Computable Kripke Models and Intermediate Logics

Cdmtcs Research Report Series Computable Kripke Models and Intermediate Logics

We introduce e ectiveness considerations into model theory of intuitionistic logic. We investigate e ectiveness of completeness (by Kripke) results for intermediate logics such as for example, intuitionistic logic, classical logic, constant domain logic, directed frames logic, Dummett's logic, etc.

Kripke Completeness for Intermediate Logics

Hypersequent Calculi for some Intermediate Logics with Bounded Kripke Models

In this paper we define cut-free hypersequent calculi for some intermediate logics semantically characterized by bounded Kripke models. In particular we consider the logics characterized by Kripke models of bounded width Bwk, by Kripke models of bounded cardinality Bck and by linearly ordered Kripke models of bounded cardinality Gk. The latter family of logics coincides with finite-valued Gödel...

Krlpke Models and Intermediate Logics

In [10], Kripke gave a definition of the semantics of the intuitionistic logic. Fitting [2] showed that Kripke's models are equivalent to algebraic models (i.e., pseudo-Boolean models) in a certain sense. As a corollary of this result, we can show that any partially ordered set is regarded as a (characteristic) model of a intermediate logic ̂ We shall study the relations between intermediate log...

Complexity of Model Checking for Logics over Kripke models

Mathematical logic and computational complexity have close connections that can be traced to the roots of computability theory and the classical decision problem. In the context of complexity, some well-known fundamental problems are: satisfiability testing of formulas (in some logic), proof complexity, and the complexity of checking if a given model satisfies a given formula. The Model Checkin...