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On the Completeness of Arbitrary Selection Strategies for Paramodulation
 In Proceedings of ICALP 2001
, 2001
"... A crucial way for reducing the search space in automated deduction are the socalled selection strategies: in each clause, the subset of selected literals are the only ones involved in inferences. For firstorder Horn clauses without equality, resolution is complete with an arbitrary selection o ..."
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Cited by 5 (1 self)
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A crucial way for reducing the search space in automated deduction are the socalled selection strategies: in each clause, the subset of selected literals are the only ones involved in inferences. For firstorder Horn clauses without equality, resolution is complete with an arbitrary selection of one single literal in each clause [dN96]. For Horn clauses with builtin equality, i.e., paramodulationbased inference systems, the situation is far more complex. Here we show that if a paramodulationbased inference system is complete with eager selection of negative equations and, moreover, it is compatible with equality constraint inheritance, then it is complete with arbitrary selection strategies. A first important application of this result is the one for paramodulation wrt. nonmonotonic orderings, which was left open in [BGNR99]. 1
Paramodulation and KnuthBendix Completion with Nontotal and Nonmonotonic Orderings
, 2001
"... Up to now, all existing completeness results for ordered paramodulation and KnuthBendix completion require the term ordering to be wellfounded, monotonic and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a wellknown ..."
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Cited by 1 (0 self)
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Up to now, all existing completeness results for ordered paramodulation and KnuthBendix completion require the term ordering to be wellfounded, monotonic and total(izable) on ground terms. For several applications, these requirements are too strong, and hence weakening them has been a wellknown research challenge. Here we
Solving, Reasoning, and Programming in Common Logic
"... Abstract. Common Logic (CL) is a recent ISO standard for exchanging logicbased information between disparate computer systems. Sharing and reasoning upon knowledge represented in CL require equation solving over terms of this language. We study computationally wellbehaved fragments of such solving ..."
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Cited by 1 (1 self)
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Abstract. Common Logic (CL) is a recent ISO standard for exchanging logicbased information between disparate computer systems. Sharing and reasoning upon knowledge represented in CL require equation solving over terms of this language. We study computationally wellbehaved fragments of such solving problems and show how they can influence reasoning in CL and transformations of CL expressions. 1
Combining Rewrite Tools for Equational Logic Programming
, 1996
"... Introducing equality into standard Horn clauses leads to a programming paradigm known as Equational Logic Programming. We propose here a scheme for the evaluation of such equational logic programs combining two powerful operational techniques: directed narrowing for the equational part and linear co ..."
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Introducing equality into standard Horn clauses leads to a programming paradigm known as Equational Logic Programming. We propose here a scheme for the evaluation of such equational logic programs combining two powerful operational techniques: directed narrowing for the equational part and linear completion for the logical part. Thus we provide a goaloriented solving procedure, keeping the wellknown advantages of Linear Completion (a reduced search space with a loop avoiding effect and the possibility to finitely synthesize an infinite set of answers) and of Directed Narrowing (search space pruning).
Modular Redundancy for Theorem Proving
, 2000
"... . We introduce a notion of modular redundancy for theorem proving. It can be used to exploit redundancy elimination techniques (like tautology elimination, subsumption, demodulation or other more refined methods) in combination with arbitrary existing theorem provers, in a refutation complete wa ..."
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. We introduce a notion of modular redundancy for theorem proving. It can be used to exploit redundancy elimination techniques (like tautology elimination, subsumption, demodulation or other more refined methods) in combination with arbitrary existing theorem provers, in a refutation complete way, even if these provers are not (or not known to be) complete in combination with the redundancy techniques when applied in the usual sense. 1 Introduction The concept of saturation in theorem proving is nowadays a wellknown, widely recognized useful concept. The main idea of saturation is that a theorem proving procedure does not need to compute the closure of a set of formulae w.r.t. a given inference system, but only the closure up to redundancy. Examples of early notions of redundancy (in the context of resolution) are the elimination of tautologies and subsumption. Bachmair and Ganzinger gave more general abstract notions of redundancy for inferences and formulae (see, e.g., [BG94...