Technical Report CS0668

Authors: N. Francez
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Abstract: In this paper I introduce the notion of {\em bilogics}, namely logics interpreted over a {\em pair} of structures, in contrast to classical logic and many of its variations, the formulae of which are interpreted over {\em one} structure. In particular, I introduce and study {\em Contrastive Logic}, suitable for expressing {\em contrast} and {\em conformity} between the two structures involved. A major reason for this study is striving towards an extension of {\em 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 {\bf but} and {\bf already}.
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