A superposition decision procedure for the guarded fragment with equality

Abstract

We give a new decision procedure for the guarded fragment with equality. The procedure is based on resolution with superposition. We argue that this method will be more useful in practice than methods based on the enumeration of certain finite structures. It is surprising to see that one does not need any sophisticated simplification and redundancy elimination method to make superposition terminate on the class of clauses that is obtained from the clausification of guarded formulas. Yet the decision procedure obtained is optimal with regard to time complexity. We also show that the method can be extended to the loosely guarded fragment with equality.

OWL rules: A proposal and prototype implementation

“…11 This would introduce RDF classes for SWRL atoms and variables, and RDF properties to link atoms to their predicates (classes and properties) and arguments (variables, individuals or data values). 12 The example rule given in Section 7.1 (that equates the style/period of art objects with the style of the artist that created them) would be mapped into RDF as follows:…”

“…<owlr:Variable rdf:ID="x"/> <owlr:Variable rdf:ID="y"/> <owlr:Variable rdf:ID="z"/> <owlr:Rule> <owlr:antecedent rdf:parseType="Collection"> <owlr:classAtom> <owlr:classPredicate rdf:resource="&ulan;Artist"/> <owlr:argument1 rdf:resource="#x" /> </owlr:classAtom> <owlr:classAtom> <owlr:classPredicate rdf:resource="&aat;Style"/> <owlr:argument1 rdf:resource="#y" /> </owlr:classAtom> <owlr:individualPropertyAtom> <owlr:propertyPredicate rdf:resource="&aatulan;artistStyle"/> <owlr:argument1 rdf:resource="#x" /> <owlr:argument2 rdf:resource="#y" /> </owlr:individualPropertyAtom> <owlr:individualPropertyAtom> <owlr:propertyPredicate rdf:resource="&vra;creator"/> <owlr:argument1 rdf:resource="#x" /> <owlr:argument2 rdf:resource="#z" /> </owlr:individualPropertyAtom> </owlr:antecedent> <owlr:consequent rdf:parseType="Collection"> <owlr:individualPropertyAtom> <owlr:propertyPredicate rdf:resource="&vra;style/period"/> <owlr:argument1 rdf:resource="#z" /> <owlr:argument2 rdf:resource="#y" /> </owlr:individualPropertyAtom> </owlr:consequent> </owlr:Rule> where &ulan;, &aat;, &aatulan; and &vra; are assumed to expand into the appropriate 11 http://www.w3.org/TR/owl-xmlsyntax/owlxml2rdf.xsl 12 The result is similar to the RDF syntax for representing disjunction and quantifiers proposed in [30]. namespace names.…”

“…Paramasivam and Plaisted, for example, have investigated the use of FOL reasoning for DL classification [36], while Ganzinger and de Nivelle have developed decision procedures for the guarded fragment, a fragment of FOL that includes many description logics [11]. The most widely known work in this area was by Hustadt and Schmidt [26], who used the SPASS FOL prover to reason with propositional modal logics, and, via well known correspondences [45], with description logics.…”

Using Vampire to Reason with OWL

“…Paramasivam and Plaisted, for example, have investigated the use of FOL reasoning for DL classification [26], while Ganzinger and de Nivelle have developed decision procedures for the guarded fragment, a fragment of FOL that includes many description logics [10]. The most widely known work in this area was by Hustadt and Schmidt [20], who used the SPASS FOL prover to reason with propositional modal logics, and, via well known correspondences [30], with description logics.…”

A Tableaux Based Decision Procedure for a Broad Class of Hybrid Formulae with Binders

“…Satisfiability of formulae in the fragment FHL \ ↓2 can be tested by translation, by use of any calculus for the guarded fragment, such as the tableau calculi defined in [9,10], or the decision procedure based on resolution given in [7]. The translation can be obtained in polynomial time [13], hence the theoretical complexity does not increase.…”