Completeness of Resolution for Definite Answers Tanel Tammet

We investigate the problem of finding a computable witness for the existential quantifier in a formula of the classical first-order predicate logic. The A-resolution calculus based on the program derivation algorithm A of C-L. Chang, R. C-T. Lee and R.Waldinger is used for finding a definite substitution t for an existentially bound variable y in some formula F , such that Fft=yg is provable. The term t is built of the function and predicate symbols in F , plus Boolean functions and a case splitting function if , defined in the standard way: if (True; x; y) = x and if (False; x; y) = y. We prove that the A-resolution calculus is complete in the following sense: if such a definite substitution exists, then the A-calculus derives a clause giving such a substitution. The result is strengthened by allowing the usage of liftable criterias R of a certain type, prohibiting the derivation of the substitution terms t for which R(t) fails. This enables us to specify, for example, tha..