Koizumi, Hirotaka, Maruoka, Akira and Paterson, Michael S. (1993) Consistency of natural relations on sets. University of Warwick. Department of Computer Science. (Department of Computer Science research report). (Unpublished)

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Abstract

Five natural relations for sets, such as inclusion, disjointness, intersection, etc., are introduced in terms of the emptiness of the subsets defined by Boolean combinations of the sets. Let N denote {1,2,...,n} and (N 2) denote {(i,j) | i,j in N and i < j}. A function mu on (N 2) specifies one of these relations for each pair of indices. Then mu is said to be "consistent on" M, a subset of N, if and only if there exists a collection of sets corresponding to indices in M such that the relations specified by mu hold between each associated pair of the sets. In this paper it is proved that if mu is consistent on all subsets of N of size three then mu is consistent on N. Furthermore, conditions that make mu consistent on a subset of size three are given explicitly.

Item Type:	Report
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH):	Set theory
Series Name:	Department of Computer Science research report
Publisher:	University of Warwick. Department of Computer Science
Official Date:	1993
Dates:	Date Event 1993 Completion
Number:	Number 253
Number of Pages:	10
DOI:	CS-RR-253
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Funder:	British Council
Related URLs:	Organisation

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