Agent-Knowledge Logic for Alternative Epistemic Logic

Epistemic logic is known as a logic that captures the knowledge and beliefs of agents and has undergone various developments since Hintikka (1962). In this paper, we propose a new logic called agent-knowledge logic by taking the product of individual knowledge structures and the set of relationships among agents. This logic is based on the Facebook logic proposed by Seligman et al. (2011) and the Logic of Hide and Seek Game proposed by Li et al. (2021). We show two main results; one is that this logic can embed the standard epistemic logic, and the other is that there is a proof system of tableau calculus that works in finite time. We also discuss various sentences and inferences that this logic can express.