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.
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But but us no buts, as they say.
Also partially supported by Nijmegen University, Toernooiveld, 6525 ED Nijmegen, The Netherlands.
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Ch. Meyer, J.J., van der Hoek, W. A modal contrastive logic: The logic of ‘but’. Ann Math Artif Intell 17, 291–313 (1996). https://doi.org/10.1007/BF02127972
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DOI: https://doi.org/10.1007/BF02127972