Logics for Moderate Belief-Disagreement Between Agents

Abstract

A moderate belief-disagreement between agents on proposition p means that one agent believes p and the other agent does not. This paper presents two logical systems, $\mathbf {MD}$ and $\mathbf {MD}^D$, that describe moderate belief-disagreement, and shows, using possible worlds semantics, that $\mathbf {MD}$ is sound and complete with respect to arbitrary frames, and $\mathbf {MD}^D$ is sound and complete with respect to serial frames. Syntactically, the logics are monomodal, but two doxastic accessibility relations are involved in their semantics. The notion of moderate belief-disagreement, which is in accordance with the understanding of belief-disagreement in everyday life, is an epistemic one related to multiagent situations, and $\mathbf {MD}$ and $\mathbf {MD}^D$ are two epistemic logics.