We extend the algebraic-coalgebraic specification language CoCasl by full coalgebraic modal logic based on predicate liftings for functors. This logic is more general than the modal logic previously used in CoCasl and supports the specification of a variety of modal logics, such as graded modal logic, majority logic, and probabilistic modal logic. CoCasl thus becomes a modern modal language tha...

In this note we investigate modal logics of submaximal and nodec spaces when the modal diamond is interpreted as the closure operator of a topological space. We axiomatize the modal logic of nodec spaces. We show that the modal logic of submaximal spaces is a proper extension of the modal logic of nodec spaces, axiomatize it, and prove that it coincides with the modal logics of door spaces and ...

The modal logic S4F provides an account for the default logic of Reiter, and several modal nonmonotonic logics of knowledge and belief. In this paper we focus on a fragment of the logic S4F concerned with modal formulas called modal defaults, and on sets of modal defaults — modal default theories. We present characterizations of S4F-expansions of modal default theories, and show that strong and...

We introduce distributive unimodal logic as a modal logic of binary relations over posets which naturally generalizes the classical modal logic of binary relations over sets. The relational semantics of this logic is similar to the relational semantics of intuitionistic modal logic and positive modal logic, but it generalizes both of these by placing no restrictions on the accessibility relatio...

In this thesis, we investigate the modal logic of forcing and the modal logic of grounds of generic multiverses. Hamkins and Löwe showed that the ZFC-provable modal principles of forcing, as well as of grounds, are exactly the theorems of the modal logic S4.2 (see [16],[17]). We prove that the modal logic of forcing of any generic multiverse is also exactly S4.2 by showing that any model of ZFC...

In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal...

Abstract There are two different modal logics: the logic T assuming contingency and K = logical determinism. In paper, I show that Aristotelian treatise On Interpretation (???? ?????????, De Interpretatione ) has introduced some modal-logical relationships which correspond to . this logic, it is supposed there contingent events. The N?g?rjunian ??vara-kart?tva-nir?k?ti?-vi??o?-ekakart?tva-nir?k...

Coalgebraic modal logic serves as a unifying framework to study a wide range of modal logics beyond the relational realm, including probabilistic and graded logics as well as conditional logics and logics based on neighbourhoods and games. Coalgebraic predicate logic (CPL), a generalization of a neighbourhoodbased first-order logic introduced by Chang, has been identified as a natural first-ord...