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 \(\mathcal {L}\) 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 \(n \ge 1\). Then we can effectively list all the finite normal predicate logic programs \(Q_0,Q_1,\ldots \) over \(\mathcal L\). Given some property \(\mathcal{P}\) of finite normal predicate logic programs over \(\mathcal L\), we define the index set \(I_\mathcal{P}\) to be the set of indices e such that \(Q_e\) has property \(\mathcal P\). Then we shall classify the complexity of the index set \(I_\mathcal{P}\) within the arithmetic hierarchy for various natural properties of finite predicate logic programs.