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.
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References
H. Andreka and I. Nemeti, The generalized completeness of Horn predicate logic as a programming language, Acta Cybernetica 4 (1978) 3–10.
K.R. Apt, Logic programming, in: Handbook of Theoretical Computer Science, ed. J. van Leeuven (MIT Press, 1990).
K. Apt, H.A. Blair and A. Walker, Towards a theory of declarative knowledge, in: Foundations of Deductive Databases and Logic Programming, ed. J. Minker (Morgan Kaufmann, 1987) pp. 89–142.
K.R. Apt and H.A. Blair, Arithmetical classification of perfect models of stratified programs, Fundamenta Informaticae 13 (1990) 1–17.
D.R. Bean, Effective coloration, J. Symbolic Logic 41 (1976) 469–480.
D. Cenzer and J.B. Remmel, Index sets for П 01 -classes, Annals of Pure and Applied Logic 93 (1998) 3–61.
D. Cenzer and J.B. Remmel, П 01 -classes in mathematics, in: Handbook of Recursive Mathematics, Vol. 2, eds. Yu.L. Ershov, S.S. Goncharov, A. Nerode and J.B. Remmel, Studies in Logic and the Foundations of Mathematics, Vol. 139 (Elsevier, 1998) pp. 623–822.
D. Cenzer, J.B. Remmel and A.K.C.S. Vanderbilt, Locally determined logic programs, in: Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR99) (Springer, 1999) pp. 34–49.
P. Cholewi´nski, Stratified default theories, in: Proceedings of CSL'94, Lecture Notes in Computer Science, Vol. 933 (Springer, 1995).
A. Ferry, A topological characterization of the stable and minimal model classes of propositional logic programs, Ann. Math. Artificial Intelligence 15 (1995), 325–355.
M. Gelfond and V. Lifschitz, The stable semantics for logic programs, in: Proceedings of the 5th International Symposium of Logic Programming (MIT Press, 1988) pp. 1070–1080.
C.G. Jockusch and R.I. Soare, Degrees of members of П 01 classes, Paciific Journal of Mathematics 40 (1972) 605–616.
C.G. Jockusch and R.I. Soare, П 01 classes and degrees of theories, Transactions of American Mathematical Society 173 (1972) 33–56.
V. Lifschitz and H. Turner, Splitting a logic program, in: Proceedings of the Eleventh International Conference on Logic Programming, ed.. Van Hentenryck (1994) pp. 23–37.
W. Marek, A. Nerode and J.B. Remmel, Nonmonotonic rule systems I, Annals of Mathematics and Artificial Intelligence 1 (1990) 241–273.
W. Marek, A. Nerode and J.B. Remmel, Nonmonotonic rule systems II, Annals of Mathematics and Artificial Intelligence 5 (1992) 229–264.
W. Marek, A. Nerode and J.B. Remmel, How complicated is the set of stable models of a recursive logic program? Ann. Pure and Appl. Logic 56 (1992), 119–135.
W. Marek, A. Nerode and J.B. Remmel, The stable models of predicate logic programs, in: Proceedings of International Joint Conference and Symposium on Logic Programming, ed. K.R. Apt (MIT Press, 1992) pp. 446–460.
W. Marek, A. Nerode and J.B. Remmel, The stable models of predicate logic programs, Journal of Logic Programming 21 (1994) 129–154.
W. Marek, A. Nerode and J.B. Remmel, Context for belief revision: Forward chaining-normal nonmonotonic rule systems, Annals of Pure and Applied Logic 67 (1994) 269–324.
W. Marek and J.B. Remmel, The failure of compactness in nonmonotonic reasoning systems (in preparation).
R. Reiter, A logic for default reasoning, Artificial Intelligence 13 (1980) 81–132.
D. Scott, Domains for denotational semantics, in: Proceedings of ICALP-82 (Springer, 1982) pp. 577–613.
R.M. Smullyan, Theory of Formal Systems, Annals of Mathematics Studies, Vol. 47 (Princeton University Press, 1961).
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Cenzer, D., Remmel, J.B. & Vanderbilt, A. Locally Determined Logic Programs and Recursive Stable Models. Annals of Mathematics and Artificial Intelligence 40, 225–262 (2004). https://doi.org/10.1023/B:AMAI.0000012868.41613.e7
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DOI: https://doi.org/10.1023/B:AMAI.0000012868.41613.e7