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A Logical Theory of Joint Ability in the Situation Calculus

Logic-based formalizations of dynamical systems are central to the field of knowledge representation and reasoning. These formalizations can be used to model agents that act, reason, and perceive in a changing and incompletely known environment. A key aspect of reasoning about agents and their behaviors is the notion of joint ability. A team of agents is jointly able to achieve a goal if despite any incomplete knowledge or even false beliefs about the world or each other, they still know enough to be able to get to a goal state, should they choose to do so. A particularly challenging issue associated with joint ability is how team members can coordinate their actions. Existing approaches often require the agents to communicate to agree on a joint plan. In this thesis, we propose an account of joint ability that supports coordination among agents without requiring communication, and that allows for agents to have incomplete (or even false) beliefs about the world or the beliefs of other agents. We use ideas from game theory to address coordination among agents. We introduce the notion of a strategy for each agent which is basically a plan that the agent knows how to follow. Each agent compares her strategies and iteratively discards those that she believes are not good considering the strategies that the other agents have kept. Our account is developed in the situation calculus, a logical language suitable for representing and reasoning about action and change that is extended to support reasoning about multiple agents. Through several examples involving public, private, and sensing actions, we demonstrate how symbolic proof techniques allow us to reason about team ability despite incomplete specifications about the beliefs of agents.