A system is classified as multimodal if its language has more than one modal operator as primitive, and such operators are not interdefinable. We extend the anodic and cathodic modal systems, introduced in [BS09a] and [BS10], to a class of the so-called basilar multimodal systems generating, in this way, the classes of anodic and cathodic multimodal logics. The cathodic multimodal systems are d...

In modal logics we are interested in classes of frames which determine the logic under consideration. Such classes are usually distinguished by their respective frame properties, often also called the modal logic's background theory. In general these characterizations are not unique and it is desireable (and that not only from a theorem prover's perspective) to nd a strongest possible. In this ...

Kripke-style models with two accessibility relations, one intuitionistio and the other modal, are given for analogues of the modal system K based on Heyting's propositional logic. I t is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddi...

We present the experience gained from implementing a new decision procedure for both graded and probabilistic modal logic. While our approach uses standard tableaux for propositional connectives, modal rules are given by linear constraints on the arguments of operators. The implementation uses binary decision diagrams for propositional connectives and a linear programming library for the modal ...

Enabling reasoning as simulations with concrete objects and relations has a merit of grounding reasoning to more basic perceptual mechanisms. In a hybrid artificial intelligence architecture that uses both logical and non-logical computational methods, the use of simulations for enabling logical inferences allows one to alternate between the logical method and a non-logical one that uses, for e...

7.1 Introduction This chapter is about decidability and complexity issues in modal logic; more specifically, we confine ourselves to satisfiability (and the complementary validity) problems. The satisfiability problem is the following: for a fixed class of models, to determine whether a given formula ϕ is satisfiable in some model of that class (a more precise definition will follow). The gener...

The talk will began remembering results on papers [22, 15, 16] where the authors model uncertainty measures as fuzzy modalities on a many-valued residuated logics. the basic idea is that uncertainty measures is not a truth degree but could be interpreted as a truth degree of the fuzzy sentence ”the probability of φ”. The main properties being that the language does not allow nested modalities a...