Modal operator

About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.

Nonmonotonic databases and epistemic queries

Abstract: The approach to database query evaluation developed by Levesque and Reiter treats databases as first order theories, and queries as formulas of the language which includes, in addition to the language of the database, an epistemic modal operator. In this epistemic query language, one can express questions not only about the external world described by the database, but also about the database itself-- about what the database knows. On the other hand, epistemic formulas are used in knowledge representation for the purpose of expressing defaults. Autoepistemic logic is the best known epistemic nonmonotonic formalism; the logic of grounded knowledge, proposed recently by Lin and Shoham, is another such system. This paper brings these two directions of research together. We describe a new version of the Lin/Shoham logic, similar in spirit to the Levesque/Reiter theory of epistemic queries. Using this formalism, we can give meaning to epistemic queries in the context of nonmonotonic databases, including logic programs with negation as failure.

A Resolution Calculus for Modal Logics

Abstract: A syntax transformation is presented that eliminates the modal logic operators from modal logic formulae by shifting the modal context information to the term level. The formulae in the transformed syntax can be brought into conjunctive normal form such that a clause based resolution calculus without any additional inference rule, but with special modal unification algorithms, can be defined. The method works for first-order modal logics with the two operators □ and ♦ and with constant-domain Kripke semantics where the accessibility relation is serial and may have any combination of the following properties: reflexivity, symmetry, transitivity. In particular the quantified versions of the modal systems T, S4, S5, B, D, D4 and DB can be treated. Extensions to non-serial and varying-domain systems are possible, but not presented here.

Expressivity of coalgebraic modal logic: the limits and beyond

Abstract: 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 of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.