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Multi-Agent Only Knowing
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This paper provides an axiom system that captures the authors' desiderata, and shows that it has a semantics that corresponds to it, and provides a complete axiomatization for satisfiability in the logic K45.Abstract:
Levesque introduced a notion of ``only knowing'', with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multi-agent case. Although there are a number of similarities in their approaches, there are some significant differences. In this paper, we reexamine the notion of only knowing, going back to first principles. In the process, we simplify Levesque's completeness proof, and point out some problems with the earlier definitions. This leads us to reconsider what the properties of only knowing ought to be. We provide an axiom system that captures our desiderata, and show that it has a semantics that corresponds to it. The axiom system has an added feature of interest: it includes a modal operator for satisfiability, and thus provides a complete axiomatization for satisfiability in the logic K45.read more
Citations
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Journal ArticleDOI
Mathematical Foundations for Joining Only Knowing and Common Knowledge (Extended Version)
Marcos Cramer,Bart Bogaerts +1 more
TL;DR: In this article , a multi-agent epistemic logic with common knowledge and only knowing operators is defined, and a three-valued model semantics for it is defined based on a canonical Kripke structure.
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A Comparative Study of Compliance Management Frameworks: PENELOPE vs. PCL
Ho-Pun Lam,Mustafa Hashmi +1 more
TL;DR: In this paper, the authors propose methodologies to formally evaluate compliance management frameworks, compliance languages and systems, in particular the underlying formal language of a CMF; and present the formal evaluation of two prominent formal language-based CMFs with a business contract using formal analysis approach.
References
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Book
An Introduction to Modal Logic
Max J. Cresswell,G. E. Hughes +1 more
TL;DR: This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic with all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing clarity of exposition and approachability.
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Semantical considerations on nonmonotonic logic
TL;DR: This paper gives a reconstruction of nonmonotonic logic as a model of an Ideally rational agent's reasoning about his own beliefs, and defines an Intuitively based semantics for which it can show autoeplstemlc logic to be both sound and complete.
Journal ArticleDOI
A guide to completeness and complexity for modal logics of knowledge and belief
Joseph Y. Halpern,Yoram Moses +1 more
TL;DR: It is shown that while the problem of deciding satisfiability of an S5 formula with one agent is NP-complete, the problem for many agents is PSPACE-complete and the problem becomes complete for exponential time once a common knowledge operator is added to the language.
Journal ArticleDOI
All I know: a study in autoepistemic logic
TL;DR: This research attempts to show how some of these patterns of reasoning can be captured using only the classical notions of logic, by extending a logic of belief so that it is possible to say that only a certain proposition is believed.