Probability in a Logical Semantics of Discourse

Martijn van Otterlo (University of Twente)

While traditional logico-semantic systems used for the interpretation
and analysis of natural language were of a static nature, more modern
treatments are dynamic. Examples of dynamic systems are DPL, DRT and US.
In these dynamic logical systems, the interpretation of utterances is
taken as a function on information states. Other dynamic theories can be
found in areas of belief revision and probability theory. In the logical
systems, knowledge is taken as the main epistemic attitude towards
sentences, whereas in probability theory we have degrees of belief as
our main epistemic attitude. Actually, (probabilistic) degrees of belief
can be viewed as a generalization of the classic attitude knowledge.

In this talk I will present an extension of a particular model, that of 'Coreference and Modality' (by Groenendijk, Stokhof and Veltman (1996)), in which the classic attitudes of truth and falsity are replaced by probabilistic beliefs. I will present probabilistic belief states as a context for discourse interpretation, where discourses are represented in first-order modal logic. These belief states give semantics to probabilistic beliefs about world knowledge and discourse knowledge. Dynamic update rules are given for conditioning on information contained in the discourse. The main advantage of this step is that all facts p which are not certain (yet) can be given a rational degree of belief, instead of only being able to say that p 'might' be true. A more general result is that some insight is given in the connection between dynamic theories in the semantics of natural language and the dynamic theory of probability theory.