The domain of set-valued feature structures

Linguistics and Philosophy 17 (6):607-631 (1994)
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Abstract

It is well-known that feature structures can be fruitfully viewed as forming a Scott domain. Once a linguistically motivated notion of set value in feature structures is countenanced, however, this is no longer possible inasmuch as unification of set values in general fails to yield a unique result. In Pollard and Moshier 1990 it was shown that, while falling short of forming a Scott domain, the set of feature structures possibly containing set values satisfies the weaker condition of forming a 2/3 SFP domain when equipped with an appropriate notion of subsumption: that is, for any finite setS of feature structures, there is a finite setM of minimal upper bounds ofS such that any upper bound ofS is approximated by a member ofM. Unfortunately, the 2/3 SFP domains are not as pleasant to work with as Scott domains since they are not closed under all the familiar domain constructions; and the question has remained open whether the feature structure domain satisfies the added condition of profiniteness. In this paper we resolve this question in the affirmative

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Carl Pollard
Ohio State University

References found in this work

Non-Well-Founded Sets.Peter Aczel - 1988 - Palo Alto, CA, USA: Csli Lecture Notes.
Domain theory in logical form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.
Unifying partial descriptions of sets.Carl J. Pollard & Drew Moshier - 1990 - In Philip P. Hanson (ed.), Information, Language and Cognition. University of British Columbia Press. pp. 1--285.

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