1040 Wien, Seminarraum “Gödel”, Favoritenstr. 9

Joint Lecture of the Kurt Goedel Society and the Wolfgang Pauli Institute (WPI) Vienna

Abstract: By adding one unary connective to propositional logic, a modality, mysterious connections are formed. The logic becomes a decidable fragment of first order logic, whose semantics correspond to topological frames. Modalities have formalized a variety of concepts such as belief, time, and provability. The epistemic applications, especially recent trends of reasoning about information update, are mostly based on classical settings and their computations use the full power of negation.

Questions arise. Theoretically: can modal epistemic computations become constructive? On the foundational side: can dual modalities be defined in a positive setting? In practice: can positive modalities still model useful concepts?

I will show that by using methods from algebraic and categorical logic, pairs of positive adjoint modalities can be defined. These come equipped with simple unfolding rules and can interpret dynamic and epistemic concepts. I will show how they are applied to reason about information flow in a wide range of scenarios, from our daily lives when we learn from communication, to artificial intelligence for location detection in robot navigation.