Completeness of Flat Coalgebraic Fixpoint Logics
نویسندگان
چکیده
منابع مشابه
Completeness for Flat Modal Fixpoint Logics
This paper exhibits a general and uniform method to prove completeness for certain modal fixpoint logics. Given a set Γ of modal formulas of the form γ(x, p1, . . . , pn), where x occurs only positively in γ, the language L♯(Γ) is obtained by adding to the language of polymodal logic a connective ♯γ for each γ ∈ Γ. The term ♯γ(φ1, . . . , φn) is meant to be interpreted as the least fixed point ...
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We introduce an axiomatization for the coalgebraic fixed point logic which was introduced by Venema as a generalization, based on Moss’ coalgebraic modality, of the well-known modal mucalculus. Our axiomatization can be seen as a generalization of Kozen’s proof system for the modal mu-calculus to the coalgebraic level of generality. It consists of a complete axiomatization for Moss’ modality, e...
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A long and fertile tradition in theoretical computer science, going back to the work of Büchi and Rabin, links the field of (fixpoint) logic to that of automata theory. In particular, automata operating on potentially infinite structures such as streams, trees, graphs or transition systems, provide an invaluable tool for the specification and verification of the ongoing behavior of systems. An ...
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While reasoning in a logic extending a complete Boolean basis is coNP-hard, restricting to conjunctive fragments of modal languages sometimes allows for tractable reasoning even in the presence of greatest fixpoints. One such example is the EL family of description logics; here, efficient reasoning is based on satisfaction checking in suitable small models that characterize formulas in terms of...
متن کاملFlat Coalgebraic Fixed Point Logics
Fixed point logics are widely used in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the μ-calculus and its relatives. However, popular fixed point logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the μ-calculus. The family of such flat fixed po...
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ژورنال
عنوان ژورنال: ACM Transactions on Computational Logic
سال: 2018
ISSN: 1529-3785,1557-945X
DOI: 10.1145/3157055