9.30: Sam van Gool, Model-completeness and automata
10.30 — 11.00: Coffee break
11.00: Samson Abramsky,
Relating Structure to Power:
back and forth between finite model theory and categorical semantics
12.00 — 14.00: Lunch
14.00: Paul-André Melliès, Template games: a bicategorical and interactive interpretation of linear logic (abstract)
ABSTRACT: Game semantics is the art of interpreting formulas (types) as games and proofs (programs) as strategies interacting in space and time with their environment. In order to reflect the interactive behaviour of programs, strategies are required to follow specific scheduling policies. Typically, in the case of a purely sequential programming language, the program (Player) and its environment (Opponent) play one after the other, in a strictly alternating way. In the case of a concurrent language, on the other hand, Player and Opponent are allowed to play several moves in a row, in a non alternating way. In the two cases, the scheduling policy is designed very carefully in order to ensure that the strategies synchronise properly and compose well when plugged together. A longstanding conceptual problem has been to understand when and why a given scheduling policy works and is compositional in that sense. In this talk, I will introduce the notion of template game and exhibit a number of simple and fundamental combinatorial properties which ensure that a given scheduling policy defines a monoidal closed bicategory of games, strategies and simulations. The notion of template game will be illustrated by constructing two game models of linear logic with different flavors (alternating and non alternating) using the same categorical combinatorics, performed in the category of small categories.
15.00 — 15.30: Coffee break
15.30:
Célia Borlido, Stone duality and the Substitution Principle