Pseudo-models and propositional Horn inference

Authors:
Bernhard Ganter;Rüdiger Krauíe
Affiliations:
Institut für Algebra, Technische Universität Dresden, Zellescher Weg 12-14, D-01062 Dresden, Germany;Institut für Algebra, Technische Universität Dresden, Zellescher Weg 12-14, D-01062 Dresden, Germany
Venue:
Discrete Applied Mathematics - Ordinal and symbolic data analysis (OSDA 2000)
Year:
2005

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Abstract

A well-known result is that the inference problem for propositional Horn formulae can be solved in linear time. We show that this remains true even in the presence of arbitrary (static) propositional background knowledge. Our main tool is the notion of a cumulated clause, a slight generalization of the usual clauses in Propositional Logic. We show that each propositional theory has a canonical irredundant base of cumulated clauses, and present an algorithm to compute this base.