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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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Proceedings Article
01 Jan 2007
TL;DR: The original contribution of this paper is an Autoepistemic Many-valued Logic with intuitionistic implication, epistemic negation and Moore's modal operator: the inference reasoning of this logic is able to change its belief in the truth value of ground facts which come from external sources, and to preserve its internal consistency.
Abstract: It is well known that the standard 3-valued logic programs with constraints can be inconsistent. Because of that we can not use it for a data integration where mutually inconsistent information comes from different data sources. We argue that a natural way to answer to this challenge, without collapsing all sentences into inconsistency, is by passing to 4-valued bilattice-based logic (with logic values: true, false, unknown and possible), and by interpreting the inconsistent information with a logic value ”possible”. Differently from the paraconsistent approach we adopt the belief-revision approach, but in such many-valued repairing of inconsistent information we do not eliminate mutually inconsistent information as in the case of a 2-valued database repairing. The original contribution of this paper is an Autoepistemic Many-valued Logic with intuitionistic implication, epistemic negation and Moore’s modal operator: the inference reasoning of this logic is able to change its belief in the truth value of ground facts which come from external sources, and to preserve its internal consistency. We show that each Autoepistemic Logic Program is consistent and we define its minimal many-valued Herbrand models.

1 citations

Journal Article
TL;DR: This paper analyzes the conditional logic approach to default logic, the logic that formalizes reasoning about default assumptions, and discusses different usages of preference orderings for defeasible conditional logics.
Abstract: In this paper we analyze the conditional logic approach to default logic, the logic that formalizes reasoning about default assumptions. Conditional logic is a popular framework to formalize defeasible reasoning. The conditional sentence if β (the antecedent or condition) then by default α (the consequent or conclusion) is represented in this framework by the formula β > α, where '>' is some kind of implication of conditional logic. In this paper different usages of preference orderings for defeasible conditional logics are discussed. The different usages, so-called minimizing and ordering, are represented by different modal operators. Each operator validates different inference rules. Hence, the combination of different modal operators imposes restrictions on the proof theory of the logic. The restriction discussed in this paper is that a proof rule can be blocked in a derivation due to the fact that another proof rule has already been used earlier in the derivation. We call this the two-phase approach in the proof theory.

1 citations

Proceedings ArticleDOI
01 Aug 2020
TL;DR: A new direction of tow modifications of the two standard modal operators "necessity" and "possibility" is discussed and four new operators are introduced and studied.
Abstract: Ever since the first publication over intuitionistic fuzzinsess, the two standard modal operators "necessity" ( □ ) and "possibility" (◊) are introduced over intuitionistic fuzzy sets. In the years, these two operators are object of a lot of extensions and modifications. In the present paper, a new direction of tow modifications of the two standard modal operators is discussed. We introduce four new operators and study their properties.

1 citations

Dissertation
15 May 2007
TL;DR: In this article, soundness and completeness theory and correspondence theory of normal and non-normal modal logics are presented, and the second part is devoted to investigation of distribution of the modal operator over disjunction.
Abstract: This master's thesis consists of two parts. First part is a survey of basic concepts in modal logics. Syntax and semantics for normal and non-normal modal logics are presented. Then soundness and completeness theory and correspondence theory of normal modal logic are presented. The second part is devoted to investigation of distribution of the modal operator over disjunction, i.e.

1 citations

Book ChapterDOI
01 Jan 2008
TL;DR: In this paper, Suhrawardi's modal syllogistic in the Philosophy of Illumination looks to be quite different from Avicenna's, and it can be seen as a kind of peripatetic philosophy which he attacks and reformulates.
Abstract: On first encounter, Suhrawardī's modal syllogistic in the Philosophy of Illumination looks to be quite different from Avicenna's. Closer inspection, however, reveals that Suhrawardī's system is deeply Avicennan, more so than, for example, the system in Najm al-Dīn al-Kātibī's Shamsiyya . This chapter examines what Suhrawardī achieves by reading all modal propositions as embedded in the phrase 'by necessity', what help it can offer the historian of Arabic logic, and what it means for assessing Suhrawardī's larger philosophical project. Scholars who have looked at Suhrawardī's treatment of modal syllogisms to date have tended to take it to be one of the areas of Peripatetic philosophy which he attacks and reformulates. To model Avicenna's modal propositions, we need to use what in modern logic are presented as different kinds of modal operators: a de dicto operator in which the proposition is embedded, and a de re operator which modifies the predicate. Keywords: Avicenna's modal propositions; modal syllogisms; Najm al-Dīn al-Kātibī's Shamsiyya ; Philosophy of Illumination ; Suhrawardī's system

1 citations


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