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Superposition for Fixed Domains

MPG-Autoren
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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Volltexte (frei zugänglich)

superFixDom_TR.pdf
(beliebiger Volltext), 334KB

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Zitation

Horbach, M., & Weidenbach, C.(2009). Superposition for Fixed Domains (MPI-I-2009-RG1-005). Saarbrücken: Max-Planck-Institut für Informatik.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-1A71-C
Zusammenfassung
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the theory. Proving universal properties with respect to a saturated theory directly leads to a modification of the minimal model's term-generated domain, as new Skolem functions are introduced. For many applications, this is not desired. Therefore, we propose the first superposition calculus that can explicitly represent existentially quantified variables and can thus compute with respect to a given domain. This calculus is sound and refutationally complete in the limit for a first-order fixed domain semantics. For saturated Horn theories and classes of positive formulas, we can even employ the calculus to prove properties of the minimal model itself, going beyond the scope of known superposition-based approaches.