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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.


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Journal ArticleDOI
TL;DR: A new approach to the modal operators of necessity and possibility is introduced, based on the existence of two negations in certain lattices that the authors call bi-Heyting algebras, by iterating certain combinations of these negations and going to the limit.
Abstract: The aim of this paper is to introduce a new approach to the modal operators of necessity and possibility. This approach is based on the existence of two negations in certain lattices that we call bi-Heyting algebras. Modal operators are obtained by iterating certain combinations of these negations and going to the limit. Examples of these operators are given by means of graphs.

70 citations

BookDOI
01 Jan 2003
TL;DR: It is argued that policy-based intentions exhibit non-monotonic behaviour which could be captured through a non-Monotonic system like defeasible logic, which alleviates most of the problems related to logical omniscience.
Abstract: Most of the theories on formalising intention interpret it as a unary modal operator in Kripkean semantics, which gives it a monotonic look. We argue that policy-based intentions(Bratman 1990) exhibit non-monotonic behaviour which could be captured through a non-monotonic system like defeasible logic. To this end we outline a defeasible logic of intention. The proposed technique alleviates most of the problems related to logical omniscience. The proof theory given shows how our approach helps in the maintenance of intention-consistency in agent systems like BDI.

70 citations

Book ChapterDOI
22 Jan 2012
TL;DR: This paper proposes a natural integration of information flow properties into linear-time temporal logics (LTL), adding a new modal operator, the hide operator, expressing that the observable behavior of a system is independent of the valuations of a secret variable.
Abstract: Most analysis methods for information flow properties do not consider temporal restrictions. In practice, however, such properties rarely occur statically, but have to consider constraints such as when and under which conditions a variable has to be kept secret. In this paper, we propose a natural integration of information flow properties into linear-time temporal logics (LTL). We add a new modal operator, the hide operator, expressing that the observable behavior of a system is independent of the valuations of a secret variable. We provide a complexity analysis for the model checking problem of the resulting logic SecLTL and we identify an expressive fragment for which this question is efficiently decidable. We also show that the path based nature of the hide operator allows for seamless integration into branching time logics.

70 citations

Book ChapterDOI
06 Jul 2010
TL;DR: AABB properly extends interesting interval temporal logics recently investigated in the literature, such as the logic BB of Allen's "begun by/begins" relations and propositional neighborhood logic AA, in its many variants (including metric ones).
Abstract: In this paper, we focus our attention on the fragment of Halpern and Shoham's modal logic of intervals (HS) that features four modal operators corresponding to the relations "meets", "met by", "begun by", and "begins" of Allen's interval algebra (AABB logic). AABB properly extends interesting interval temporal logics recently investigated in the literature, such as the logic BB of Allen's "begun by/begins" relations and propositional neighborhood logic AA, in its many variants (including metric ones). We prove that the satisfiability problem for AABB, interpreted over finite linear orders, is decidable, but not primitive recursive (as a matter of fact, AABB turns out to be maximal with respect to decidability). Then, we show that it becomes undecidable when AABB is interpreted over classes of linear orders that contains at least one linear order with an infinitely ascending sequence, thus including the natural time flows N, Z, Q, and R.

70 citations

Journal ArticleDOI
TL;DR: In this article, the epistemic modals possible, probable, likely, and certain require a semantics which explains their behavior both as modal operators and as gradable adjectives, and an analysis of these items in terms of Kennedy & McNally's theory of gradability suggests that they are associated with a single, fully closed scale of possibility.
Abstract: The epistemic modals possible, probable, likely, and certain require a semantics which explains their behavior both as modal operators and as gradable adjectives. An analysis of these items in terms of Kennedy & McNally's theory of gradability suggests that they are associated with a single, fully closed scale of possibility. An implementation using the standard theory of modality due to Kratzer is shown to make incorrect predictions in several domains. However, if the scale of possibility is identified with standard numerical probability, the facts about gradability are explained and the undesirable predictions of Kratzer's theory are avoided.

69 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202222
202138
202035
201946
201844