Metamathematics of contexts
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This document outlines a formal system of contexts and metamathematics. It introduces context sequences and partial truth assignments. A model maps context sequences to sets of partial truth assignments. The vocabulary of a context is the set of meaningful atoms. Satisfaction is defined for well-formed formulas over contexts and atoms. Theorems about consistency, truth, and flatness models are discussed as extensions to reason about properties of contexts.
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Metamathematics of contexts
This document outlines a formal system called metamathematics of contexts. It describes contexts as sets that define the meaningful vocabulary within that context. Formulas are built from propositional atoms using context operators. Models are functions that map context sequences to partial truth assignments. The semantics define satisfaction in a model based on the vocabulary of a context. The system has provability rules and useful theorems. Extensions examine consistency models where contexts cannot assign different truth values, truth models with a single assignment, and flatness models where contexts have identical vocabularies regardless of sequence.
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Metamathematics of contexts
This document outlines a formal system called metamathematics of contexts. It describes contexts as sets that define the meaningful vocabulary within that context. Formulas are built from propositional atoms using context operators. Models are functions that map context sequences to partial truth assignments. The semantics define satisfaction in a model based on the vocabulary of a context. The system has provability rules and useful theorems. Extensions examine consistency models where contexts cannot assign different truth values, truth models with a single assignment, and flatness models where contexts have identical vocabularies regardless of sequence.
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Merge Sort follows the divide and conquer approach to sort a list by recursively dividing it into smaller sub-lists, sorting those sub-lists using the same approach, and then merging the sorted sub-lists back together; it runs in O(n log n) time by breaking the problem into smaller problems of sorting each half of the list, combining the solutions by merging the halves back together; the document provides an overview of the merge sort algorithm and its use of divide and conquer to break down a sorting problem into subproblems.
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ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
CAKE: Sharing Slices of Confidential Data on Blockchain
Presented at the CAiSE 2024 Forum, Intelligent Information Systems, June 6th, Limassol, Cyprus.
Synopsis: Cooperative information systems typically involve various entities in a collaborative process within a distributed environment. Blockchain technology offers a mechanism for automating such processes, even when only partial trust exists among participants. The data stored on the blockchain is replicated across all nodes in the network, ensuring accessibility to all participants. While this aspect facilitates traceability, integrity, and persistence, it poses challenges for adopting public blockchains in enterprise settings due to confidentiality issues. In this paper, we present a software tool named Control Access via Key Encryption (CAKE), designed to ensure data confidentiality in scenarios involving public blockchains. After outlining its core components and functionalities, we showcase the application of CAKE in the context of a real-world cyber-security project within the logistics domain.
Paper: https://doi.org/10.1007/978-3-031-61000-4_16
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
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Metamathematics of contexts
- 2. Outline Introduction to contexts The general system Notation Syntax Semantics Models Vocabularies Satisfaction Formal System Useful theorems Extensions for the general system Consistency Model Truth Model Flatness Model
- 4. Notation • Given that X and Y are Sets then: • is the set of partial functions from X to Y. • is the set of subsets of X. • is the set of all finite sequences in X that can be treated as a tree. • is a range over . • is the empty sequence.
- 5. Syntax • Let be the set of all contexts, P be the set of all propositional atoms. • We can now build the set of all well-formed formulas (wffs) using K and P in the following recursive fashion: • We will also be using the following abbreviations
- 6. Semantics - Model • In this system, a model , will be a function which maps a context sequence to a set of partial truth assignments denoted by or . • Why a context sequence instead of a single context? • The truth assignments need to be partial. Why?
- 7. Semantics - Vocabularies • A Vocabulary of a context is the set of atoms that are meaningful in that context. • is a function that given a model , returns the vocabulary for that model. • Different contexts can have different vocabularies. That’s why the truth assignments need to be partial.
- 8. Semantics - Satisfaction • Why? Because we add a third logic value other than true, false. So X would be syntactically meaningless.
- 10. Useful Theorems
- 11. System Extensions - Consistency • Sometimes it’s desirable to ensure that all contexts are consistent. • In this extension we examine the class of consistent models . A model iff for any context sequence in the domain of that model holds. • In other words, if no two truth assignments give different truth values for the same atom, then the model that maps the context to these truth assignments can be described as consistent.
- 12. System Extension - Truth • A model is a truth model, formally iff for any context sequence in the domain of that model, • In other words, if the model has only one or less truth assignment function, it can be described as a truth model.
- 13. System Extension - Flatness • For some applications, all contexts will be identical regardless of which context are they viewed from. This is called flatness. • A model is flat, formally , iff for any context sequences and any context