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...

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...

This thesis provides a model–theoretic semantic analysis of aspects of the LF logical framework. The LF logical framework is the λΠ-calculus together with the judgements-as-types representation mechanism. A denotational semantics is provided for the λΠ-calculus in terms of Kripke λΠ-models. These are a generalization of the Kripke lambda models of Mitchell and Moggi to dependent types and are b...

We establish a connection between term definability of Boolean functions and definability of finite modal frames. We introduce a bijective translation between functional terms and uniform degree-1 formulas and show that a class of Boolean functions is defined by functional terms if and only if the corresponding class of Scott-Montague frames is defined by the translations of these functional te...