Finding finite herbrand models

Authors:
Stefan Borgwardt;Barbara Morawska
Affiliations:
Theoretical Computer Science, TU Dresden, Germany;Theoretical Computer Science, TU Dresden, Germany
Venue:
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2012

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Abstract

We show that finding finite Herbrand models for a restricted class of first-order clauses is ExpTime-complete. A Herbrand model is called finite if it interprets all predicates by finite subsets of the Herbrand universe. The restricted class of clauses consists of anti-Horn clauses with monadic predicates and terms constructed over unary function symbols and constants. The decision procedure can be used as a new goal-oriented algorithm to solve linear language equations and unification problems in the description logic FL0. The new algorithm has only worst-case exponential runtime, in contrast to the previous one which was even best-case exponential.