Logic of Awareness in Agent's Reasoning
Yudai Kubono, Teeradaj Racharak, Satoshi Tojo
TL;DR
Awareness Logic with Partition (ALP) addresses logical omniscience by tying agent awareness to indistinguishable possible worlds via an equivalence relation $\equiv^i_j$, and by composing this with each agent's accessibility $R_j$ into $(R_j \circ \equiv^i_j)^+$. The paper presents a formal syntax with operators $A^i_j$, $L_j$, $[\equiv]^i_j$, $C^i_j$, and $K^i_j$, a Kripke-style semantics incorporating both awareness sets and indistinguishability relations, and a complete Hilbert-style axiom system for ALP. It demonstrates the framework on a running example (convenience-store expansion) where conventional reasoning misrepresents what agents can deduce about others' knowledge, illustrating the necessity of world-distinction via awareness. Epistemic actions are introduced with dynamic operators $[+\\varphi]^i_j$ and $[-\\varphi]^i_j$ to model updates in awareness, setting the stage for richer action-model integration and future work on common knowledge. Overall, ALP provides a rigorous foundation for formalizing practical agent communication and reasoning under awareness in multi-agent settings, with clear implications for game-theoretic analysis and rational behavior under incomplete awareness.
Abstract
The aim of this study is to formally express awareness for modeling practical agent communication. The notion of awareness has been proposed as a set of propositions for each agent, to which he/she pays attention, and has contributed to avoiding \textit{logical omniscience}. However, when an agent guesses another agent's knowledge states, what matters are not propositions but are accessible possible worlds. Therefore, we introduce a partition of possible worlds connected to awareness, that is an equivalence relation, to denote \textit{indistinguishable} worlds. Our logic is called Awareness Logic with Partition ($\mathcal{ALP}$). In this paper, we first show a running example to illustrate a practical social game. Thereafter, we introduce syntax and Kripke semantics of the logic and prove its completeness. Finally, we outline an idea to incorporate some epistemic actions with dynamic operators that change the state of awareness.