Index Sets for Finite Normal Predicate Logic Programs with Function Symbols.

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 Q(0), Q(1), ... over L. Given some property P of finite normal predicate logic programs over L, we define the index set I-P to be the set of indices e such that Q(e) has property P. Then we shall classify the complexity of the index set I-P within the arithmetic hierarchy for various natural properties of finite predicate logic programs.