Index sets for finite normal predicate logic programs with function symbols

Abstract

We study the recognition problem in the metaprogramming of finite normal predicate logic programs. That is, let L be a computable first order predicate language with infinitely many constant symbols and infinitely many n-ary predicate symbols and n-ary function symbols for all n ≥ 1. Then we can effectively list all the finite normal predicate logic programs Q0,Q1, . . . over L. Given some property P of finite normal predicate logic programs over L, we define the index set IP to be the set of indices e such that Qe has property P. Then we shall classify the complexity of the index set IP within the arithmetic hierarchy for various natural properties of finite predicate logic programs.