A type theoretic approach to information state update in issue based dialogue management

Although Barwise came from the model theoretic tradition in logic he was sceptical of the kind of model theoretic analysis of natural language that Montague proposed based on the notion of natural languages as sets of model theoretically interpreted sentences, i.e. as formal languages. Instead Barwise sought to build a mathematical approach to language which incorporated an Austinian view of language as speech events relating to small parts of the world (situations). The classic book in situation semantics (Barwise and Perry, 1983) was thought provoking and ground breaking although it did not give a mathematically precise theory of the kind of compositional semantics that Montague had proposed. It also suffered in many parts of the linguistic community because it was trying to address questions about communication rather than a theory of meaning in the classical Montagovian sense. Barwise was interested in characterising the information which an agent can extract from an utterance event rather than the meaning of an expression. This did not sit easily with the linguistic tradition based on the formal language approach which followed Montague. Such questions of communication and information (rather than meaning) do, however, arise when we try to create theories relating to what is known as dialogue management in computational dialogue systems. In this paper we try to show how a formal theory of dialogue management could be approached by using type theory as a tool to characterise a kind of dialogue management (issue-based dialogue management) developed by Larsson (2002) using the information state update approach and based on Ginzburg’s (1996a,b) work on “questions under discussion” which was carried out in a situation semantic framework. The exercise leads us to some conclusions about the possibility of unifying the formal language approach with the Austinian approach that Barwise advocated.