Fuzzy logic differs from conventional logical systems in that it aims at providing a model for approximate rather than precise reasoning.

Logics and languages

Local and fuzzy logics

Rules for assigning phrasal intonation to sentences are often assumed to require an autonomous level of "intonational structure", distinct from what is usually thought of as surface syntactic structure. The present paper argues that the requisite notion of structure can be subsumed under the generalised notion of surface structure that emerges from the combinatory extension of Categorial Grammar. According to this theory, the syntactic structures and the intonational structures of English are one, and can be captured in a single unified grammar. The interpretations that the grammar provides for such constituents correspond to the entities and open propositions that are concerned in certain discourse-related aspects of intonational meaning that have variously been described as "theme" and "rheme", "given" and "new", or "presupposition" and "focus". Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-90-45. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/571 Structure and Intonation MS-CIS-90-45 LINC LAB 174

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Structure and Intonation

This paper offers an explanation of the fact that sentences of the form (1) ‘X may A or B’ may be construed as implying (2) ‘X may A and X may B’, especially if they are used to grant permission. It is suggested that the effect arises because disjunctions are conjunctive lists of epistemic possibilities. Consequently, if the modal may is itself epistemic, (1) comes out as equivalent to (2), due to general laws of epistemic logic. On the other hand, on a deontic reading of may, (2) is only implied under exceptional circumstances – which usually obtain when (1) is used performatively.

Free Choice Disjunction and Epistemic Possibility

We review and re-examine possible-worlds semantics for propositional logics of knowledge and belief with four particular points of emphasis: (1) we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief, (2) we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system, (3) we discuss how notions of common knowledge and implicit knowledge among a group of agents fit into the possible-worlds framework, and (4) we consider to what extent the possible-worlds approach is a viable one for modelling knowledge and belief. As far as complexity is concerned, we show among other results that while the problem of deciding satisfiability of an S5 formula with one knower is NP-complete, the problem for many knowers is PSPACE-complete. Adding an implicit knowledge operator does not change the complexity substantially, but once a common knowledge operator is added to the language, the problem becomes complete for exponential time.

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A guide to the modal logics of knowledge and belief: preliminary draft

L'A. s'interesse dans cet article aux descriptions des usages des definis en anglais. Il analyse l'unicite associee a ces expressions comme etant a la fois conventionnelle, en ce qu'elle est une presupposition conventionnelle plus qu'une implicature conversationnelle, et pragmatique, en ce que la presupposition ne fait pas seulement allusion a l'unicite de la denotation du defini dans le monde, mais surtout a son statut unique au regard des informations apportees par les participants du discours. De plus, l'unicite mise en question, avec la presupposition de familiarite, est posee comme une propriete relative a la signification de tous les definis anglais, y compris les pronoms. Cependant, il existe des faits supplementaires dans l'interpretation des pronoms qui masquent cette singularite dans beaucoup de contextes.

Logics and languages

Citations

Local and fuzzy logics

Structure and Intonation

Free Choice Disjunction and Epistemic Possibility

A guide to the modal logics of knowledge and belief: preliminary draft

Uniqueness in Definite Noun Phrases

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