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

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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. (2002). Cancellative Abelian Monoids and Related Structures in Refutational Theorem Proving (Part I). Journal of Symbolic Computation, 33, 777-829.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2F2E-3
Abstract
We present superposition calculi in which the axioms of cancellative abelian monoids and, optionally, the torsion-freeness axiom are integrated. Cancellative abelian monoids comprise abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Our calculi require neither extended clauses nor explicit inferences with the theory axioms. Compared with AC-superposition calculi, the number of variable overlaps is significantly reduced by strong ordering restrictions.