Rigid E -Unification and, Its Applications to Equational Matings

Publisher Summary The method of matings can be extended to the first-order languages with equality, and this extension is both sound and complete. The method of matings exploits the fundamental property given by the Skolem–Herbrand–Godel theorem. The extension to equational matings is nontrivial and requires proving of the Skolem–Herbrand–Godel theorem. It also requires extending the concept of a mating so that an equational mating is a set of sets of literals mated sets, where a mated set consists of several positive equations and a single negated equation and a form of unification modulo equational theories, or E-unification. The method of matings is an incremental proof procedure that interleaves two steps: quantifier-duplication steps and search for matings.

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