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...

I characterize the first-order definable, bi-orthogonally closed subsets of a quasiquantum Kripke frame satisfying a reasonable assumption. The techniques are generalization of those in Goldblatt’s paper published in 1984. Combining these techniques with Goldblatt’s idea, I prove that quantum Kripke frames are not firstorder definable in the class of quasi-quantum Kripke frames.

We present Kripke modal transition systems (Kripke MTSs), a generalization of modal transition systems [27,26], as a foundation for three-valued program analysis. The semantics of Kripke MTSs are presented by means of a mixed power domain of states; soundness and consistency are proved. Two major applications, model checking partial state spaces and three-valued program shape analysis, are pres...

This paper proves some independence results for weak fragments of Heyting arithmetic by using Kripke models. We present a necessary condition for linear Kripke models of arithmetical theories which are closed under the negative translation and use it to show that the union of the worlds in any linear Kripke model of HA satisfies PA. We construct a two-node PA-normal Kripke structure which does ...

We show how to generate multi-agent Kripke models from message exchanges, and conversely, how to interpret message exchanges with respect to initial multi-agent Kripke models. Any multimodal S5 Kripke model is a suitable initial model for updating by means of message exchange.

We deene a notion of Kripke logical predicate for models of classical linear logic. A Kripke logical predicate on a type A will be a set of generalised elements of A satisfying certain closure properties. Denotations of proofs of A will be characterised as those global elements of A satisfying all Kripke logical predicates on A.

We consider a class of Kripke Structures in which the atomic propositions are events. This enables us to represent worlds as sets of events and the transition and satisfaction relations of Kripke structures as the subset and membership relations on sets. We use this class, called event Kripke structures, to model concurrency. The obvious semantics for these structures is a true concurrency sema...