Perhaps the most celebrated topological completeness result in modal logic is the McKinseyTarski theorem that if we interpret modal diamond as topological closure, then S4 is complete for the real line or indeed any dense-in-itself separable metrizable space [10]. This result was proved before relational semantics for modal logic was introduced. In the last 15 years, utilizing relational semant...

This paper gives an overview on translation methods we have developed for nonclassical logics, in particular for modal logics. Optimized ’functional’ and semi-functional translation into predicate logic is described. Using normal modal logic as an intermediate logic, other logics can be translated into predicate logic as well. As an example, the translation of modal logic of graded modalities i...

In the paper we study a new and natural modal interpretat ion of defaults. We show that under this interpretat ion there are whole families of modal nonmonotonic logics that accurately represent default reasoning. One of these logics is used in a definition of possible-worlds semantics for default logic. This semantics yields a characterization of default extensions similar to the characterizat...

Like modal logic, temporal logic, or description logic, separation logic has become a popular class of logical formalisms in computer science, conceived as assertion languages for Hoare-style proof systems with the goal to perform automatic program analysis. We present similarities with modal and temporal logics, and we present landmark results about decidability, complexity and expressive power.

It becomes evident in recent years a surge of interest to applications of modal logics for specification and validation of complex systems. It holds in particular for combined logics of knowledge, time and actions for reasoning about multiagent systems (Dixon, Nalon & Fisher, 2004; Fagin, Halpern, Moses & Vardi, 1995; Halpern & Vardi, 1986; Halpern, van der Meyden & Vardi, 2004; van der Hoek & ...

Spatial constraint systems are algebraic structures from concurrent constraint programming to specify spatial and epistemic behavior in multi-agent systems. We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages. In particular, we shall identify the weakest condition...

CoLoSS, the Coalgebraic Logic Satisfiability Solver, decides satisfiability of modal formulas in a generic and compositional way. It implements a uniform polynomial space algorithm to decide satisfiability for modal logics that are amenable to coalgebraic semantics. This includes e.g. the logics K, KD, Pauly’s coalition logic, graded modal logic, and probabilistic modal logic. Logics are easily...

We show that modal logics characterized by a class of frames satisfying the insertion property are suitable for Reiter's default logic. We reene the canonical x point construction deened by Marek, Schwarz and Truszczy nski for Reiter's default logic and thus we address a new paradigm for nonmonotonic logic. In fact, diierently from the construction deened by these authors, we show that suitable...

In mono-modal logic there is a fair number of high-powered results on completeness covering large classes of modal systems, witness for example Fine [74,85] and Sahlqvist [75]. Mono-modal logic is therefore a well-understood subject in contrast to poly-modal logic where even the most elementary questions concerning completeness, decidability etc. have been left unanswered. Given that so many ap...

A formal logical system dealing with both uncertainty (possibility) and vagueness (fuzziness) is investigated. It is many-valued and modal. The system is related to a many-valued tense logic. A completeness theorem is exhibited. K E Y W O R D S : fuzzy logic, modal logic, possibilistic logic, comparative approach