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A Probabilistic Temporal Epistemic Logic: Strong Completeness

Zoran Ognjanović, Angelina Ilić Stepić & Aleksandar Perović

Logic Journal of the IGPL (forthcoming)

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Propositional temporal logics: decidability and completeness.O. Lichtenstein & A. Pneuli - 2000 - Logic Journal of the IGPL 8 (1):55-85.details A sound and complete axiomatic system and a tableau-based decision procedure are presented for propositional temporal logic over linear and discrete time models. The axiomatic system and decision procedure are presented for the full logic, including the past operators, but contain a clear identification of the parts whose omission yields axiomatization and a decision procedure for the future fragment. The paper summarizes work of over 20 years and is intended to provide a definitive reference to the version of propositional temporal (...) Download Export citation Bookmark 16 citations
First order common knowledge logics.Frank Wolter - 2000 - Studia Logica 65 (2):249-271.details In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" (...) Download Export citation Bookmark 11 citations
The completeness of the first-order functional calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (3):159-166.details Download Export citation Bookmark 111 citations
Knowledge and Belief: An Introduction to the Logic of the Two Notions.Jaakko Hintikka - 1962 - Studia Logica 16:119-122.details Download Export citation Bookmark 684 citations
Syntactic cut-elimination for common knowledge.Kai Brünnler & Thomas Studer - 2009 - Annals of Pure and Applied Logic 160 (1):82-95.details We first look at an existing infinitary sequent system for common knowledge for which there is no known syntactic cut-elimination procedure and also no known non-trivial bound on the proof-depth. We then present another infinitary sequent system based on nested sequents that are essentially trees and with inference rules that apply deeply inside these trees. Thus we call this system “deep” while we call the former system “shallow”. In contrast to the shallow system, the deep system allows one to give (...) Download Export citation Bookmark 9 citations

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