Presuppositions in Spoken Discourse

Chapter 2
updated context is subtracted from the original context. In this example, we first
update c to obtain all worlds where Julia does have a bicycle and then we subtract
this context from the original c. The result is all worlds where Julia does not have a
bicycle.
If a presupposition is not defined in the context then trying to update will
result in undefinedness. But fortunately the satisfaction theory has a way to get
around this by using some additional rules that allow for presupposition
accommodation. Let’s pretend we need to update an empty context with the
following sentence:
(56) Julia’s bicycle is red.
We start with an empty context c. The sentence we want to update with contains
the information contributed by the definite NP Julia’s bicycle and this presupposes
that Julia has a bicycle, p. So updating c become c+[S{p}]. First we have to test if
the presupposition is satisfied in the context. Because the context is empty the
answer must be no; c still contains worlds where Julia doesn’t have a bicycle. But
we can pretend that the context already included the presupposed information by
revising the context c to a context that satisfies the presupposition by taking on
those worlds where Julia has a bicycle, a revised context we can call c’. Then we
update with S using c’+[S{p}] rather than c. The presupposition is satisfied in the
revised context and the sentence can be processed without any problems.
Accommodation is less straightforward in the satisfaction theory when
dealing with presuppositions triggered under embeddings. If we take an example
where a presupposition is triggered under negation, we can illustrate both local and
global accommodation. Look at the following example:
(57) S: Julia’s bicycle is not red.
We start with a new context c and then we analyze the sentence S. S induces the
presupposition p that Julia has a bicycle. Because we have an empty context we
know that the context we are dealing with contains not only the worlds where the
presupposition is true, but also where it is false (e.g. because an empty context
contains all possible worlds, it contains worlds where the presupposition is both
true as well as those where the presupposition doesn’t hold). We want to evaluate
our sentence only in those worlds where the presupposition holds so we have to
first remove the worlds where the presupposition is not true. Note that according
to the rules of embedding given above the update of the context c+[ ¬S{p}] = c –
(c+[ S{p}]) = c’. We can accommodate the presupposition globally or locally.
Global accommodation of the presupposition in c – (c+[ S{p}]) amounts to
revising both contexts, in effect c+p – (c+p+[S{p}]). Thus, contextual update
with S is then performed only on the set of worlds where the presupposition is
satisfied. In our example this would amount to first taking only the worlds where
Julia has a bicycle, and then updating with the information that the bicycle is not
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