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From: mark@adler.philosophie.uni-stuttgart.de (Mark Johnson)
Subject: Re: Sorts, Types in logic and programming languages
In-Reply-To: lex@cogsci.ed.ac.uk's message of 22 May 91 18:29:10 GMT
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Date: 24 May 91 12:13:32
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In reply to Lex Holt (lex@uk.ac.ed.cogsci), I suspect that the fact that
'sort' and 'type' are being used as virtual synonyms shows that the
distinction between syntax and semantics is being lost.  In my own area
of feature structure logics, I sometimes get the feeling that researchers
almost deliberately try to confuse the issue, and don't want to say if
their entities are semantic objects (something _in_ the domain of
discourse, where it would make sense to talk about _sorts_ of feature
structure elements), or if they are constraints on such entities
--- abstractly, a kind of expression from a 'language' for talking 
about feature structures (even if the 'expressions' of this language
are directed graphs) --- so it would make sense to talk about
_types_ of feature structure constraints.

Regarding my Montague Grammar example, Lex Holt (lex@uk.ac.ed.cogsci)
correctly notes that:
> ...
> Except that Montague and his followers would tend to call e/t and e//t
> `categories', or `syntactic categories', and call <e,t> a type.  Given
> this usage, it is expressions of Montague's formal fragment of English
> that have categories, while types apply to expressions of the logic
> IL.  This is not to deny that in studies of, for example, combinatory
> systems for syntactic categories (such as the Lambek calculus)
> categories are often called types.
> ...
Yes, Lex is right.  I had forgotten that Montague defines the meaning of
English expressions by translating them into expressions of another
language which he called IL, and expressions of categories e/t and e//t
in English are both translated into expressions of _type_  <e,t> in IL.
So in Montague's system the terms 'category' and 'type' classify
expressions of the respective languages.  (Since Montague defines the
semantics of English via translation into IL, a lot of linguists
_mistakenly_ think that the IL expression itself is the semantics of the
English it translates, whereas it is the semantics of that IL translation
that is the semantics of the English expression).

Comments?

Mark
--
Mark Johnson
Institut fuer maschinelle Sprachverarbeitung - Computerlinguistik
Universitaet Stuttgart
Keplerstrasse 17
D-7000 Stuttgart 1
West Germany.  (you need "West" otherwise mail from the US is not delivered!)
work phone: 0711 - 121 3132.

On leave until mid July 1991 from:
	Cognitive and Linguistic Sciences, Box 1978
	Brown University
	Providence, RI 02912
	USA

email addresses: 
	mark@adler.philosophie.uni-stuttgart.de
	mj@cs.brown.edu
