Modular proof systems for partial functions with Evans equality

Harald Ganzinger, Viorica Sofronie-Stokkermans, Uwe Waldmann
2006 Information and Computation  
The paper presents a modular superposition calculus for the combination of first-order theories involving both total and partial functions. The modularity of the calculus is a consequence of the fact that all the inferences are pure-only involving clauses over the alphabet of either one, but not both, of the theorieswhen refuting goals represented by sets of pure formulae. The calculus is shown to be complete provided that functions that are not in the intersection of the component signatures
more » ... e 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.
doi:10.1016/j.ic.2005.10.002 fatcat:nbdf4na2ibbppabvatomqr7aja