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Conference Paper

Modular Proof Systems for Partial Functions with Weak Equality

MPS-Authors
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Ganzinger,  Harald
Programming Logics, MPI for Informatics, Max Planck Society;

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Sofronie-Stokkermans,  Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Waldmann,  Uwe       
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

/persons/resource/persons44075

Basin,  David
Programming Logics, MPI for Informatics, Max Planck Society;

Rusinowitch,  Michael
Max Planck Society;

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Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2977-7
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.