On WEDNESDAY, February 26, we will have a LIRa session with Giovanni Cinà.
Everyone is cordially invited!
Speaker: Giovanni Cinà (University of Amsterdam)
Title: Modal Logics for Presheaf Categories
Date and Time: Wednesday, February 26, 2014, 16:30-18:00
Venue: Science Park 107, Room F1.15
In this talk we will outline some work in progress in the area at the interface of Modal Logic and Category Theory. We will focus on presheaf categories and on a construction called the category of elements. Such construction can be applied in two distinct ways, depending on how we want to conceptualize the base category.
If the objects of the base category are regarded as path objects (that is, computational-path shapes) then we follow the steps of Winskel, Nielsen and others, who investigated the characterization of the notion of bisimulation in terms of spans of open maps. In this context we are naturally inclined to introduce a “path logic”, a logic that described how paths are interlinked. Together with Sebastian Enqvist we are looking into correspondence results for this modal formalism.
If the objects of the base category are seen as types then it makes sense to perform a different variant of the category of elements. We can then show that, via such construction, each presheaf category is categorically equivalent to a special kind of transition systems (or rather, to the corresponding category). This prompts the quest for a logic that axiomatizes such class of transition systems. We propose a sound proof system and offer some remarks on the completeness proof.