Logic of Conditional Beliefs

Abstract

In this paper I present a simple logic for conditional beliefs in a multi-agent doxastic context (CDL). Conditional beliefs Bi((/() encode beliefs in ( we would have if we were to learn new information (. The account of this notion is close to the classical theory of belief revision (AGM) and the standard conditional logic, as developed by Stalnaker and Lewis. I give both semantic and axiomatic characterization of conditional beliefs. They are interpreted in terms of plausibility or preference ordering on worlds. I also investigate the relation between notions of belief and knowledge. The logic may be used, for example, for epistemic analysis of some extensive form games.