Modal Frame Incompleteness: An Account through Second Order Logic (Mircea Dumitru)

The Logic and Metaphysics Workshop will meet on May 16th from 4:15-6:15 (NY time) via Zoom for a talk by Mircea Dumitru (Bucharest).

Title: Modal Frame Incompleteness: An Account through Second Order Logic

Abstract: Propositional modal logic is usually viewed as a generalization and extension of propositional classical logic. The main argument of this paper is that a good case can be made that modal logic should be construed as a restricted form of second order classical logic. The paper makes use of the embedding of modal logic in second order logic and henceforth it goes on examining one aspect of this second order connection having to do with an incompleteness phenomenon. The leading concept is that modal incompleteness is to be explained as a kind of exemplification of standard order incompleteness. Moreover the modal incompleteness phenomenon is essentially rooted in the weaker expressive power of the language of sentential modal logic as compared to the stronger expressive power of the language of second order logic.

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