The temporal logic of coalitional goal assignments in concurrent multi-player games

Valentin Goranko

Stockholm University




Abstract: I will present the recently introduced Temporal Logic of Coalitional Goal Assignments (TLCGA), which is a natural extension of the Alternating time temporal logic ATL. TLCGA features just one, but quite expressive, coalitional strategic operator, called “coalitional goal assignment operator”. It is based on a mapping assigning to each set (coalition) of players in the game its coalitional goal, formalised by a path formula of the language of TLCGA representing a temporalised objective for the respective coalition describing the property of the plays on which that objective is satisfied.

I will illustrate the use of the logic TLCGA with some examples. In particular, I will introduce the new solution concept of “co-equilibrium”, which is particularly suitable for multi-player games with qualitative coalitional objectives, and will show that it can be naturally expressed in TLCGA.

Time permitting, I will then briefly outline our main technical results for that logic, including: fixpoint characterizations of the temporal goal assignment operators in a mu-calculus extension of TLCGA, bisimulation invariance and Hennessy-Milner property with respect to a suitably defined notion of bisimulation; a sound and complete axiomatic system, and decidability of satisfiability via finite model property.

The talk will be relatively self-contained, though it will assume some general background on temporal logics in computer science.

The talk is based on the following paper:

Sebastian Enqvist and Valentin Goranko,
The temporal logic of coalitional goal assignments in concurrent multi-player games.
ACM Transactions of Computational Logic, Vol. 23, No. 4, Article 21, 2022.
Available from: https://link.springer.com/article/10.1007/s10458-021-09531-9