Title: Coalgebre, automi e linguaggi nominali ecc

Lecturer: Bartek Klin

Period: Monday June 27, 11:00-13:00; Tuesday June 28, 10:00-13:00; Thursday June 30, 10:00-13:00; Thursday June 30, 16:00-18:00 - always in Aula Seminari Ovest

Title: A bialgebraic approach to Structural Operational Semantics

Structural Operational Semantics (SOS) is a simple but powerful formalism for defining transition systems of various kinds, and operations on them. SOS specifications are usually presented as families of inference rules. This presentation is simple and intuitive, but a bit ad-hoc and difficult to generalize. Bialgebras and distributive laws are more abstract and more mathematical notion of well-behaved SOS specification, based on coalgebra as an abstract theory of transition systems.

I will present the basics of the bialgebraic approach to SOS, and a coalgebraic approach to modal logics that can be used to define properties of transition systems. I will then show how to combine both approaches to derive logical distributive laws, a general theory of logical compositionality on SOS-defined systems.

The course will use some basic notions of category theory: categories, functors, natural transformations, and a little bit of monads. I will introduce these notions as needed.

The plan of the course is as follows:

- Classical SOS theory: labeled transition systems, bisimulations, Hennessy-Milner logic, SOS rules, GSOS and other formats
- Basics of category theory and coalgebra
- Coalgebraic modal logic by dual adjunctions
- Distributive laws, bialgebras, abstract GSOS
- Logical distributive laws