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.

Information, Issues, and Attention

Abstract: A sentence is informative if there are possible worlds that are eliminated from the common ground by each of the proposed updates, and it is inquisitive if it proposes two or more alternative updates, requesting information from other participants in order to establish at least one of these updates. This chapter argues that this notion of meaning has an additional advantage. It discusses a recapitulation of inquisitive semantics, and presents the definition of the semantics. The chapter shows how attentive content can be captured in a natural extension of this framework. It examines pragmatic aspects of the interpretation of sentences that are not merely informative, but also inquisitive and/or attentive. The chapter describes the behaviour of might in certain embedded contexts, and argues that the semantic meaning of might sentences is strengthened in a particular way before being composed with the semantic meaning of the embedding operator. Keywords: attentive content; epistemic modal operator; informative content; inquisitive semantics

A general approach for determining the validity of commonsense assertions using conditional logics

Abstract: An approach to theorem proving for the class of normal conditional logics is presented. These logics have been shown to be appropriate for representing a wide variety of commonsense assertions, including default and prototypical properties, counterfactuals, notions of obligation, and others. the logics are based on a possible worlds semantics but unlike the better-known modal logics of necessity and possibility, they contain a binary “variable conditional” operator, ⟹, rather than a unary modal operator. the truth of a statement A ⟹ B depends both on the accessibility relation between worlds and on the proposition expressed by the antecedent A. The approach develops an extension of the semantic tableaux approach to theorem proving. Basically, it consists in attempting to find an interpretation which will falsify a sentence or set of sentences. If successful, then a specific falsifying truth assignment is obtained; if not, then the sentence is valid. Since this method is based directly on the notion of truth, it is arguably more natural and intuitive than those based on proof-theoretic methods. the approach has been proven correct for the class of normal conditional logics. In addition, it has been implemented and tested on a number of different logics. Various heuristics have been incorporated, and the implementation, while exponential in the worst case, is shown to be reasonably efficient for a large set of test cases.

Rank-1 modal logics are coalgebraic

Abstract: Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular generic decision procedures and upper complexity bounds, become applicable to arbitrary rank 1 modal logics, without regard to their semantic status; we thus obtain purely syntactic versions of these results. As an extended example, we apply our framework to recently defined deontic logics.

A logical foundation of graded modal operators defined by fuzzy measures

Abstract: To give rigid semantics to graded modal operators, an extended fuzzy-measure-based model is defined as a family of minimal models for modal logic, each of which corresponds to an intermediate value of a fuzzy measure. Soundness and completeness results of several systems of modal logic are proved with respect to classes of newly introduced models based on intermediate values of fuzzy, possibility, necessity, and Dirac measures, respectively. It is emphasized that a fuzzy measure inherently contains a multimodal logical structure. >