Nissim Francez: CONTRASTIVE LOGIC (Revised Version of TR 668).
Abstract:
n this paper I introduce the notion of bilogics, namely logics interpreted over a pair of structures, in contrast to classical logic and many of its variations, the formulae of which are interpreted over one structure. In particular, I introduce and study Contrastive Logic, suitable for expressing contrast and conformity between the two structures involved. A major reason for this study is striving towards an extension of truth-conditional semantics to cover several natural-language particles, which have been hitherto considered not to be amenable to such an extensional treatment, and were delegated to the level of non- extensional pragmatics. Examples of such particles are but and already.
J. -J. Ch. Meyer and W. van der Hoek, 2005
Annals of Mathematics and Artificial Intelligence
Springer Netherlands
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.
But but us no buts, as they say.
