuzzy logic and fuzzy sets. It introduces fuzzy logic as an extension of classical binary logic that can handle imprecise and vague concepts. Fuzzy sets assign elements a membership value between 0 and 1 rather than crisp inclusion/exclusion. Common fuzzy set operations like union, intersection, complement and containment are defined based on the membership values. Membership functions are used to represent fuzzy sets graphically. Fuzzy logic can model human decision making and common sense in applications where information is uncertain or probabilistic.
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This document summarizes a research paper that proposes a new algorithm for solving the random assignment problem when agents' preferences allow for indifference between objects. The algorithm extends the probabilistic serial mechanism to the full preference domain by interpreting it as an iterative algorithm to compute maximum flow in a network. However, the authors also prove that on the full preference domain, it is impossible for any mechanism to find an assignment that is both envy-free and ordinally efficient while also satisfying a weak strategyproofness property.
This document provides an overview of propositional logic and introduces first-order predicate logic. It discusses formal systems, soundness and completeness. It also covers topics like the truth table, tautology, first-order logic syntax and semantics, properties of well-formed formulae, conversion to clausal form, inference rules, and the unification algorithm.
Fuzzy logic was introduced in 1965 by Lofti Zadeh based on fuzzy set theory. It allows for intermediate values between 0 and 1, unlike boolean logic which only considers true or false. A fuzzy logic system uses fuzzification to convert crisp inputs to fuzzy values, applies a rule base and inference engine to the fuzzy values, and then uses defuzzification to convert the fuzzy output to a crisp value. Fuzzy logic is useful for approximate reasoning and has applications in areas like control systems, decision making, and pattern recognition.
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- Knowledge and its representation are distinct but related entities that are central to intelligent systems. Knowledge describes the world while representation defines how knowledge is encoded and manipulated.
- There are various ways to represent knowledge, including logical representations, inheritance hierarchies, rules-based systems, and procedural representations. Different types of knowledge require different representation schemes.
- Issues in knowledge representation include ensuring representations are adequately expressive and support effective inference, as well as how to structure knowledge at the appropriate level of granularity and represent sets of objects. Choosing the right representation approach is important for building intelligent systems.
Ph d course on formal ontology and conceptual modelingNicola Guarino
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1. The importance of ontological analysis to understand the content and assumptions behind information systems, in order to improve semantic interoperability.
2. Concepts, properties, relations, and the distinction between intension and extension. Concepts represent general principles used to determine reference.
3. What constitutes a conceptualization from a cognitive perspective - how humans isolate relevant invariances from physical reality based on perception, cognition, and language to form conceptual domains and relations.
ERGM (Exponential Random Graph Models) are statistical models for social networks that specify the probability of a graph as a function of network statistics. Three key points:
1. ERGMs express the probability of a graph as proportional to an exponential family form involving network statistics. This allows modeling dependencies between ties.
2. The conditional probability of a tie is derived from the ERGM and gives insight into how the model parameters influence individual tie formation.
3. Examples of classic network models like Bernoulli graphs and p1 models are shown to be special cases within the ERGM framework, connecting logistic regression approaches to the more general ERGM.
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We receive information about the world through our sensors and influence the world through our effectors. Such low-level data has gradually come to play a greater role in AI during its 70-year history. I see this as occurring in four steps, two of which are mostly past and two of which are in progress or yet to come. The first step was to view AI as the design of agents which interact with the world and thereby have sensorimotor experience; this viewpoint became prominent in the 1980s and 1990s. The second step was to view the goal of intelligence in terms of experience, as in the reward signal of optimal control and reinforcement learning. The reward formulation of goals is now widely used but rarely loved. Many would prefer to express goals in non-experiential terms, such as reaching a destination or benefiting humanity, but settle for reward because, as an experiential signal, reward is directly available to the agent without human assistance or interpretation. This is the pattern that we see in all four steps. Initially a non-experiential approach seems more intuitive, is preferred and tried, but ultimately proves a limitation on scaling; the experiential approach is more suited to learning and scaling with computational resources. The third step in the increasing role of experience in AI concerns the agent’s representation of the world’s state. Classically, the state of the world is represented in objective terms external to the agent, such as “the grass is wet” and “the car is ten meters in front of me”, or with probability distributions over world states such as in POMDPs and other Bayesian approaches. Alternatively, the state of the world can be represented experientially in terms of summaries of past experience (e.g., the last four Atari video frames input to DQN) or predictions of future experience (e.g., successor representations). The fourth step is potentially the biggest: world knowledge. Classically, world knowledge has always been expressed in terms far from experience, and this has limited its ability to be learned and maintained. Today we are seeing more calls for knowledge to be predictive and grounded in experience. After reviewing the history and prospects of the four steps, I propose a minimal architecture for an intelligent agent that is entirely grounded in experience.
