A Logic for Conditional Local Strategic Reasoning

TL;DR

This paper introduces ConStR, a logic extending Coalition Logic with conditional strategic reasoning operators, formalizing how agents and observers predict others' actions based on objectives in multi-agent systems.

Contribution

It formalizes conditional strategic reasoning in multi-agent systems by extending Coalition Logic with new modal operators, providing semantics, bisimulation invariance, and axiomatic systems.

Findings

Introduces ConStR with three new modal operators

Provides formal semantics and bisimulation invariance proofs

Develops axiomatic systems for the logic

Abstract

We consider systems of rational agents who act and interact in pursuit of their individual and collective objectives. We study and formalise the reasoning of an agent, or of an external observer, about the expected choices of action of the other agents based on their objectives, in order to assess the reasoner's ability, or expectation, to achieve their own objective. To formalize such reasoning we extend Pauly's Coalition Logic with three new modal operators of conditional strategic reasoning, thus introducing the Logic for Local Conditional Strategic Reasoning ConStR. We provide formal semantics for the new conditional strategic operators in concurrent game models, introduce the matching notion of bisimulation for each of them, prove bisimulation invariance and Hennessy-Milner property for each of them, and discuss and compare briefly their expressiveness. Finally, we also propose systems of axioms for each of the basic operators of ConStR and for the full logic.