the fragment behaves with respect to these sentences.
We'll start with an infostate containing two possibilities. In one
-possibility (w1), Alice is hungry; in the other (w2), she is not.
+possibility, Alice is hungry (call this possibility "hungry"); in the
+other, she is not (call it "full").
- = {(w1,n,r,g), (w2,n,r,g)}[Alice isn't hungry][Alice might be hungry]
- = {(w2,n,r,g)}[Alice might be hungry]
+ {hungry, full}[Alice isn't hungry][Alice might be hungry]
+ = {full}[Alice might be hungry]
= {}
As usual in dynamic theories, a sequence of sentences is treated as if
the sentence were conjoined. This is the same thing as updating with
the first sentence, then updating with the second sentence.
Update with *Alice isn't hungry* eliminates the possibility in which
-Alice is hungry (w1), leaving only the possibility containing w2.
+Alice is hungry, leaving only the possibility in which she is full.
Subsequent update with *Alice might be hungry* depends on the result
of updating with the prejacent, *Alice is hungry*. Let's do that side
calculation:
- {(w2,n,r,g)}[Alice is hungry]
+ {full}[Alice is hungry]
= {}
Because the only possibility in the information state is one in which
We'll start with the same two possibilities.
- = {(w1,n,r,g), (w2,n,r,g)}[Alice might be hungry][Alice isn't hungry]
- = {(w1,n,r,g), (w2,n,r,g)}[Alice isn't hungry]
- = {(w2,n,r,g)}
+ = {hungry, full}[Alice might be hungry][Alice isn't hungry]
+ = {hungry, full}[Alice isn't hungry]
+ = {full}
Update with *Alice might be hungry* depends on the result of updating
with the prejacent, *Alice is hungry*. Here's the side calculation:
- {(w1,n,r,g), (w2,n,r,g)}[Alice is hungry]
- = {(w1,n,r,g)}
+ {hungry, full}[Alice is hungry]
+ = {hungry}
Since this update is non-empty, all of the original possibilities
survive update with *Alice might be hungry*. By now it should be