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This presentation by Sue Austin discusses her experience with deep sea diving in a wheelchair. It highlights quotes about creativity, taking risks, and defying limitations. The presentation explains how Austin worked to create an underwater wheelchair and dive despite being told by engineers it would not work. It concludes by thanking the audience.
esta presentacion habla acerca de los fines que tiene este sistema educativo en mexico y el mundo para saciar de empleados a las empresas que intervinieron para llevar a cabo este modelo
Fuzzy logic can be applied in geology to deal with imprecise concepts. Fuzzy set theory involves membership functions to indicate the degree to which objects belong to sets, unlike classical set theory which involves sharp boundaries. A case study applied formal concept analysis to 9 fossils characterized by attributes like spine size and body shape. This generated a fuzzy concept lattice that revealed natural concepts and hierarchies in the data. Fuzzy similarity relations were also useful for analyzing relationships between fossils. Fuzzy logic has also been applied to problems like stratigraphic modeling, paleobiological taxonomy, and earthquake research.
This document provides an introduction to homotopy type theory, including:
- Types represent objects, propositions, functions, and proofs.
- Equalities are represented as paths between types, with properties like reflexivity and transitivity.
- Dependent types allow the output of a function to depend on the input.
- Identity types represent proofs of equality between elements of a type.
- Function extensionality and univalence are axioms in homotopy type theory.
This document discusses fuzzy logic and fuzzy sets. It introduces fuzzy logic as an extension of classical binary logic that can handle imprecise and vague concepts. Fuzzy sets assign elements a membership value between 0 and 1 rather than crisp inclusion/exclusion. Common fuzzy set operations like union, intersection, complement and containment are defined based on the membership values. Membership functions are used to represent fuzzy sets graphically. Fuzzy logic can model human decision making and common sense in applications where information is uncertain or probabilistic.
A Solution To The Random Assignment Problem On The Full Preference DomainJoe Andelija
This document summarizes a research paper that proposes a new algorithm for solving the random assignment problem when agents' preferences allow for indifference between objects. The algorithm extends the probabilistic serial mechanism to the full preference domain by interpreting it as an iterative algorithm to compute maximum flow in a network. However, the authors also prove that on the full preference domain, it is impossible for any mechanism to find an assignment that is both envy-free and ordinally efficient while also satisfying a weak strategyproofness property.
This document provides an overview of propositional logic and introduces first-order predicate logic. It discusses formal systems, soundness and completeness. It also covers topics like the truth table, tautology, first-order logic syntax and semantics, properties of well-formed formulae, conversion to clausal form, inference rules, and the unification algorithm.
Fuzzy logic was introduced in 1965 by Lofti Zadeh based on fuzzy set theory. It allows for intermediate values between 0 and 1, unlike boolean logic which only considers true or false. A fuzzy logic system uses fuzzification to convert crisp inputs to fuzzy values, applies a rule base and inference engine to the fuzzy values, and then uses defuzzification to convert the fuzzy output to a crisp value. Fuzzy logic is useful for approximate reasoning and has applications in areas like control systems, decision making, and pattern recognition.
The document discusses knowledge representation issues in artificial intelligence. It covers several key topics:
- Knowledge and its representation are distinct but related entities that are central to intelligent systems. Knowledge describes the world while representation defines how knowledge is encoded and manipulated.
