Ed, (01)
There are multiple interrelated issues.
> We have apparently switched from what the logic is to what the notation is. (02)
Following is an earlier paper (from 1995), in which I discussed the
relationships between Peirce-Davidson event variables, Barwise-Perry
situations, and John McCarthy contexts: (03)
http://www.jfsowa.com/pubs/context.pdf
Syntax, Semantics, and Pragmatics of Contexts (04)
Short summary: they assume different ontologies (i.e., what their
quantified variables refer to), it's possible to relate them, but
their different ontologies enable some things to be stated in one
that cannot be stated in the others. (05)
Example: Consider the sentence s, "Sue gives a child a book."
And two theories that represent the proposition expressed by s: (06)
Theory t1: (∃ x1, x2, x3)(Sue=x1 & child(x2) & book(x3)
& gives(x1,x2,x3)). (07)
Theory t2: (∃ x1, x2, x3, x4)(Sue=x1 & child(x2) & book(x3)
& gives(x4) & agent(x4,x1) & recipient(x4,x2)
& theme(x4,x3)). (08)
Theory t2 is a Peircean (or Davidsonian) version of t1. Since
t1 and t2 are true in exactly the same models, t2 is a refinement
of t1 that uses an ontology that makes finer distinctions. (09)
> But I could use your syntactic "context" notation and translate
> it to a Davidsonian form instead. (010)
A B-P situation can contain multiple events and their participants,
and some events may overlap multiple situations. The same is true
about John McC contexts, but they are not equivalent. See the
context.pdf article. (011)
> I would argue that your "syntactic context" approach still requires
> that theory of time, and that creating ternary or quaternary relations
> with time arguments makes that theory harder to use. (012)
I agree with both clauses of that sentence. The reason why I did
that mapping was *theoretical*: I was trying to show that the
syntax of contexts -- by themselves -- does *not* go beyond the
expressive power of FOL. When you use them to represent propositions,
they raise other issues, but they can still be expressed in FOL. (013)
In fact, the flat notation of the laws.pdf article is similar to the
SNePS notation by Stuart Shapiro and his colleagues. For an example
and brief summary (with references), see Figure 8 of (014)
http://www.jfsowa.com/pubs/semnet.htm
Semantic Networks (015)
John (016)
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