A MODAL CONTRASTIVE LOGIC - THE LOGIC OF BUT

In this paper we present a modal approach to ''contrastive logic'', th e logic of contrasts as these appear in natural language conjunctions such as 'but'. We use a simple modal logic, which is an extension of t he well-known S5 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 w ith 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 qui te natural results, and indicate how nestings of other contrastive ope rators can be done adequately. Finally we discuss the example of the H angman's Paradox and some similarities (and differences) with default reasoning.