Cool Logic

Sumit Sourabh (ILLC)

Duality Theory in Logic

December 14th at 17:30, in Science Park D1.113

Duality theory in general, is the study of the back and forth mappings between different classes of mathematical objects. Duality helps in developing better insights and gaining new perspectives about these objects. In logic, dualities play an important role, since they have been used for relating syntactic and semantic approaches.

In this talk, I'll give a basic introduction to duality theory, in the setting of classical propositional logic and modal logic. Using duality and the algebraic semantics for modal logic, one can have a better understanding of a number a concepts in modal logic. I'll use Correspondence theory as a specific example, to illustrate my claim.

Finally, I'll mention a few applications of Duality theory outside logic, in Automata theory and Formal languages. The presentation does not assume any prior knowledge about algebra, topology or category theory and will be accessible to everyone.