Intuitionistic axiomatizations for bounded extension Kripke models

Intuitionistic axiomatizations for bounded extension Kripke models

We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of co5nal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic (HA) is strongly comple...

Intuitionistic and Classical Satisfiability in Kripke Models

A class P ∗ of formulas was defined in [4] which whenever satisfied in a classical structure associated with a node of a Kripke model must also be forced at that node. Here we define a dual class R of formulas which whenever forced at a node of a Kripke model must be satisfied in the classical structure associated with that node.

Decidable Kripke Models of Intuitionistic Theories

Rudimentary Kripke Models for the Intuitionistic Propositional Calculus

DoSen, K., Rudimentary Kripe models for the intuitionistic propositional calculus, Annals of Pure and Applied Logic 62 (1993) 21-49. It is shown that the intuitionistic propositional calculus is sound and complete with respect to Kripke-style models that are not quasi-ordered. These models, called rudimentary Kripke models, differ from the ordinary intuitionistic Kripke models by making fewer a...

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...