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  Modular Proof Systems for Partial Functions with Weak Equality

Ganzinger, H., Sofronie-Stokkermans, V., & Waldmann, U. (2004). Modular Proof Systems for Partial Functions with Weak Equality. In Automated reasoning: Second International Joint Conference, IJCAR 2004 (pp. 168-182). Berlin: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2977-7 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-3432-F
Genre: Conference Paper

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 Creators:
Ganzinger, Harald1, Author           
Sofronie-Stokkermans, Viorica1, 2, Author           
Waldmann, Uwe1, 2, Author                 
Basin, David1, Editor           
Rusinowitch, Michael3, Editor
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              
2Automation of Logic, MPI for Informatics, Max Planck Society, ou_1116545              
3Max Planck Society, ou_persistent13              

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 Abstract: The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. Modularity means that inferences are pure, only involving clauses over the alphabet of either one, but not both, of the theories. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures are declared as partial. This result also means that if the unsatisfiability of a goal modulo the combined theory does not depend on the totality of the functions in the extensions, the inconsistency will be effectively found. Moreover, we consider a constraint superposition calculus for the case of hierarchical theories and show that it has a related modularity property. Finally we identify cases where the partial models can always be made total so that modular superposition is also complete with respect to the standard (total function) semantics of the theories.

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Language(s): eng - English
 Dates: 2005-02-022004
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 231253
Other: Local-ID: C1256104005ECAFC-827C5504FD548DB8C1256EAC0033F34D-Ganzinger-SofronieStokkermans-Waldmann-ijcar-2004
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Title: Untitled Event
Place of Event: Cork, Ireland
Start-/End Date: 2004-07-04

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Title: Automated reasoning : Second International Joint Conference, IJCAR 2004
Source Genre: Proceedings
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Publ. Info: Berlin : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 168 - 182 Identifier: ISBN: 3-540-22345-2

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Title: Lecture Notes in Artificial Intelligence
Source Genre: Series
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Pages: - Volume / Issue: 3097 Sequence Number: - Start / End Page: - Identifier: -