# Tech Reports

## ULCS-04-016

### On the Logic of Co-operation and Propositional Control

Wiebe van der Hoek and Michael Wooldridge

### Abstract

Cooperation logics have recently begun to attract attention within the multi-agent systems community. Using a cooperation logic, it is possible to represent and reason about the strategic powers of agents and coalitions of agents in game-like multi-agent systems. These powers are generally assumed to be implicitly defined within the structure of the environment, and their origin is rarely discussed. In this paper, we study a cooperation logic in which agents are each assumed to control a set of propositional variables – the powers of agents and coalitions then derive from the allocation of propositions to agents. The basic modal constructs in this Coalition Logic of Propositional Control (CL-PC) allow us to express the fact that a group of agents can cooperate to bring about a certain state of affairs. After motivating and introducing CL-PC, we provide a complete axiom system for the logic, and prove that the model checking and satisfiability problems for CL-PC are both PSPACEcomplete. We then investigate the issue of characterising control in CL-PC with respect to the underlying power structures of the logic, and formally investigate the relationship between CL-PC and Pauly’s Coalition Logic. We conclude by discussing our results and how CL-PC sits in relation to other logics of cooperation.

[Full Paper]