> >...I think it is potentially confusing, and at
>>the least out of keeping with standard usage in logic, to call
>>anything proof theoretic "semantics".
>
>In computer science, programs have operational semantics. I read a
>paper a few years ago describing an inference engine the author
>wrote, which said "The semantics of our engine is what it computes." (01)
But that can also be understood in a
model-theoretic sense, if what it computes are
understood to be recursive functions or some
similar kind of infinite mathematical entity
(e.g. a continuation). It is usually not
considered very good form to base the semantics
of a *language* on what a particular *engine*
computes, at least to many theoreticians. (02)
>A proof theory for a logic would correspond to operational semantics
>for a theorem prover based on that proof theory.
>
>Logicians might not use the word "semantics" for this, but computer
>scientists do. (03)
Some of them. Others, in more theoretical
traditions, stick to a more model-theoretic
usage. So for example there was once (the problem
is long since solved) a great to-do about
providing a "semantics for the lambda calculus",
which was always trivial if 'semantics' were
understood operationally, but is highly
nontrivial when it is understood
model-theoretically. Semantic theories for
Prolog-style systems are also understood
model-theoretically. (04)
Pat (05)
>K
>
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