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Conference Paper

Decidability Results for Saturation-Based Model Building

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44642

Horbach,  Matthias
Automation of Logic, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45719

Weidenbach,  Christoph
Automation of Logic, MPI for Informatics, Max Planck Society;

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Citation

Horbach, M., & Weidenbach, C. (2009). Decidability Results for Saturation-Based Model Building. In R. Schmidt (Ed.), 22nd International Conference on Automated Deduction (CADE-22) (pp. 404-420). Heidelberg: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-1A4E-D
Abstract
Saturation-based calculi such as superposition can be successfully instantiated to decision procedures for many decidable fragments of first-order logic. In case of termination without generating an empty clause, a saturated clause set implicitly represents a minimal model for all clauses, based on the underlying term ordering of the superposition calculus. In general, it is not decidable whether a ground atom, a clause or even a formula holds in this minimal model of a satisfiable saturated clause set. We extend our superposition calculus for fixed domains with syntactic disequality constraints in a non-equational setting. Based on this calculus, we present several new decidability results for validity in the minimal model of a satisfiable finitely saturated clause set that in particular extend the decidability results known for ARM (Atomic Representations of term Models) and DIG (Disjunctions of Implicit Generalizations) model representations.