MPI-INF/SWS Research Reports 1991-2021

2. Number - All Departments


Superposition for fixed domains

Horbach, Matthias and Weidenbach, Christoph

November 2009, 49 pages.

Status: available - back from printing

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.

  • MPI-I-2009-RG1-005.pdf
  • Attachement: MPI-I-2009-RG1-005.pdf (333 KBytes)

URL to this document:

Hide details for BibTeXBibTeX
  AUTHOR = {Horbach, Matthias and Weidenbach, Christoph},
  TITLE = {Superposition for fixed domains},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2009-RG1-005},
  MONTH = {November},
  YEAR = {2009},
  ISSN = {0946-011X},