Consistency of natural relations on sets
Koizumi, H., Maruoka, A. and Paterson, M.S. (1993) Consistency of natural relations on sets. Technical Report. Department of Computer Science, Coventry, UK.
- Published Version
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 and (N 2) denote . 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:||Monograph (Technical Report)|
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||Faculty of Science > Computer Science|
|Depositing User:||Mr Ebrahim Ardeshir|
|Date Deposited:||19 Dec 2011 09:13|
|Last Modified:||01 Nov 2012 18:06|
Actions (login required)