Modular Proof Systems for Partial Functions with Weak Equality

Harald Ganzinger, Viorica Sofronie-Stokkermans, and Uwe Waldmann

In David Basin and MichaŽl Rusinowitch, editors, Automated Reasoning, Second International Joint Conference, IJCAR 2004, LNAI 3097, pages 168-182, Cork, Ireland, July 4-8, 2004. Springer-Verlag.

Revised version: Modular Proof Systems for Partial Functions with Evans Equality, in I&C, 204:1453-1492, 2006.

Corrected version of the proceedings article: [Postscript file, 168 kB]

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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Uwe Waldmann <uwe@mpi-inf.mpg.de>, 2005-11-10.