Dear all,
Giovanni Cinà will defend his PhD thesis
Categories for the working modal logician
on Friday, June 16th, 2017. The ceremony will start at 11:00 and last till 12:30 in the Aula of the Lutherse Kerk.
On the same day there will be a workshop associated to the defense. It will be titled Interweaving Modal Logic and Category Theory and will take place in the afternoon. More details will be announced later.
*Thesis abstract* We attempt to build a ladder connecting the heavens of Category Theory to the interests of modal logicians, in particular those concerned with modelling tasks and therefore involved with specific models and languages. The body of work presented in this theses witnesses two possible modes of interaction. The first is the study of hybrid models, namely structures that are on one hand significant from a category-theoretic perspective and on the other hand lend themselves to a treatment with modal languages. We show how presheaf models can be seen as particular relational structures and develop a hierarchy of modal languages to express their properties. To argue in favor of the flexibility of this framework we review several applications; we especially dive into the details of a modal logic for social choice functions. Furthermore, we highlight how in this setting some of the traditional issues of Modal Logic, e.g. completeness, expressivity and decidability, receive an original twist and can be resolved with alternative solutions. A second mode, more heuristic in nature, consists of regarding a given class of models as a category. The benefit of this stance is the baggage of questions that come with it. The right notion of morphism for these models, its closure under composition, the functoriality of some uniform constructions, these are some of the basic issues that get raised in this context. In the second half of the thesis we explicate how they can shape research in Modal Logic and how they are intertwined with existing problems.
Hope to see you there!
The LIRa team