Syntactic cut-elimination for common knowledge
نویسندگان
چکیده
منابع مشابه
Syntactic Cut-elimination for Common Knowledge
We see a cut-free infinitary sequent system for common knowledge. Its sequents are essentially trees and the inference rules apply deeply inside of these trees. This allows to give a syntactic cut-elimination procedure which yields an upper bound of φ20 on the depth of proofs, where φ is the Veblen function.
متن کاملAbout cut elimination for logics of common knowledge
The notions of common knowledge or common belief play an important role in several areas of computer science (e.g. distributed systems, communication), in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for co...
متن کاملInducing Syntactic Cut-Elimination for Indexed Nested Sequents
The key to the proof-theoretical study of a logic is a cutfree proof calculus. Unfortunately there are many logics of interest lacking suitable proof calculi. The proof formalism of nested sequents was recently generalised to indexed nested sequents in order to yield cutfree proof calculi for extensions of the modal logic K by Geach (LemmonScott) axioms. The proofs of completeness and cut-elimi...
متن کاملCut-free common knowledge
Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in Alberucci and Jäger [1], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.
متن کاملSyntactic cut-elimination for a fragment of the modal mu-calculus
For some modal fixed point logics, there are deductive systems that enjoy syntactic cut-elimination. An early example is the system in Pliuskevicius [15] for LTL. More recent examples are the systems by the authors of this paper for the logic of common knowledge [5] and by Hill and Poggiolesi for PDL [8], which are based on a form of deep inference. These logics can be seen as fragments of the ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2009
ISSN: 0168-0072
DOI: 10.1016/j.apal.2009.01.014