2008/09/04 by Matthias Horbach, Horbach, Matthias, Christoph Weidenbach +1
Computer Science · #Artificial Intelligence (cs.AI) #F.4.1 #FOS: Computer and information sciences #I.2.3 #Logic in Computer Science (cs.LO) #Robotic Path Planning Algorithms #cs.AI #cs.LO
paper · pdf · doi:10.48550/arxiv.0809.0922
34 pages; to appear in ACM Transactions on Computational Logic
openalex publication_date 2008/09/04 · arxiv created 2009/11/30 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.