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  Refutational Theorem Proving for Hierarchic First-Order Theories

Bachmair, L., Ganzinger, H., & Waldmann, U. (1994). Refutational Theorem Proving for Hierarchic First-Order Theories. Applicable Algebra in Engineering, Communication and Computing (Aaecc), 5(3/4), 193-212.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0014-AD9C-E Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0014-AD9D-C
Genre: Journal Article

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 Creators:
Bachmair, Leo1, Author           
Ganzinger, Harald1, Author           
Waldmann, Uwe1, 2, Author           
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              
2Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              

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 Abstract: We extend previous results on theorem proving for first-order clauses with equality to hierarchic first-order theories. Semantically such theories are confined to conservative extensions of the base models. It is shown that superposition together with variable abstraction and constraint refutation is refutationally complete for theories that are sufficiently complete with respect to simple instances. For the proof we introduce a concept of approximation between theorem proving systems, which makes it possible to reduce the problem to the known case of (flat) first-order theories. These results allow the modular combination of a superposition-based theorem prover with an arbitrary refutational prover for the primitive base theory, whose axiomatic representation in some logic may remain hidden. Furthermore they can be used to eliminate existentially quantified predicate symbols from certain second-order formulae.

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Language(s): eng - English
 Dates: 2010-03-121994
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 519899
Other: Local-ID: C1256104005ECAFC-DBD34269BBD3C1BFC125614C004A7057-BachmairGanzingerWaldmann-94-aaecc
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Title: Applicable Algebra in Engineering, Communication and Computing (Aaecc)
Source Genre: Journal
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Publ. Info: -
Pages: - Volume / Issue: 5 (3/4) Sequence Number: - Start / End Page: 193 - 212 Identifier: ISSN: 0938-1287