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A modal contrastive logic: The logic of ‘but’

A modal contrastive logic: The logic of ‘but’ In this paper we present a modal approach to “contrastive logic”, the logic of contrasts as these appear in natural language conjunctions such as ‘but’. We use a simple modal logic, which is an extension of the well-knownS5 logic, and base the contrastive operators proposed by Francez in [2] on the basic modalities that appear in this logic. We thus obtain a logic for contrastive operators that is more in accord with the tradition of intensional logic, and that, moreover — we argue — has some more natural properties. Particularly, attention is paid to nesting contrastive operators. We show that nestings of ‘but’ give quite natural results, and indicate how nestings of other contrastive operators can be done adequately. Finally, we discuss the example of the Hangman's Paradox and some similarities (and differences) with default reasoning. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

A modal contrastive logic: The logic of ‘but’

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References (27)

Publisher
Springer Journals
Copyright
Copyright
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/BF02127972
Publisher site
See Article on Publisher Site

Abstract

In this paper we present a modal approach to “contrastive logic”, the logic of contrasts as these appear in natural language conjunctions such as ‘but’. We use a simple modal logic, which is an extension of the well-knownS5 logic, and base the contrastive operators proposed by Francez in [2] on the basic modalities that appear in this logic. We thus obtain a logic for contrastive operators that is more in accord with the tradition of intensional logic, and that, moreover — we argue — has some more natural properties. Particularly, attention is paid to nesting contrastive operators. We show that nestings of ‘but’ give quite natural results, and indicate how nestings of other contrastive operators can be done adequately. Finally, we discuss the example of the Hangman's Paradox and some similarities (and differences) with default reasoning.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Aug 13, 2005

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