Syntactic Knowledge: A Logic of Reasoning, Communication and Cooperation
Thomas Ågotnes, Michał Walicki · 2004
This paper presents a logic for reasoning about the explicit knowledge of agents who represent their knowledge as finite sets of logical formulae, and who can change their knowledge by reasoning and communicating. No assumptions about closure or consistency conditions on the sets, or about soundness or completeness of the reasoning mechanisms, are made. Traditional epistemic logic, based on modal logic, is not a good model for the explicit knowledge of such agents, among other things because of the logical omniscience problem. We are interested in agents who can make different choices about how to reason and communicate, and in reasoning about how the agents can use communication to achieve common goals. To this end, our logic is partly based on Alternating-time Temporal Logic. The resulting logic allows the expression of properties about an agent’s reasoning mechanism on the form “the agent knows modus ponens (MP)” – meaning that the agent’s reasoning mechanism can perform the reasoning steps described by MP. Instead of a common closure condition such as “if the agent knows both p and p→ q, then he must also know q”, the following holds in our logic: “if the agent knows p, p → q and MP, then he has a strategy to get to know q in the future”.