Dear Matthew, (01)
You can think of a context as a container for one or more propositions.
McCarthy's 'ist' operator is an abbreviation for "is true in". Note
that the preposition 'in' suggests a container. (02)
PH
> I asked John [McCarthy] about his basic logical construct 'ist',
> written as ist(c, p)
>
> and read as meaning "p is true in the context c". The question was, is
> the 'p' in this formula a sentence or a proposition? It is *written* in
> the McCarthy/Guha/Makarios context logics as a sentence; but to my
> delight, John said it was a proposition. Which is exactly what it is in
> the IKL way of writing this as a logical relation between two things, a
> context and a proposition. (03)
MW
> How is ist different from simple inference? i.e. from
> If c then p. (04)
An if-then statement of the form "If c then p" is a sentence that
relates two other sentences c and p. (05)
The statement ist(c,p) -- or as Pat and I would prefer to write it
ist(c, (that p)) -- relates a context c to sentence p. It does not
say that c implies p. Instead, it says that p is true *in* c. (06)
To get the effect of an implication, you could use the following
axiom to specify a kind of context logic: (07)
If (p implies q) then (ist(c,p) implies ist(c,q)). (08)
This axiom says that if p is true in a context c, then any sentence
in the deductive closure of p is also true in c. (09)
Without this axiom (or something similar), 'ist' would not have
the effect of an implication. (010)
For more discussion of these issues, see Pat's article about IKL: (011)
http://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.html#ContextsModalities (012)
Or see my article from the AAAI symposium on contexts: (013)
http://www.jfsowa.com/pubs/fs95.pdf (014)
John (015)
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