Ancestral Kripke models and nonhereditary Kripke models for the Heyting propositional calculus.

Ancestral Kripke Models and Nonhereditary Kripke Models for the Heyting Propositional Calculus

This is a sequel to two previous papers, where it was shown that, for the Heyting propositional calculus H, we can give Kripke-style models whose accessibility relation R need not be a quasi-ordering relation, provided we have: x\=A &Vy(xRy=* y VA). From left to right, this is the heredity condition of standard Kripke models for H, but, since R need not be reflexive, the converse is not automat...

Rudimentary Beth Models and Conditionally Rudimentary Kripke Models for the Heyting Propositional Calculus

This paper continues the investigation of rudimentary Kripke models, i.e. non-quasiordered Kripke-style models for the Heyting propositional calculus H. Three topics, which make three companion pieces of [3], are pursued. The first topic is Beth-style models for H called rudimentary Beth models. Rudimentary Kripke models may be conceived as a particular type of these models, which are analogous...

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...

Kripke-Style models for typed lambda calculus

Kripke Models for the Second-Order Lambda-Calculus

We define a new class of Kripke structures for the second-order λ-calculus, and investigate the soundness and completeness of some proof systems for proving inequalities (rewrite rules) or equations. The Kripke structures under consideration are equipped with preorders that correspond to an abstract form of reduction, and they are not necessarily extensional. A novelty of our approach is that w...