Locally Determined Logic Programs and Recursive Stable Models

Authors:
Douglas Cenzer;Jeffrey B. Remmel;Amy Vanderbilt
Affiliations:
Department of Mathematics, University of Florida, PO Box 118105, Gainesville, FL 32611-8105, USA E-mail: cenzer@ufl.edu;University of California at San Diego, USA E-mail: jremmel@ucsd.edu;Xavier University, USA E-mail: vanderbilt@xu.edu
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2004

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Abstract

In general, the set of stable models of a recursive logic program can be quite complex. For example, it follows from results of Marek, Nerode, and Remmel [Ann. Pure and Appl. Logic (1992)] that there exists finite predicate logic programs and recursive propositional logic programs which have stable models but no hyperarithmetic stable models. In this paper, we shall define several conditions which ensure that recursive logic program P has a stable model which is of low complexity, e.g., a recursive stable model, a polynomial time stable model, or a stable model which lies in a low level of the polynomial time hierarchy.