## Patterns of modal interaction in discourse

Kees Vermeulen (Utrecht University)

I will report on ongoing investigations of modal interaction in
discourse.  For these investigations I have collected examples from
The Bank of English', a large corpus of contemporary English texts.
In the presentation I show some of the more interesting examples and
use them to illustrate the tools that I have developed for the
classification of modal interaction patterns. Then I will sketch a
logic that can describe the patterns that occur in the examples.

There are lots of well known examples of interaction between modal expressions in discourse. Standard examples are cases of modal subordination as in:

A lion might come in. It would eat you first. Then it could eat me (later).

Here we see a chain of modalised propositions. Each element of the chain is to be evaluated in the light of the previous elements of the chain. Hence a good approximation of the meaning of the example in a simple modal logic is:

$\Diamond (lion) \wedge (lion \rightarrow \Box (you)) \wedge (lion \wedge you \rightarrow \Diamond (me)).$

This form of chaining of modalities is known as modal subordination. Here we see a chain of length three, but shorter and longer chains are easy to come up with. Also other patterns of modal interaction are available, as in:

It may rain. Or there may be snow. Either way, we would get wet.

Here we see a summation of (disjoint) options: the sentence means something like:
$\Diamond (rain) \wedge \Diamond (snow) \wedge (rain \vee snow \rightarrow \Box (wet))$

These are made up' examples that do not tell us which patterns of interaction occur naturally. Therefore, I have formed a small corpus of 127 English texts with lots of modal expressions. The corpus was extracted from the `Bank of English', a large corpus of contemporary English texts used by Collins publishing house for the production of dictionaries, among others.

I am investigating this selection of texts and classifying them according to the patterns of interaction between the modalities. The patterns can be described by diagrams built up from a relative small number of basic patterns: case distinction, chaining (=subordination), summation.

This means that a logic for describing modal interaction that can handle these three basic types of interaction is a good tool for the analysis of the phenomenon. I will present such a logic and an update semantics for it.