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MPI-I-2009-RG1-005

Superposition for fixed domains

Horbach, Matthias and Weidenbach, Christoph

MPI-I-2009-RG1-005. November 2009, 49 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.
Acknowledgement:
References to related material:

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Hide details for BibTeXBibTeX
@TECHREPORT{Horbach2009,
  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},
}