Friday, August 10
Saturday, August 11
Title: Coalgebraic Logics: A Computer Science Perspective
Abstract: In this talk I will give an introduction to coalgebraic logics from a computer science perspective and discuss both genericity and modularity for coalgebraic logics. Lazyness being one of the prime qualifications of a computer scientist, one likes to develop algorithms and proofs that apply uniformly to a wide variety of different logics. This results, in an application context, in software tools that are easier to develop and to maintain. Modularity, on the other hand, allows us to infer properties and to synthesize algorithms for combined systems from a small number of basic building blocks. This would ideally pave the way for larger-scale applications. In the second part of the talk I want to take the opportunity to present and discuss some open problems in the area and outline some research directions.
Title: Coalgebra and Modal Logic: Notes from a Research Program
Abstract: Different researchers come at one and the same subject from many points of motivation. In my case, I followed a trail to coalgbraic versions of modal logic which began from work on circularity and non-wellfounded sets. I have never had the chance to present the 'big picture' here, and so this is what I want to do in this talk. I also want to explore two of the pleasant 'small details' of the picture: one is a detour into probabilistic modal logic, a detour related to ongoing work. A second is an approach to the weak completeness of modal logics that comes from coalgebraic ideas.
Title: A dynamic distributive law
Title: Copower functors
Abstract: We unify and characterize various functors representing types of generalized labeled transition systems. In particular, we are interested in the case where the transition labels carry various algebraic structures and we relate their algebraic properties to corresponding functorial properties. We also plan to discuss the correponding coalgebraic logics.
Title: Definable Model Classes in Polynomial Coalgebraic Logic
Abstract: Standard ideas and results (definable model classes, canonical model construction) do not lift readily from propositional modal logic to the logic of T-coalgebras when a polynomial functor T has infinite constant components. This talk will discuss ways of overcoming this obstacle by introducing modified notions of ultraproduct and ultrafilter extension, and developing an infinitary proof theory for finite formulas.
Title: Coalgebraic Trace Theory
Abstract: This talk will give an overview of results on the coalgebraic approach to traces, as developed by Ichiro Hasuo, Ana Sokolova and the speaker. A basic ingredient is the existence of final coalgebras in Kleisli categories.
Title: Tutorial: A Mathematical Theory of Substitution and its Applications to Syntax and Semantics