Re: SUO: *Date 24 Mar 2002 -- Program Semantics
Leo,
I agree with your summary, but I'd like to add a couple more points:
> M. Arbib has done much in formal languages, theory of computation,
> for quite some time. Note that denotational semantics is really
> model-theoretic semantics. Scott and Strachey's text (circa 1977) opened
> the field up a bit for mainstream computer science. Montague (1968,
> etc.) opened the field up a bit for formal semantics in linguistics --
> before which there wasn't much in the way of formal semantics, by the
> way. Category theory is a very general useful tool. It however needs
> applications at much lower levels of abstraction in general, so I am
> interested in this text just for that purpose (applications mostly are
> still pretty theoretical, in my knowledge: type theory, denotational
> semantics of programming languages, program specification, etc.) I hope
> the IFF can bring it down to a reasonable "ontology" level (which itself
> is probably fairly abstract for most of the human race).
I agree that Montague did a good job, but I also want to emphasize that
the computer science people had done a lot more work in the area, which
was earlier and in some respects better than what M. had done.
By the mid 1960s, compiler technology was quite respectable, and the
techniques of "syntax-directed compilation" were well established.
The basic idea is that for every grammar rule, there exists a semantic
rule that determines how the syntactic components are to be transformed
to generate the semantic structures.
In 1967, Bill Woods applied those techniques to English question
answering systems for his PhD dissertation (which was not officially
published until 1979, but he published parts of it in the late 60s and
early 70s along with his implementation in a question-answering system
about moon rocks). He did not apply his methods to modal logic, but
he did apply them to a much larger range of quantifiers (including what
the linguists have since called "generalized quantifiers"). And he
certainly used a larger vocabulary than Montague's 37 words.
I agree that Montague's system has had more influence among professional
linguists, but that is primarily because liguists feel that a logician
is more prestigious and worthy of a citation than a mere computer
programmer. But much as I like lambda calculus, I believe that
Montague's formalism was a disaster that has done more to hinder wide
spread use of logic than it has done to promote it.
In my publications, I give Montague an obligatory citation (because
reviewers would give me black marks if I didn't), but I always cite
the computer scientists first, for the simple reason that they did it
first, and in many respects, they did it better.
The methods that I use for generating conceptual graphs from language
are closer to the compiler-writers' approach in technique, but they
are logically equivalent to Montague's lambda-calculus approach in
denotation. As a result, the methods are computationally more efficient
and much easier for mere human beings to visualize, understand, and
implement. If the linguists would bother to look beyond their narrow
domain, they might find methods that would be much more productive for
their theorizing and pedogogically more effective for teaching their
students.
John Sowa