We present non-clausal resolution systems for propositional modal logics whose Kripke models do not involve symmetry, and for first order versions whose Kripke models do not involve constant domains. We give systems for K, T , K4 and S4; other logics are also possible. Our systems do not require preliminary reduction to a normal form and, in the first order case, intermingle resolution steps wi...

We present a general method for providing Kripke semantics for the family of fully-structural multiple-conclusion propositional sequent systems. In particular, many well-known Kripke semantics for a variety of logics are easily obtained as special cases. This semantics is then used to obtain semantic characterizations of analytic sequent systems of this type, as well as of those admitting cut-a...

Rewrite theories and their associated Kripke structures constitute a flexible and executable framework in which a wide range of systems can be studied. We present a general notion of simulation between Kripke structures, study its categorical aspects, and propose rewriting logic as a framework in which these simulations can be represented. Several representability results showing that rewriting...

The property of strong neighbourhood completeness was introduced in the first part of this paper. By modifying the ultrabouqet construction, we prove this property for all Kripke-complete normal K4-logics and for a large class of Kripke-complete polymodal logics (called ‘acyclic). On the other hand, we present a simple counterexample of a polymodal logic with the f.m.p. which is not strongly ne...

Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they a...

The idea of only knowing is a natural and intuitive notion to precisely capture the beliefs of a knowledge base. However, an extension to the many agent case, as would be needed in many applications, has been shown to be far from straightforward. For example, previous Kripke frame-based accounts appeal to proof-theoretic constructions like canonical models, while more recent works in the area a...

Simulations are a very natural way of relating concurrent systems, which are mathematically modeled by Kripke structures. The range of available notions of simulations makes it very natural to adopt a categorical viewpoint in which Kripke structures become the objects of several categories while the morphisms are obtained from the corresponding notion of simulation. Here we define in detail sev...

Resource bisimilarity has been proposed in the literature on concurrency theory as a notion of bisimilarity over labeled transition systems that takes into account the number of choices that a system has. Independently, g-bisimilarity has been defined over Kripke models as a suitable notion of bisimilarity for graded modal logic. This note shows that these two notions of bisimilarity coincide o...

Every group is isomorphic to the automorphism group of a Kripke structure with Boolean part equal to a power set Boolean algebra. More generally, we prove that the category of Kripke structures with Boolean part equal to a power set Boolean algebra and morphisms with complete Boolean part is alg-universal, which means that it contains any category of universal algebras as a full subcategory.

IPV is IPV (which is essentially IS 2 ) with polynomial-induction on Σ 1 -formulas disjoined with arbitrary formulas in which the induction variable does not occur. This paper proves that IPV is sound and complete with respect to Kripke structures in which every world is a model of CPV (essentially S 2 ). Thus IPV is sound with respect to such structures. In this setting, this is a strengthenin...