We develop possible worlds (Kripke) semantics at the categorical abstract model theoretic level provided by the so-called ‘institutions’. Our general abstract modal logic framework provides a method for systematic Kripke semantics extensions of logical systems from computing science and logic. We also extend the institution-independent method of ultraproducts of [R. Diaconescu, Institution-inde...

A class of Kripke frames is called modally definable if there is a set of modal formulas such that the class consists exactly of frames on which every formula from that set is valid, i. e. globally true under any valuation. Here, existential definability of Kripke frame classes is defined analogously, by demanding that each formula from a defining set is satisfiable under any valuation. This is...

Proving that two programs are contextually equivalent is notoriously hard, particularly for functional languages with references (i.e., local states). Many operational techniques have been designed to prove such equivalences, and fully abstract denotational model, using game semantics, have been built for such languages. In this work, we marry ideas coming from trace semantics, an operational v...

We introduce e ectiveness considerations into model theory of intuitionistic logic. We investigate e ectiveness of completeness (by Kripke) results for intermediate logics such as for example, intuitionistic logic, classical logic, constant domain logic, directed frames logic, Dummett's logic, etc.

The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the so-called Gelfond-Lifschitz transform. The primary goal of this work is to present an alternative and epistemic based characterization of the stable mo...

We introduce three relations between models of Peano Arithmetic (PA), each of which is characterized as an arithmetical accessibility relation. A relation R is said to be an arithmetical accessibility relation if for any modelM of PA,M Prπ(φ) iffM′ φ for allM′ withM RM′, where Prπ(x) is an intensionally correct provability predicate of PA. The existence of arithmetical accessibility relations y...

Goldblatt and Thomason’s theorem on modally definable classes of Kripke frames and Venema’s theorem on modally definable classes of Kripke models are generalised to coalgebras.

Usually, in the Kripke semantics for intuitionistic propositional logic (or for superintuitionistic logics) partially ordered frames are used. Why? In this paper we propose an intrinsically intuitionistic motivation for that. Namely, we show that every Kripke frame (with an arbitrary accessibility relation), whose set of valid formulas is a superintuitionistic logic, is logically equivalent to ...