We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our attention to finite structures. Many decidability and undecidability results for the elementary modal logics were proved separately for general satisfiability and fo...

Gödel’s modal logic approach to analyzing provability attracted a great deal of attention and eventually led to two distinct mathematical models. The first is the modal logic GL, also known as the Provability Logic, which was shown in 1979 by Solovay to be the logic of the formal provability predicate. The second is Gödel’s original modal logic of provability S4, together with its explicit coun...

To direct at the characteristic of the decision system based on Rough set theory, the proposition modal logic is extended by adding the attribute constants as the basic symbols, and the formal system of the extended propositional modal logic as well as its semantics are described. Since every decision system based on Rough set theory can be expressed by a decision system based on the semantics ...

Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties – up to the point that canonical models may fail to exist, as is the case e.g. in most probabilistic logics. Here, we present a...

AGM-style revision operators are defined for several systems of classical modal logic. · · · draft of November 28, 2009 · · · Within AGM, consistency maintenance is done by classical logic. But the reliance on classical consistency presents a problem for exporting AGM revision to non-classical logics in general, and to modal logic in particular. A general technique for solving this problem is t...

Hybrid logics extends modal logic with a special sort of variables, called nominals, which are evaluated to singletons in Kripke models by valuations, thus acting as names for states in models, see e.g., [1], [2] and [7]. Various other connectives which capitalize on this naming power of the nominals and, in so doing, enhance the expressive power of these languages even further, can be included...

This paper is a survey on modal logic of multiverses. It summarizes known results by Hamkins, Inamdar, Leibman, and the second author about the modal logics of forcing, grounds, and inner models in a general abstract setting. Most results in this survey come from a series of papers co-authored by the second author [19, 20, 18, 24]. Exceptions are the discussion of spiked Boolean algebras and th...

We investigate a simple modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action.

We present a proposal on how to develop nonmonotonic reasoning based on the modal logic S4. As a consequence of our results we show how to present the well known semantics of answer sets, under a restricted fragment of modal formulas, using this approach. Moreover, by considering the full set of modal formulas we obtain an interesting generalization of answer sets with modal connectives. We sho...

Inspired by Hintikka’s treatment of question embedding verbs in [8] and the variations of noncontingency operator, we propose a logic with strong noncontingency operator N as the only primitive modality. A proposition is strongly noncontingent, if no matter whether it is true or false, it does it necessarily; otherwise, it is weakly contingent. This logic is not a normal modal logic, since N(φ ...