NICHOLAS ASHER BELIEF IN DISCOURSE REPRESENTATION THEORY* 1. INTRODUCTION What we believe shapes our world, our language and ourselves. Accordingly, philosophers have had an abiding interest in belief. This interest, however, has not led to a satisfactory semantics for belief reports. Philosophers and linguists have traditionally analyzed the truth conditions of a belief report to involve three components, the subject or believer, a proposition (that which the believer believes) and a relation (the relation of believing that obtains between the sub- ject and the proposition). Various formalizations of this analysis have produced well-developed theories of rational belief (Hintikka, 1962; Montague, 1970) but these theories fail to provide either correct truth conditions for ordinary belief reports or a theory of “ordinary” belief. The chief difficulty, at least for the more sophisticated treat- ment of Montague’s, was that his theory incorrectly predicted that belief contexts were closed under substitution of logically equivalent expressions (LE). Ordinary belief contexts notoriously resist closure under most logically valid inferences.‘** Attempts at improving Montague’s treatment to block (LE), however, have often met with logical difficulties.3 Adding to this unhappy state of affairs, the study of the behaviour of singular terms, in particular the failure of the sub- stitution of coreferential directly referential expressions (SC), within belief reports has revealed a whole cluster of problems with which most proposed semantics have considerable difficulty (Quine, 1976; Mates, 1952; Kripke, 1979; Van Fraassen, 1978; Reddam, 1982; Kvart, 1983; Cresswell, 1983). I hope here to make some headway on the seemingly intractable problems with the semantics for belief reports. I will focus on provid- ing solutions to some of the well-known puzzle involving singular terms and belief contexts within a novel framework that blocks (LE). These puzzles show forcefully that the theory of belief requires a Journal of Philosophical Logic 15 (1986) 127- 189. 0 1986 by D. Reidel Publishing Company.