Cancellative Superposition Decides the Theory of Divisible Torsion-Free Abelian Groups

Authors:
Uwe Waldmann
Affiliations:
-
Venue:
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Year:
1999

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Abstract

In divisible torsion-free abelian groups, the efficiency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivadent clause without unshielded variables. We show that the resulting calculus is not only refutationally complete (even in the presence of eirbitrary free function symbols), but that it is also a decision procedure for the theory of divisible torsion-free abelisin groups.