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.

Łukasiewicz Public Announcement Logic

Abstract: In this work we lay a theoretical framework for developing dynamic epistemic logics in a many-valued setting. We consider in particular the logic of Public Announcements, which is one of the simplest and best-known dynamic epistemic systems in the literature. We show how to develop a Public Announcement Logic based on finite-valued Łukasiewicz modal logic. We define our logic through a relational semantics based on many-valued Kripke models, and also introduce an alternative but equivalent algebra-based semantics using MV-algebras endowed with modal operators. We provide a Hilbert-style calculus for our logic and prove completeness with respect to both semantics.

Agent Logic and the True-False Subset Semantics

Abstract: Formal frameworks for the specification of rational agents are commonly based on logic of belief, desire and intention. In order to eliminate the problems with existing logic of belief, desire and intention, and to provide a proper semantic representation for non-normal modal operator, the problems with existing logic of belief, desire and intention are addressed, the true-false subset semantics, which is developed by the authors, and its application in the formalization of agent are introduced. The proposed framework invalidates the problematic properties of intention, and by imposing certain constraints on the algebraic structure of the models, it is showed that many desirable properties can be obtained. Finally the true-false subset semantics is analyzed. Thus the true-false subset semantics provides a proper semantic representation for non-normal modal operator. It is an important development of classical possible worlds semantics for normal modal operators, and is proved to be a powerful tool for the logical specification of rational agent behavior. It can be applied to establish a new proper agent logic system.

Explaining referential/attributive

Abstract: Kaplan, Stalnaker and Wettstein all urge a two-stage theory of language whereon the propositions expressed by sentences are generated prior to being evaluated. A new ambiguity for sentences emerges, propositional rather than syntactic or semantic. Kaplan and Wettstein then propose to explain Donnellan's referential/attributive ambiguity as simply being two-stage propositional ambiguity. This is tacitly seen as further confinnation for twostage theory. Modal ambiguities are prime motivators for two-stage theory, which distinguishes local from exotic evaluation to explain them. But if sentences can be found which exhibit both modal and referential/attributive ambiguity, an apparent paradox arises for a two-stage account. The theory recognizes both singular and general propositions, in Kaplan's senses. But reflecting one sense of such a doubly ambiguous sentence, two-stage theory would seem to need a proposition both singular and general with respect to a definite description attributively used. Since modal operators will come into rendering the problem sentences, an obvious idea is to let scope distinctions rescue two-stage theory from the apparent paradox. But while a rescue based on multiple renderings is proposed, it is not strictly a scope rescue, though different scopes are involved. Readers are asked to trust the author on missing formalities of an intuitively transparent two-sorted modal language that is employed. Two-stage theorists explicitly oppose scope treatments of modal ambiguities seeing them as rivals. Stalnaker, in particular, argues against them. But his arguments are shown not to count against the proposed rescue, on which the anticipated rivalry proves to be minimal.

A modal logic for subject-oriented spatial reasoning

Abstract: We present a modal logic for representing and reasoning about space seen from the subject's perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete.