Decidable Kripke models of intuitionistic theories

Decidable Kripke Models of Intuitionistic Theories

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.

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...

Decidable Models of ω-Stable Theories

We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T , every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many co...

Canonical Kripke Models and the Intuitionistic Semantics of Logic Programs

Motivated by the problem of extending stable semantics (SS) and well-founded semantics (WFS) while avoiding their drawbacks, we propose a new simple and intuitive semantics for (normal) logic programs, called canonical Kripke model semantics. Our approach is based on formulating stability in an intuitionistic framework which helps us overcome several drawbacks. As a consequence, every normal pr...