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Cancellative Abelian Monoids and Related Structures in Refutational Theorem Proving (Part II)

MPG-Autoren
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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Zitation

Waldmann, U. (2002). Cancellative Abelian Monoids and Related Structures in Refutational Theorem Proving (Part II). Journal of Symbolic Computation, 33, 831-861.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-2F30-C
Zusammenfassung
Cancellative superposition is a refutationally complete calculus for first-order equational theorem proving in the presence of the axioms of cancellative abelian monoids, and, optionally, the torsion-freeness axioms. Thanks to strengthened ordering restrictions, cancellative superposition avoids some of the inefficiencies of classical AC-superposition calculi. We show how the efficiency of cancellative superposition can be further improved by using variable elimination techniques, leading to a significant reduction of the number of variable overlaps. In particular, we demonstrate that in divisible torsion-free abelian groups, variable overlaps, AC-unification and AC-orderings can be avoided completely.