The result of an interaction is influenced by its epistemic state, and several epistemic notions are related to multiagent situations. Strong belief-disagreement on a certain proposition between agents means that one agent believes the proposition and the other believes its negation. This paper presents a logical system describing strong belief-disagreement between agents and demonstrates its soundness and completeness. The notion of belief-disagreement as well as belief-agreement can facilitate gaining a clearer understanding of the acts of trade and speech.

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, \ and \, that describe moderate belief-disagreement, and shows, using possible worlds semantics, that \ is sound and complete with respect to arbitrary frames, and \ 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 \ and \ are two epistemic logics. (shrink)

When a person performs a certain action, it signifies that he is causing a certain event to occur. Therefore the action is conveying a certain true sentence. Playing a game is a mutual activity, namely the listener and the speaker undertake an exchange through a linguistic dialogue or communicate through action. Because of the peculiar nature of the action, the actions in games belong to an activity where the speaker speaks true words and the listener hears true words. A static (...) game is a process through which the participants are simultaneously speaking and listening ; and a dynamic game is a process where speaking and listening take place in turn. Each step of a dynamic game is a speaking-listening exchange. Through listening and speaking, changes in the epistemic states of the participants occur. Of course, the degree of change depends on the type of game being played. In a dynamic game, each participant proceeds through a process of induction, and thus forms new epistemic states. (shrink)