The Stable Models of a Predicate Logic Program

We study the family of stable models of finite and recursive predicate logic programs. We show that the family of stable models of a recursive predicate logic program is, up to a recursive coding, a ∏ 1 0 class (i.e. an effectively closed set) and, vice versa, that each ∏ 1 0 class is, up to a recursive coding, the family of stable models of a finite predicate logic program. Since the structure of the Turing degrees of elements of ∏ 1 0 classes has been extensively studied, these coding results automatically imply many results about the degrees of stable models of finite predicate logic programs. For example, there exists a finite predicate logic program which has a stable model but which has no stable model which is hyperarithmetic and the existence problem for stable models of finite predicate logic programs is a ∑ 1 1 -complete problem.