On Decidability of Intuitionistic Modal Logics
نویسندگان
چکیده
We prove a general decidability result for a class of intuitionistic modal logics. The proof is a slight modification of the Ganzinger, Meyer and Veanes [6] result on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic.
منابع مشابه
Intuitionistic Modal Logics as Fragments of Classical Bimodal Logics
Godel's translation of intuitionistic formulas into modal ones provides the well-known embedding of intermediate logics into extensions of Lewis' system S4, which re ects and sometimes preserves such properties as decidability, Kripke completeness, the nite model property. In this paper we establish a similar relationship between intuitionistic modal logics and classical bimodal logics. We als...
متن کاملBisimulation Quantified Logics: Undecidability
In this paper we introduce a general semantic interpretation for propositional quantification in all multi-modal logics based on bisimulations (bisimulation quantification). Bisimulation quantification has previously been considered in the context of isolated modal logics, such as PDL (D’Agostino and Hollenberg, 2000), intuitionistic logic (Pitts, 1992) and logics of knowledge (French 2003). We...
متن کاملA general method for proving decidability of intuitionistic modal logics
We generalise the result of [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34] on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic. I...
متن کاملThe proof theory and semantics of intuitionistic modal logic
Possible world semantics underlies many of the applications of modal logic in computer science and philosophy. The standard theory arises from interpreting the semantic definitions in the ordinary meta-theory of informal classical mathematics. If, however, the same semantic definitions are interpreted in an intuitionistic metatheory then the induced modal logics no longer satisfy certain intuit...
متن کاملNested Sequents for Intuitionistic Modal Logics
We present cut-free deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending K with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents. We show a uniform cut elimination argument and a terminating proof search procedure. As a corollary we get the decidability of all modal logics in the intuitionistic S5-c...
متن کامل