Abstract This paper is dedicated to extending and adapting modal logic the approach of fractional semantics classical logic. a multi-valued governed by pure proof-theoretic considerations, whose truth-values are rational numbers in closed interval $[0,1]$ . Focusing on K , proposed methodology relies three key components: bilateral sequent calculus, invertibility logical rules, stability (proof...

These notes were written by Wang Yafeng following a course of three intensive lectures on classical themes in mathematical modal logic given by Johan van Benthem in the Berkeley-Stanford Logic Circle, San Francisco, May 2015. Some of this material was collected in the monograph van Benthem [13], [16], other parts come from later publications. We will provide some references to further relevant ...

Modal Logic is traditionally concerned with the intensional operators “possibly” and “necessary”, whose intuitive correspondence with the standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies the well-known translation from propositional modal logic with operators ♦ and , possibly indexed, into the first-order language over...

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is clos...

We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces. §

The objective of this paper is to introduce the hybrid logic methodology into possibilistic reasoning. It has been well-known that possibilistic logic has some strong modal logic flavor. However, modal logic lacks the capability of referring to states or possible worlds though states are crucial to its semantics. Hybrid logic circumvents the problem by blending the classical logic mechanism int...

We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended with intuitionistic disjunction. Furthermore, we show that the expressive power of modal logic with intuitionistic disjunction and extended modal dependence ...

First-order modal logic is clearly more than classical first-order logic, because modalities can be used to phrase more advanced necessity and possibility properties. At the same time, first-order modal logic and non-modal first-order logic are not entirely different either. Modalities quantify over all ( ) or some (♦) worlds. Quantifiers also quantify over all (∀) or some (∃) objects (yet not ...

This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad. In essence, modal logic is a simple formalism for working with relational structures (or multigraphs). But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representa...

Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence ...