Information Flow and Impossible Situations

Classical semantic information (CSI) assigns the same body of semantic information (Cont) as well as the same amount of semantic information (cont or inf) to logically equivalent sentences. A corollary of this fact is that all logically true sentences will receive a null assignment of semantic information via Cont as well as a zero measure of semantic information via cont or inf. The originators of CSI allowed that there be (but did not develop) a sensible notion of psychological information (PI) whereby its measure on logically true sentences would be greater than zero. By extension they allowed that this notion of PI would be such that non-identical measures could be assigned to logically equivalent sentences in general. The task undertaken in the article is to specify the basis of a theory of PI that satisfies these constraints. This project utilizes the frame semantics of substructural logics. The threat of a perceived ad hoc association is countered by an independent argument for the explication of the incomplete and inconsistent worlds (impossible situations) constituting frame semantics in terms of confused doxastic states. Combined with existing interpretations of frame semantics in terms of information flow, the result is a specification of the basis of a novel theory of the information flow between the doxastic states of agents, i.e. the specification of the basis of a novel theory of PI. A substructural logic no stronger than the linear logic DMALL is proposed as providing the appropriate semantics. I am indebted to Luciano Floridi, Greg Restall, Antony Eagle, Joel Mason and especially Patrick Allo for saving me from myself on more than one occasion. I would also like to thank an anonymous referee at Logique et Analyse for making many insightful suggestions and for bringing several errors to my attention. Any that remain are entirely my responsibility. Faculty of Philosophy and IEG, Computing Laboratory, The University of Oxford, Great Britain. “03sequoiah” 2006/11/13 page 372 i i