Motivated by the problem of extending stable semantics (SS) and well-founded semantics (WFS) while avoiding their drawbacks, we propose a new simple and intuitive semantics for (normal) logic programs, called canonical Kripke model semantics. Our approach is based on formulating stability in an intuitionistic framework which helps us overcome several drawbacks. As a consequence, every normal pr...

We introduce the class of rational Kripke models and study symbolic model checking of the basic tense logic Kt and some extensions of it in models from that class. Rational Kripke models are based on (generally infinite) rational graphs, with vertices labeled by the words in some regular language and transitions recognized by asynchronous two-head finite automata, also known as rational transdu...

Building on the fact that descriptive frames are coalgebras for the Vietoris functor on the category of Stone spaces, we introduce and study the concept of a Vietoris bisimulation between two descriptive modal models, together with the associated notion of bisimilarity. We prove that our notion of bisimilarity, which is defined in terms of relation lifting, coincides with Kripke bisimilarity (w...

Let T be a first-order theory. A T -normal Kripke structure is one in which every world is a classical model of T . This paper gives a characterization of the intuitionistic theory HT of sentences intuitionistically valid (forced) in all T -normal Kripke structures and proves the corresponding soundness and completeness theorems. For Peano arithmetic (PA), the theory HPA is a proper subtheory o...

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.