- There are various ways to represent knowledge, including logical representations, inheritance hierarchies, rules-based systems, and procedural representations. Different types of knowledge require different representation schemes.
- Issues in knowledge representation include ensuring representations are adequately expressive and support effective inference, as well as how to structure knowledge at the appropriate level of granularity and represent sets of objects. Choosing the right representation approach is important for building intelligent systems.
Ph d course on formal ontology and conceptual modelingNicola Guarino
The document discusses conceptual modeling and ontological analysis. It covers several key topics:
1. The importance of ontological analysis to understand the content and assumptions behind information systems, in order to improve semantic interoperability.
2. Concepts, properties, relations, and the distinction between intension and extension. Concepts represent general principles used to determine reference.
3. What constitutes a conceptualization from a cognitive perspective - how humans isolate relevant invariances from physical reality based on perception, cognition, and language to form conceptual domains and relations.
ERGM (Exponential Random Graph Models) are statistical models for social networks that specify the probability of a graph as a function of network statistics. Three key points:
1. ERGMs express the probability of a graph as proportional to an exponential family form involving network statistics. This allows modeling dependencies between ties.
2. The conditional probability of a tie is derived from the ERGM and gives insight into how the model parameters influence individual tie formation.
3. Examples of classic network models like Bernoulli graphs and p1 models are shown to be special cases within the ERGM framework, connecting logistic regression approaches to the more general ERGM.
UML (Unified Modeling Language) is used to model software systems and define nine types of diagrams used at different stages of development. The key diagrams are use case diagrams, which show interactions from an external perspective; class diagrams, which show object relationships; sequence diagrams, which show message passing over time; and deployment diagrams, which show how software components are distributed across physical infrastructure. UML provides a standardized way for developers, analysts, and clients to communicate about a system's design.
Brains@Bay Meetup: The Increasing Role of Sensorimotor Experience in Artifici...Numenta
We receive information about the world through our sensors and influence the world through our effectors. Such low-level data has gradually come to play a greater role in AI during its 70-year history. I see this as occurring in four steps, two of which are mostly past and two of which are in progress or yet to come. The first step was to view AI as the design of agents which interact with the world and thereby have sensorimotor experience; this viewpoint became prominent in the 1980s and 1990s. The second step was to view the goal of intelligence in terms of experience, as in the reward signal of optimal control and reinforcement learning. The reward formulation of goals is now widely used but rarely loved. Many would prefer to express goals in non-experiential terms, such as reaching a destination or benefiting humanity, but settle for reward because, as an experiential signal, reward is directly available to the agent without human assistance or interpretation. This is the pattern that we see in all four steps. Initially a non-experiential approach seems more intuitive, is preferred and tried, but ultimately proves a limitation on scaling; the experiential approach is more suited to learning and scaling with computational resources. The third step in the increasing role of experience in AI concerns the agent’s representation of the world’s state. Classically, the state of the world is represented in objective terms external to the agent, such as “the grass is wet” and “the car is ten meters in front of me”, or with probability distributions over world states such as in POMDPs and other Bayesian approaches. Alternatively, the state of the world can be represented experientially in terms of summaries of past experience (e.g., the last four Atari video frames input to DQN) or predictions of future experience (e.g., successor representations). The fourth step is potentially the biggest: world knowledge. Classically, world knowledge has always been expressed in terms far from experience, and this has limited its ability to be learned and maintained. Today we are seeing more calls for knowledge to be predictive and grounded in experience. After reviewing the history and prospects of the four steps, I propose a minimal architecture for an intelligent agent that is entirely grounded in experience.
Models and methods of explanation: dynamical systems, agent models, reflexiveJohn Bradford
This document discusses different types of studies used to explain phenomena, including case studies, cross-sectional studies, and longitudinal studies. It also outlines the steps to create and test causal hypotheses or explanations, including devising a model, identifying other possible causes, and refuting or supporting implications of the hypotheses. Finally, it introduces some unorthodox approaches to modeling like dynamical systems modeling and agent-based modeling, which allow depicting the system structure and linking it to dynamics through simulation.
