Titlebook: Deduction Systems; Rolf Socher-Ambrosius,Patricia Johann Textbook 1997 Springer-Verlag New York, Inc. 1997 Syntax.automated deduction.calc

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Improving Deduction Efficiency, every fair derivation out of ., the empty clause lies in the resolution search space generated from . by that calculus. In particular, since fair derivation strategies provide means of traversing entire resolution search spaces, in proving the refutation completeness of a given resolution calculus

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1868-0941 ns of formulae over their associated universes. We will see that the upshot of this discovery is that the validity of a formula in the predicate calculus can be978-1-4612-7479-7978-1-4612-2266-8Series ISSN 1868-0941 Series E-ISSN 1868-095X

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,Normal Forms and Herbrand’s Theorem,that in applying a quantifier rule, the bound variables of the formula will never be instantiated by the “right” substitution terms. We will see in Theorems 6.2.1 and 6.3.2 that restricting the syntactic forms that formulae to be proved may have, and then showing that every formula can be converted

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Resolution and Unification,unification, a technique for eliminating brute-force enumeration of ground clauses from our refutation method for arbitrary formulae by enabling the systematic recognition of ground instances of nonground clauses which are relevant to refutations. The remainder of this section is dedicated to descri

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https://doi.org/10.1007/978-3-658-34310-1that in applying a quantifier rule, the bound variables of the formula will never be instantiated by the “right” substitution terms. We will see in Theorems 6.2.1 and 6.3.2 that restricting the syntactic forms that formulae to be proved may have, and then showing that every formula can be converted

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https://doi.org/10.1007/978-3-658-19115-3t of completion procedures—based on the Knuth-Bendix algorithm—for equational logic. The second tendency is that of using knowledge about special functions or predicates to arrive at more powerful unification algorithms. The fundamental idea behind this latter approach is to hand over the lion’s sha