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-known $5 Iogic, 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.
Based on the contrastive operators proposed by Francez, a modal approach to contrastive logic is presented in REF .Their contrastive logic is actually a simple modal logic which is an extension to the well-known S5 logic with Francez's contrastive operator.
A modal contrastive logic: The logic of ‘but’
Annals of Mathematics and Artificial Intelligence
Annals of Mathematics and Artificial Intelligence
Mathematics Computer Science