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Conference Paper

A Superposition Calculus for Divisible Torsion-Free Abelian Groups

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons45689

Waldmann,  Uwe
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Waldmann, U. (1997). A Superposition Calculus for Divisible Torsion-Free Abelian Groups. In M. P. Bonacina, & U. Furbach (Eds.), Proceedings of the International Workshop on First-Order Theorem Proving (FTP-97) (pp. 130-134). Linz, Austria: Johannes Kepler Universität.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-39D3-3
Abstract
Variable overlaps are one of the main sources for the inefficiency of AC or ACU theorem proving calculi. In the presence of the axioms of abelian groups or at least cancellative abelian monoids, ordering restrictions allow us to avoid some of these overlaps, but inferences with unshielded variables remain necessary. In divisible torsion-free abelian groups, for instance the rational numbers, every clause can be transformed into an equivalent clause without unshielded variables. We show how such a variable elimination algorithm can be integrated into the cancellative superposition calculus. The resulting calculus is refutationally complete with respect to the axioms of divisible torsion-free abelian groups and allows us to dispense with variable overlaps altogether. If abstractions are performed eagerly, the calculus makes it furthermore possible to avoid the computation of AC unifiers and AC orderings.