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
$ \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.