Set containment inference and syllogisms
type: Item
instance of: scholarly article
title: Set containment inference and syllogisms
zbMATH Open document ID: 0662.68090
DOI: 10.1016/0304-3975(86)90011-3
author: Paolo Atzeni
author: D. Stott Parker
published in: Theoretical Computer Science
publication date: 1988-01-01T00:00:00Z
review text: Type hierarchies and type inclusion is standard in many knowledge representation schemes. In this paper, it is shown how to determine consistency and inference for collections of statements of the form: ``mammal isa vertebrate''. These containment statements relate to contents of two sets or types. The work here is new in permitting statements with negative information: disjointness of sets, or non- inclusion of sets. It is shown that binary containment inference is solved by rules essentially equivalent to Aristoteles' syllogisms. Necessary and sufficient conditions for consistency as well as sound and complete sets of inference rules, are presented for binary containment. The sets of inference rules are compact, and lead to polynomial-time inference algorithms, so permitting negative constraints does not result in intractability for this problem.
Mathematics Subject Classification ID: 68T99
Mathematics Subject Classification ID: 68P20
Mathematics Subject Classification ID: 68P05
zbMATH DE Number: 4083020
zbMATH Keywords: knowledge representation schemes
zbMATH Keywords: negative information
zbMATH Keywords: binary containment inference
reviewed by: Horst Zeitler
MaRDI profile type: Publication
full work available at URL: 0304-3975(86)90011-3
OpenAlex ID: W2010611126
cites work: DAL -- a logic for data analysis
cites work: Q3696560
cites work: Q4742734
cites work: Q4198056
cites work: Q3668890
cites work: Rough sets
cites work: Q3326832
description: scientific article; zbMATH DE number 4083020