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.

Some Connections between Topological and Modal Logic

Abstract: We study modal logics based on neighbourhood semantics using methods and theorems having their origin in topological model theory. We thus obtain general results concerning completeness of modal logics based on neighbourhood semantics as well as the relationship between neighbourhood and Kripke semantics. We also give a new proof for a known interpolation result of modal logic using an interpolation theorem of topological model theory.

Mixing modes of linguistic description in Categorial Grammar

Abstract: Recent work within the field of Categorial Grammar has seen the development of approaches that allow different modes of logical behaviour to be displayed within a single system, something corresponding to making available differing modes of linguistic description. Earlier attempts to achieve this goal have employed modal operators called structural modalities, whose use presents a number of problems. I propose an alternative approach, involving co-existence and interrelation of different sublogics, that eliminates the need for structural modalities, whilst maintaining the descriptive power they provide.

A proof system for temporal reasoning with sequential information

Abstract: A new logic, sequence-indexed linear-time temporal logic (SLTL), is obtained semantically from the standard linear-time temporal logic LTL by adding a sequence modal operator which represents a sequence of symbols. By the sequence modal operator of SLTL, we can appropriately express "sequential information" in temporal reasoning. A Gentzen-type sequent calculus for SLTL is introduced, and the completeness and cut-elimination theorems for this calculus are proved. SLTL is also shown to be PSPACE-complete and embeddable into LTL.

Modal logics of higher-order probability

Abstract: This paper discusses the relationship between probability and modal logic. We show that it is both natural and useful to think of probability as a modal operator. Contrary to popular belief in AI, a probability ranging between 0 and 1 represents a range between impossibility and necessity, not between simple falsity and truth. We examine two classes of probability models: flat and staged. The flat models are straightforward generalizations of models for alethic logic. We show that one of the more interesting constraints relating higher- and lower-order probabilities forces all higher-order probabilities in flat models to be either zero or one. We introduce staged models as a means of avoiding this problem. Constraints on the two types of models define various classes of probability logics. We relate some of these probability logics to alethic logic.

The Logic of Tune - A Proof-Theoretic Analysis of Intonation

Abstract: This paper presents a proof-theoretic sign-based grammar founded on non-associative non-commutative linear logic which models a compositional theory of the 'information packaging' meaning of intonational contours. Cross-language comparison reveals that in expressing information packaging, different languages exploit word order and prosody in different ways: one single informational construct can be realized by drastically different structural means across languages. Thus for languages such as English and Dutch it can be argued that, roughly speaking, information packaging is structurally realized by means of alternative intonational contours of identical strings, while languages such as Catalan and Turkish have a constant prosodic structure and realize information packaging by means of string order permutations. Such cross-linguistic generalizations suggest that information packaging involves syntax as well as prosody, so that any attempt to reduce informational aspects to either syntax (for Catalan or Turkish) or prosody (for English or Dutch) must be inadequate from a cross-linguistic point of view. The present paper proposes to treat the different structural realizations of information packaging by means of a both intonationally/syntactically and semantically/informationally interpreted sign-based version of the non-associative Lambek calculus, the 'pure logic of residuation'. The signs, the grammatical resources of this formalism, are formmeaning units which reflect the fact that the dimensions of form and meaning contribute to well-formedness in an essentially parallel way. The proof-theoretic categorial engine of the formalism represents phonological head/non-head dependencies in terms of a doubling of the pure logic of residuation which is enriched with unary modal operators, where the unary brackets that come with these operators function as demarcations of specific intonational domains.