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  Superposition for Divisible Torsion-Free Abelian Groups

Waldmann, U. (1998). Superposition for Divisible Torsion-Free Abelian Groups. In C. Kirchner, & H. Kirchner (Eds.), Proceedings of the 15th International Conference on Automated Deduction (CADE-98) (pp. 144-159). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-3894-C Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-3895-A
Genre: Conference Paper

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 Creators:
Waldmann, Uwe1, 2, Author           
Affiliations:
1Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              
2Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 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.

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Language(s): eng - English
 Dates: 2010-03-121998
 Publication Status: Issued
 Pages: -
 Publishing info: Berlin, Germany : Springer
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 519852
Other: Local-ID: C1256104005ECAFC-09757C0868827458C125664E0075D568-Waldmann1998
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Title: Untitled Event
Place of Event: Lindau, Germany
Start-/End Date: 1998

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Title: Proceedings of the 15th International Conference on Automated Deduction (CADE-98)
Source Genre: Proceedings
 Creator(s):
Kirchner, Claude, Editor
Kirchner, Hélène, Editor
Affiliations:
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 144 - 159 Identifier: ISBN: 3-540-64675-2

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Title: Lecture Notes in Artificial Intelligence
Source Genre: Series
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: -