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.