Models and methods of explanation: dynamical systems, agent models, reflexive
Fis2010 0823
1. An emergence of formal logic
induced by an internal agent
Koji Sawa
The Senior High School, Japan Women’s University, Japan
Yukio-Pegio Gunji
Kobe University, Japan
FIS2010
Beijing, China, Aug 21-24, 2010
2. Proposal
• A dynamical model of formal logic
– It is autonomously transformed.
– It is composed of a system and its subsystem.
– It is represented as transformation of directed
graphs.
3. Motivations 1: Logic
• Where does logic come from?
• Our previous work:
Dialogue models as the origin of logic
(Sawa and Gunji, 2007, 2008)
– Each model is represented in the form of a
multi-agent model.
4. Motivations 2: Multi-agent model
• The behavior of a system is influenced by
agents and interactions between agents.
→ System is not autonomous.
• Agent
– autonomy, sociality, ...
→ Agent is external to system.
5. A connection with FIS
• Brenner (2010). Information in Reality. Logic and Metaphysics
“every real complex process is accompanied, logically and functionally, by its
opposite or contradiction (Principle of Dynamic Opposition), but only in the
sense that when one element is (predominantly) present or actualized, the other
is (predominantly) absent or potentialized, alternately and reciprocally, without
either ever going to zero”
→ We realize a concept touching on above by the invalidation of reflexive law.
• Hofkirchner (2010). Four ways of thinking in information
“Reductionism, Projectivism, Disjunctivism, and Integrativism”
→ In my opinion, Reductionism and Projectivism correspond to deduction and
induction, respectively. Just as Hofkirchner claims that Integrativism must be
needed, so we also consider that the third inference abduction must be needed
(cf. Sawa and Gunji, in press).
– Actually in this presentation, we do not treat these inferences directly, however these
inferences are in the scope of our study.
6. A connection with FIS
• Collier (2010). Kinds of Information in Scientific Use
“For each kind of substantive information used in the sciences there is a distinct
level formed by bifurcations that form cohesive structures at the next higher
level. This is reflected in the information at each level, which inherits the
properties of the lower level, but produces new asymmetries at its own level
through the formation of new cohesions peculiar to the level.”
→ We propose an idea of the way to raise a level presented above:
a representation by nonhierarchical, divisible, and incorporable objects.
8. Multi-agent model
System
“Emergence” Restriction
Agent
Interaction
• Each agent is autonomous.
→ Agent is independent and external to
system.
→ System refers external.
9. Internal Agent Model
System
“Emergence” Restriction
Agent
Interaction
• Internal agent := A part of a system.
– Internal agent is sometimes abbreviated to agent.
• System never refers external.
– Internal measurement (Matsuno, 1989)
• S-IA interaction := Interaction between system and internal agent.
10. Formal logic represented
by a directed graph
Implicational relation
Arrow
Object Object
Directed Graph
11. Identity and obviousness
of object
• A implies A.
– A is A.
– There is no doubt about the obviousness of
object.
Assuming the
• Derivation of LK obviousness of object
A├ A B ├ B
A, A B ├ B C ├ C
A, A B , B C ├ C
A B, B C ├ A C
13. Soft object
• Identity: X → X
Soft Object
X
• If
X → Y, Y → Z, Z → X,
then X
X X
Y Y
Z Z.
(assuming transitive law) Y Z
Soft Object
14. Soft object
• Soft object := a cycle of arrows
• Example
Number of arrows
Soft Hard
(breakable) less (nonbreakable)
more
15. Identity and obviousness
of object
• Equivalence law:
(Condition that a set is treated as one unit)
– Reflexive law: A→A
– Symmetric law: A → B implies B → A
– Transitive law:
A → B and B → C implies A → C
• A soft object (except the hardest one (a
complete graph)) is an object in which the
equivalence law is partially invalidated.
16. Soft arrow
• Soft arrow :=
a bundle of arrows in the same direction.
• Example
Number of arrows
Soft Hard
(Breakable) Less More (Nonbreakable)
17. Summary of model
from a logical perspective
• Formal logic
– Represented by a directed graph.
– Consists of objects and arrows.
• Object
– Represented by a cycle of arrows.
