An elementary proof of the completeness of PDL
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An elementary proof of the completeness of the Segerberg axions for Propositional Dynamic Logic is given.About:
This article is published in Theoretical Computer Science.The article was published on 1981-01-01 and is currently open access. It has received 182 citations till now. The article focuses on the topics: Original proof of Gödel's completeness theorem & Structural proof theory.read more
Citations
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Book ChapterDOI
Temporal and modal logic
TL;DR: In this article, a multiaxis classification of temporal and modal logic is presented, and the formal syntax and semantics for two representative systems of propositional branching-time temporal logics are described.
Journal ArticleDOI
Results on the propositional μ-calculus
TL;DR: A propositional μ-calculus L μ is defined and study, which consists essentially of propositional modal logic with a least fixpoint operator that is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL).
Book
Dynamic Logic
TL;DR: This book provides the first comprehensive introduction to Dynamic Logic, a system of remarkable unity that is theoretically rich as well as of practical value.
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.
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.
References
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Journal ArticleDOI
Propositional dynamic logic of regular programs
TL;DR: A formal syntax and semantics for the propositional dynamic logic of regular programs is defined and principal conclusions are that deciding satisfiability of length n formulas requires time d n /log n for some d > 1, and that satisfiability can be decided in nondeterministic time cn for some c.
Proceedings ArticleDOI
Models of program logics
TL;DR: The common theory has already been shown to be complete in deterministic exponential time; the simpler proof of the upper bound is given.
Book ChapterDOI
The completeness of propositional dynamic logic
TL;DR: The completeness of a rather natural set of axioms for this logic is proved and an extension of it obtained by allowing the inverse operation which converts a program into its inverse.
Proceedings ArticleDOI
A completeness technique for d-axiomatizable semantics
TL;DR: By using the “axiomatizability” of programming constructs, a technique for showing completeness results for some of the more widely used variations of PDL is obtained.