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Re: [ontolog-forum] Role of definitions (Remember the poor human)

To: Kathryn Blackmond Laskey <klaskey@xxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 13 Feb 2007 16:15:10 -0600
Message-id: <p06230907c1f7e754dc1f@[]>
>  >...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)

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