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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. 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop (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/11858/00-001M-0000-0014-ACF1-5
Genre: Conference Paper

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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: Berlin, Germany : Springer
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 519585
Other: Local-ID: C1256104005ECAFC-AA56DA80C58704F6C125614C004A6F13-BachmairGanzingerStuber-95-compass
 Degree: -

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Title: Untitled Event
Place of Event: S. Margherita, Italy
Start-/End Date: 1995

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Title: Recent Trends in Data Type Specification. 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop
Source Genre: Proceedings
 Creator(s):
Astesiano, Egidio, Editor
Reggio, Gianna, Editor
Tarlecki, Andrzej, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1 - 29 Identifier: ISBN: 3-540-59132-X

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