We introduce a generic framework for hybrid logics, i.e. modal logics additionally featuring nominals and satisfaction operators, thus providing the necessary facilities for reasoning about individual states in a model. This framework, coalgebraic hybrid logic, works at the same level of generality as coalgebraic modal logic, and in particular subsumes, besides normal hybrid logics such as hybr...

The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues relate...

We present optimizations for the modal logic programming system MProlog, including the standard form for resolution cycles, optimized sets of rules used as meta-clauses, optimizations for the version of MProlog without existential modal operators, as well as iterative deepening search and tabulation. Our SLD-resolution calculi for MProlog in a number of modal logics are still strongly complete ...

We investigate the modal logic of the generic multiverse which is a bimodal logic with operators corresponding to the relations “is a forcing extension of” and “is a ground model of”. The fragment of the first relation is the modal logic of forcing and was studied by the authors in earlier work. The fragment of the second relation is the modal logic of grounds and will be studied here for the f...

We introduce a modal language L which is obtained from standard modal logic by adding the diierence operator and modal operators interpreted by boolean combinations and the converse of accessibility relations. It is proved that L has the same expressive power as the two-variable fragment F O 2 of rst-order logic but speaks less succinctly about relational structures: if the number of relations ...

Among non-monotonic systems of reasoning, non-monotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce non-monotonic modal logics based on many...

The paper presents the essential connections between modal-like operators, topologies and fuzzy sets. We show, for example, that each fuzzy set determines a preorder and an Alexandrov topology, and that similar correspondences hold also for the other direction. Further, a category for preorder-based fuzzy sets is defined, and it is shown that its equivalent subcategory of representatives is iso...

The weak epistemic modal operators might, possible, likely, and probable display embedding behaviors and scope interactions that are interestingly different from their logically stronger counterparts must and certain. I present two problematic sets of facts about these operators which have not received much attention in the literature. The first is that weak epistemic modals embed freely under ...

Modal logics offer natural, declarative representations for describing both the modular structure of logical specifications and the attitudes and behaviors of agents. The results of this paper further the goal of building practical, efficient reasoning systems using modal logics. The key problem in modal deduction is reasoning about the world in a model (or scope in a proof) at which an inferen...

First appearances suggest that probability operators (is as likely as, probably, is more likely than, etc) should be treated together with what we might call pure modal talk (might, may, ought, must, possibly, necessarily, etc) because: • They are non-truth-functional operators on propositions. • They interact logically with epistemic modals: R3. Must to probably. It must be that Probably R4. P...