In the last 20 years modal logic has been applied to numerous areas of computer science, including artificial intelligence, program verification, hardware verification, database theory, and distributed computing. There are twomain computational problems associated with modal logic. The first problem is checking if a given formula is true in a given state of a given structure. This problem is kn...

Abstract This paper offers a compositional take on two internally complex conditional connectives in Mandarin, zhi-yao ‘only-need’ and zhi-you ‘only-have’. While the former conveys antecedent proposition’s minimal sufficiency , latter its necessity for consequent proposition to come true. Both will be treated as pairing an exclusive particle, zhi with modal, assumption that is less controversia...

Abramsky and Hintikka style games can be seen as representatives of the two main branches of game semantics. They both model interaction but each in a different manner. Hintikka games provide models of propositional interaction in terms of classical logic connectives such as ∨, ∧, →, and ¬. Abramsky games, on the other hand, model the interaction between programs that run in different parallel ...

Intuitionistic propositional logic Int and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded just as fragments of classical modal logics containing S4. At the syntactical level, the Godel translation t embeds every intermediate logic L = Int+ into modal logics in the interval L = [ L = S4 t( ); L = Grz t( )]. Semantically this is re ected by ...

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness...

We establish that the quantifier alternation hierarchy of formulae of secondorder propositional modal logic (SOPML) induces an infinite corresponding semantic hierarchy over the class of finite directed graphs. This solves an open problem problem of van Benthem (1985) and ten Cate (2006). We also identify modal characterizations of the expressive powers of second-order logic (SO) and monadic se...