For any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ < Λ. These represent provability predicates of increasing strength. Although GLPΛ has no non-trivial Kripke frames, Ignatiev showed that indeed one can construct a universal Kripke frame for the variable-free fragment with natural number modalities, denoted GLPω. In this paper we show how to extend these con...

From classical, Fräıssé-homogeneous, (≤ ω)-categorical theories over finite relational languages (which we refer to as JRS theories), we construct intuitionistic theories that are complete, prove negations of classical tautologies, and admit quantifier elimination. The technique we use considers Kripke models as functors from a small category to the category of L-structures with morphisms, rath...

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.

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...

In this paper, we use some observations on the nature of biochemical reactions to derive interesting properties of qualitative biochemical Kripke structures. We show that these characteristics make Kripke structures of biochemical pathways suitable for assumption based distributed model checking. The number of chemical species participating in a biochemical reaction is usually bounded by a smal...

Kripke semantics plays a fundamental role for modal logics. (?) suggests a natural generalisation of Kripke semantics for modal logics to an analogous kind of semantics (generalised Kripke semantics) for a broader setting including that of substructural logics. The algebraic structure underlying a traditional Kripke model is the powerset of a set of worlds. The generalisation used here allows u...

The finite model property of the variety of S-algebras was proved by X. Caicedo using Kripke model techniques of the associated calculus. A more algebraic proof, but still strongly based on Kripke model ideas, was given by Muravitskii. In this article we give a purely algebraic proof for the finite model property which is strongly based on the fact that for every element x in a S-algebra the in...

Solovay’s proof of the arithmetical completeness of the provability logic GL proceeds by simulating a finite Kripke model inside the theory of Peano Arithmetic (PA). In this article, a new perspective on the proof of GL’s arithmetical completeness will be given. Instead of simulating a Kripke structure inside the theory of PA, it will be embedded into an arithmetically defined Kripke structure....

We consider quantitative model checking in durational Kripke structures (Kripke structures where transitions have integer durations) with timed temporal logics where subscripts put quantitative constraints on the time it takes before a property is satisfied. We investigate the conditions that allow polynomial-time model checking algorithms for timed versions of CTL and exhibit an important gap ...