Approximating Resultants of Existential Second-Order Quantifier Elimination upon Universal Relational First-Order Formulas
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چکیده
We investigate second-order quantifier elimination for a class of formulas characterized by a restriction on the quantifier prefix: existential predicate quantifiers followed by universal individual quantifiers and a relational matrix. For a given second-order formula of this class a possibly infinite sequence of universal first-order formulas that have increasing strength and are all entailed by the second-order formula can be constructed. Any first-order consequence of the second-order formula is a consequence of some member of the sequence. The sequence provides a recursive base for the first-order theory of the second-order formula, in the sense investigated by Craig. The restricted formula class allows to derive further properties, for example that the set of those members of the sequence that are equivalent to the second-order formula, or, more generally, have the same first-order consequences, is co-recursively enumerable. Also the set of first-order formulas that entails the secondorder formula is co-recursively enumerable. These properties are proven with formula-based tools used in automated deduction, such as domain closure axioms, eliminating individual quantifiers by ground expansion, predicate quantifier elimination with Ackermann’s Lemma, Craig interpolation and decidability of the Bernays-Schönfinkel-Ramsey class.
منابع مشابه
Early Steps of Second-Order Quantifier Elimination beyond the Monadic Case: The Correspondence between Heinrich Behmann and Wilhelm Ackermann 1928-1934 (Abstract)
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تاریخ انتشار 2017