Abduction of linear arithmetic constraints

Authors:
Michael J. Maher
Affiliations:
National ICT Australia, Sydney, Australia
Venue:
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Year:
2005

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Abstract

Abduction is usually carried out on partially-defined predicates. In this paper we investigate abduction applied to fully-defined predicates, specifically linear arithmetic constraints over the real numbers. Abduction in this context has application to query answering using views and type inference, and potential relevance to analysis of concurrent/constraint/logic programs. We show that only rarely do abduction problems over linear arithmetic constraints have unique most general answers. We characterize the cases where most general answers exist. In general there may be infinitely many maximally general answers, or even answers that are not represented by maximally general answers. We take steps towards representing such answers finitely.