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.

Reasoning About Space: The Modal Way

Abstract: We investigate the topological interpretation of modal logic in modern terms, using a new notion of bisimulation. We look at modal logics with interesting topological content, presenting, among others, a new proof of McKinsey and Tarski’s theorem on completeness of S4 with respect to the real line, and a completeness proof for the logic of finite unions of convex sets of reals. We conclude with a broader picture of extended modal languages of space, for which the main logical questions are still wide open.

Models for normal intuitionistic modal logics

Abstract: Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. This paper lays the ground for an investigation of intuitionistic analogues of systems stronger thanK. A brief survey is given of the existing literature on intuitionistic modal logic.

A representationalist theory of intention

Abstract: ions are relations between propositions, in which one is more abstract or general than another, let a be making a spaghetti-marinara dinner, and b be making a spaghetti dinner. In every possible world it is the case that a D b, so an intention to do a necessarily implies an intention to do b, if they are treated as normal modal operators. Normal modal operators are never abstraction free, but as we argue in the next section, intention must be. Another property of normal modal operators is that they are transparent to conjunction: L(a A b) =_ La A Lb. This means an intention to achieve a conjoined goal is 1Cohen and Levesque [9], in adopting the realism thesis, rely on claims about way an agent may change his beliefs about the connection between an intended proposition and its consequences to make their theory side-effect free. In their case, an agent who always believes that a D b is always true will incur the side-effect problem when intending a. Also, their theory will not be abstraction free or conjunction free: see below.

The Acquisition of Modality: Implications for Theories of Semantic Representation

Abstract: The set of English modal verbs is widely recognized to communicate two broad clusters of meanings: epistemic and root modal meanings A number of researchers have claimed that root meanings are acquired earlier than epistemic ones; this claim has subsequently been employed in the linguistics literature as an argument for the position that English modal verbs are polysemous (Sweetser, 1990) In this paper I offer an alternative explanation for the later emergence of epistemic interpret- ations by linking them to the development of the child's theory of mind (Wellman, 1990); if correct, this hypothesis might have important implications for the shape of the semantics of modal verbs It is widely acknowledged in the linguistic literature that modal expressions may be used to communicate at least two broad clusters of meanings: epis- temic modal meanings, which deal with the degree of speaker commitment to the truth of the proposition that forms the complement of the modal, and deontic modal meanings, concerned with the necessity or possibility of acts performed by morally responsible agents, eg obligation and permission (Lyons, 1977; Kratzer, 1981; Coates, 1983; Palmer, 1986, 1990; Sweetser, 1990; Bybee and Fleischman, 1995) The utterances in (1) and (2) (on their preferred interpretations) are examples of epistemic and deontic modality respectively:

First steps in synthetic guarded domain theory: step-indexing in the topos of trees

Abstract: We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms, predicates, and types. In particular, we show how to solve recursive type equations involving dependent types. We propose that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higher-order store and recursive types entirely inside the internal logic of S. Moreover, we give an axiomatic categorical treatment of models of synthetic guarded domain theory and prove that, for any complete Heyting algebra A with a well-founded basis, the topos of sheaves over A forms a model of synthetic guarded domain theory, generalizing the results for S.