Epc < , and Equality Generalized Subsumption in Resolution-based Automatic-theorem-proving

The standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a speciied set of) modiied deduction rules for binary clausal resolution-refutation which build-in the reeexiv-ity, symmetry, transitivity and predicate substitutivity axioms for equality. The generalized notions of subsumption and tautology, 0-subsumption and 0-tautology , respectively, are presented, and EPC < , a binary clausal system which provides an adequate deductive context for refutation completeness under deletion with respect to these generalized notions, is introduced. Additionally, some refutation completeness preserving clause \normalization" techniques including generalized forms of replacement factoring and a form of demodulation, are presented. Some reenements for the rules are ooered, as well as a possible further generalization for subsumption, and a generalized form of a special case of replacement resolution, folding. This paper surveys and reports the principal results of 10], where proofs for results stated herein may be found. The standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a speciied set of) modiied deduction rules for binary clausal resolution-refutation which build-in the reeexivity, symmetry, transitivity and predicate substitutivity axioms for equality. The equality axioms have been identiied as a source of ineeciency or even incapacity for clause reso-lution/deduction oriented refutation provers (see e. A number of approaches to \building in equality", have been ooered in the literature of automated deduction. These include paramodulation, hyper-paramodulation, and demodulation 14, 18], E-Resolution 11], RUE-Resolution 5, 6], Z-Resolution 7], and the approach suggested by Sibert in 15]. More recently, restrictions of ordered paramodulation are described in, for example, 1, 2]. However, with the exception of 15], and the work described in 1, 2], very little has yet been written on how the notions of tautology and