Proceedings ArticleDOI
Extending topological nexttime logic
Bernhard Heinemann
- pp 87-94
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TLDR
The resulting formalism enables one to reason about the change of sets in the course of (discrete) linear time and obtains a 'low' upper complexity bound of the corresponding satisfiability problem: NP.Abstract:
We provide an extension of topological nexttime logic by an operator expressing an increase of sets. The resulting formalism enables one to reason about the change of sets in the course of (discrete) linear time. We establish completeness and decidability of the new system, and determine its complexity. As for the latter, we obtain a 'low' upper complexity bound of the corresponding satisfiability problem: NP; this is due to the fact that the time operators involved in our logic are comparatively weak. It is intended that the system is applicable to diverse fields of temporal reasoning.read more
Citations
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Topics in Social Software: Information in Strategic Situations (Draft: Chapter 4)
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Modelling Change with the Aid of Knowledge and Time
TL;DR: An appropiate language of change is developed and the set of theorems of a corresponding logic is axiomatized: semantic completeness, decidability, and complexity of a given set in the course of time.
References
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Book
Reasoning About Knowledge
TL;DR: Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed systems, artificial intelligence, and game theory.
Book
Modal Logic: An Introduction
TL;DR: This chapter discusses standard models for modal logics, classical systems of modal logic, and Determination and decidability for classical systems.
Journal ArticleDOI
Knowledge and common knowledge in a distributed environment
Joseph Y. Halpern,Yoram Moses +1 more
TL;DR: It is shown that states of knowledge of groups of processors are useful concepts for the design and analysis of distributed protocols and that, formally speaking, in practical systems common knowledge cannot be attained.
Posted Content
Knowledge and common knowledge in a distributed environment
Joseph Y. Halpern,Yoram Moses +1 more
TL;DR: It is argued that the right way to understand distributed protocols is by considering how messages change the state of knowledge of a system, and a hierarchy of knowledge states that a system may be in is presented.
Book
Logics of Time and Computation
TL;DR: In this article, the basic theory of modal and temporal propositional logics is set out and applied to logics of discrete (integer), dense (rational), and continuous (real) time.