Optimal compression of propositional Horn knowledge bases: complexity and approximation
Artificial Intelligence
Attribute exploration with background knowledge
Theoretical Computer Science
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
Theory of Relational Databases
Theory of Relational Databases
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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.