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  Combining Algebra and Universal Algebra in First-Order Theorem Proving: The Case of Commutative Rings

Bachmair, L., Ganzinger, H., & Stuber, J. (1995). Combining Algebra and Universal Algebra in First-Order Theorem Proving: The Case of Commutative Rings. In E. Astesiano, G. Reggio, & A. Tarlecki (Eds.), Recent Trends in Data Type Specification (pp. 1-29). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0014-ACF0-7 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-57B6-3
Genre: Conference Paper

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Locator:
https://rdcu.be/dxCrT (Publisher version)
Description:
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OA-Status:
Not specified

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 Creators:
Bachmair, Leo1, Author           
Ganzinger, Harald1, Author           
Stuber, Jürgen1, Author           
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 Abstract: We present a general approach for integrating certain mathematical structures
in first-order equational theorem provers. More specifically, we consider
theorem proving problems specified by sets of first-order clauses that contain
the axioms of a commutative ring with a unit element. Associative-commutative
superposition forms the deductive core of our method, while a convergent
rewrite system for commutative rings provides a starting point for more
specialized inferences tailored to the given class of formulas. We adopt ideas
from the Gr{\"o}bner basis method to show that many inferences of the
superposition calculus are redundant. This result is obtained by the judicious
application of the simplification techniques afforded by convergent rewriting
and by a process called symmetrization that embeds inferences between single
clauses and ring axioms.

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Language(s): eng - English
 Dates: 2010-03-121995
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 519585
Other: Local-ID: C1256104005ECAFC-AA56DA80C58704F6C125614C004A6F13-BachmairGanzingerStuber-95-compass
DOI: 10.1007/BFb0014420
BibTex Citekey: Bachmair-et-al_ COMPASS-ADT95
 Degree: -

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Title: 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop
Place of Event: S. Margherita, Italy
Start-/End Date: 1995-05-30 - 1996-06-03

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Title: Recent Trends in Data Type Specification
  Subtitle : 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop, S. Margherita, Italy, May 30 - June 3, 1994. Selected Papers
  Abbreviation : COMPASS/ADT 1995
Source Genre: Proceedings
 Creator(s):
Astesiano, Egidio1, Editor
Reggio, Gianna1, Editor
Tarlecki, Andrzej1, Editor
Affiliations:
1 External Organizations, ou_persistent22            
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1 - 29 Identifier: ISBN: 978-3-540-59132-0

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Title: Lecture Notes in Computer Science
  Abbreviation : LNCS
Source Genre: Series
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Affiliations:
Publ. Info: -
Pages: - Volume / Issue: 906 Sequence Number: - Start / End Page: - Identifier: -