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.

A Modal Logic That is Complete with Respect to Strictly Linearly Ordered A-Models

Abstract: An axiomatization is furnished for a polymodal logic of strictly linearly ordered A-frames: for frames of this kind, we consider a language of polymodal logic with two modal operators, □< and □≺. In the language, along with the operators, we introduce a constant β, which describes a basis subset. In the language with the two modal operators and constant β, an Lα-calculus is constructed. It is proved that such is complete w.r.t. the class of all strictly linearly ordered A-frames. Moreover, it turns out that the calculus in question possesses the finite-model property and, consequently, is decidable.

The ontogeny of complex verb phrases

Abstract: This paper investigate the acquisition of V-complement constructions (complex VPs) by English-speaking children ca age 1;8-to-2;9 It suggests that the child acquires these constructions during intensive epistemic or deontic modal negotiations with the adult In the earliest stage, the main-plus-complement construction is spread over adjacent child-adult or adult-child conversational turns ( Ochs et al 1979) The early precursor of the complex VP construction is thus paratactic , with the two clauses falling under separate intonation contours Only later on is the construction condensed into a complex syntactic construction under a single intonation contour, produced by the child alone The early use of these constructions is as direct speech acts , be they epistemic or deontic (Diessel 2005), whereby the semantic focus resides in the complement clause, and the main clause acts as a modal operator But this is true of both the children and their adult interlocutors, and is also characteristic, at the text-frequency level, of adult oral language (Thomson 2001) However, this characterization of complex VPs is semantic rather than syntactic

Is this story possible? Exploring possible worlds theory

Abstract: The nature of this article is exploratory rather than argumentative, and definitely not polemic. I shall explore three notions in possible worlds theory, i.e. the pragmatic turn, modal operators and transworld identity to tentatively attempt to facilitate a discussion between the two fields of study. The first important move in this regard, taking its lead from modal logic, is the shift from a correspondence theory of reference to a pragmatic theory of reference. Possible worlds theory has resulted in the fact that fiction has come to be regarded as a pragmatic concept and is defined pragmatically. In the pragmatic view of fiction, fiction is located in a social communication situation where fiction is a convention of communication. This convention is indicated by modal operators. Such operators subsume the text. Cross-world identity relates to the way in which one identifies the same individual across world boundaries. The article questions the validity of determining the truth of ancient religious texts on the basis of the tenets of modern logic only. It poses the question whether one does not have to reckon with the pragmatics, the modality and the complexity entailed in the notion of reference too.

Modal operators with adaptable semantics for multi-agent systems

Abstract: We look at extensions of modal logic for representation and reasoning in the area of multi-agent systems. Building on dynamic logic and Henkin quantifiers, we study an unusual type of operators that present important features for capturing concurrency, independence, collaboration, and coordination between agents. The main goal of this paper is to study the semantics of these operators and to show how it can be adapted to capture different types of agents. The formalism allows a formal comparison of a variety of multi-agent systems.

Commonly Knowingly Whether

Abstract: This paper introduces `commonly knowing whether', a non-standard version of classical common knowledge which is defined on the basis of `knowing whether', instead of classical `knowing that'. After giving five possible definitions of this concept, we explore the logical relations among them both in the multi-agent case and in the single-agent case. We focus on one definition and treat it as a modal operator. It is found that the expressivity of this operator is incomparable with the classical common knowledge operator. Moreover, some special properties of it over binary-tree models and KD45-models are investigated.