– Soft object
• Arrow
– Represented by a bundle of arrows
– Soft arrow
18. Interaction between system and agent
in formal logic
× System
× Agent
• Agent influences system through pursuit of agent’s “purpose”.
• System influences agent through pursuit of system’s “purpose”.
19. Transitivity Rate (TR)
• Def. Given a directed graph G,
T R : |G | / |G | ,
where |G | : the number of arrows in G,
G : the graph transformed from G,
in which the transitive law holds
completely by adding requisite
arrows.
20. Transitivity Rate (TR)
• Example
Assuming
transitive law
TR=3/4=0.75
• Transitivity rate (TR) is one of measures of
reliability of a directed graph as formal logic.
• Agent’s purpose := increase of TR.
21. S-IA interaction
Agent → System System → Agent
– Add an arrow satisfying below – Add an arrow satisfying below
conditions to system conditions to agent
• increases TR of agent; • increases TR of system;
• does not exist in system; • does not exist in agent;
• shares at least one node with • shares at least one node with
arrows of agent. arrows of agent.
System
S-IA interaction:
succession of applications
of transitive law to two parts:
system and agent.
Agent
22. Example of time transitions
t=k by S-IA Interaction
System
Agent
t=k+1
23. Trial 1
• What kind of graphs emerge by S-IA interaction?
S-IA Interaction
Random graph ?
24. Result of Trial 1
• Initial random graph (50 nodes)
– All arrows: System
– A subset of arrows: Agent
• Convergent graph
– There are soft objects and soft
arrows among soft objects.
– All soft objects and soft arrows are
hardest ones.
– Transitive law holds among soft
arrows.
• In sum, a graph representing
formal logic in which the transitive
law holds completely.
Compress Another result
25. Trial 2
• Trial 1
S-IA Interaction
Graph representing
Random graph
formal logic
• Trial 2
What happens if the obviousness of objects is
invalidated in the emergent graph representing
formal logic?
Invalidation of the obviousness of objects
= Invalidation of reflexive law (A → A)
= Elimination of arrows in soft objects
31. Summary of results of Trial 2
• Convergent graph represents formal logic.
– Soft objects and soft arrows emerge as the hardest ones.
– Transitive law holds among soft arrows.
• “Latent” objects expected from soft arrows become valid
objects.
– Emergence of definite (=valid=“hardest”) concept
– Furthermore, emergence in the different forms than expected
ones
• Internal Agent Model realizes dynamical formal logic,
– in which logical structure is roughly retained.
35. Discussion 1:
From a logical perspective
• Premise
– Reflexive law (A → A) is invalidated.
• This corresponds to invalidation of the obviousness of the
object.
– Transitive law (A → B and B → C implies A → C) is treated
as S-IA interaction,
• which is succession of applications of transitive law to system
(whole) and agent (part).
• Result
– Emergence of objects (Trial 1),
• as the hardest ones.
• Arrows also emerge as hardest ones.
– Emergence of objects expected from arrows (Trial 2),
• in the different forms than expected ones.
• This emergence corresponds to revision of objects due to
relations (arrows) of objects.
36. Discussion 2: Object and agent
• In Internal Agent Model, both soft object and internal
agent are mere subgraphs of system.
• Soft object
– is an alternative to an ordinary object:
• nonhierarchical,
• divisible,
• incorporable.
– represents a concept.
– takes on a spatial extent.
• Internal agent
– is an object which has purpose.
• In Internal Agent Model, internal agent purposes the adequacy
of the system as formal logic.
– takes on a temporal extent.
37. Future studies
• Internal Agent Model
Agent (purpose) → Soft object (concept).
• We would like to treat
Soft object (concept) → Agent (purpose),
– by the argument of the positional relation or inclusive
relation among soft objects.
• Mediation of Object-Relation Model
(Sawa and Gunji, in press)
– represents expansion and contraction of objects and
relations among objects.
– This model implies two fundamental logical
inferences, deduction and induction in the form of
classification of C. S. Peirce. In addition, it also implies the
third inference of Peirce, abduction, which is usually
disregarded.