Conclusions
We have proved a number of results on nonmonotonic rule systems. This theory allows us to capture many constructions appearing in the current literature on the logical foundations of artificial intelligence.
Our results provide additional tools tying these constructs with traditional methods of logic and recursion theory.
In a sequel we shall deal with rule systems containing variables in the rules and with predicate logics. We shall prove results related to the properties of recursive systems that are not necessarily highly recursive. We shall also explore connections with
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References
K.R. Apt and H.A. Blair, Classification of perfect models of stratified programs, Fundamenta Informaticae 13 (1990) 1–17.
R.P. Dilworth, A decomposition theorem for partially ordered sets, Ann. Math. 51 (1950) 161–165.
D.W. Etherington, Formalizing nonmonotonic reasoning systems, Art. Int. J. 31 (1987) 41–85.
M. Gelfond and V. Lifschitz, Stable semantics for logic programs, in:Proc. 5th Int. Symp. on Logic Programming, Seattle (1988) pp. 1070–1080.
C.G. Jockusch and T.G. McLaughlin, Countable retracing functions andΠ 02 predicates, Pacific J. Math. 30 (1972) 69–93.
C.G. Jockusch and R.I. Soare,Π 01 classes and degrees of theories, Trans. Amer. Math. Soc. 173 (1972) 33–56.
C.G. Jockusch and R.I. Soare, Degrees of members ofΠ 01 classes, Pacific J. Math. 40 (1972) 605–616.
W. Just, private electronic communication.
K. Kuratowski and A. Mostowski,Set Theory (North-Holland, 1977).
A. Manaster and J. Rosenstein, Effective matchmaking, Proc. London Math. Soc. 25 (1972) 615–654.
W. Marek and A. Nerode, Decision procedure for default logic (1990) available as a report of the Mathematical Sciences Institute, Cornell University.
W. Marek, A. Nerode and J. Remmel, A theory of nonmonotonic rule systems I, Ann. Math. Art. Int. 1 (1990) 241–273.
W. Marek, A. Nerode and J. Remmel, How complicated is the set of stable models of a recursive logic program?, Ann. Pure Appl. Logic (Hyhill vol.) (1992), to appear.
W. Marek and M. Truszczyński, Autoepistemic Logic, J. ACM (1991) to appear.
W. Marek and M. Truszczyński, Relating autoepistemic and default logics, in:Principles of Knowledge Representation and Reasoning (Morgan Kaufmann, San Mateo, 1989) (Full version available as Technical Report 144-89, Computer Science, University of Kentucky, Lexington, KY 40506-0027, 1989.)
R. Reiter, A logic for default reasoning, Art. Int. 13 (1980) 81–132.
J.B. Remmel, Graph colorings and recursively boundedΠ 01 classes, Ann. Pure Appl. Logic 32 (1986) 185–194.
R.M. Smullyan,First-Order Logic (Springer, 1968).
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Work partially supported by NSF grant RII-86-10671 and Kentucky EPSCoR program and ARO contract DAAL03-89-K-0124.
Work partially supported by NSF grant DMS-89-02797 and ARO contract DAAG629-85-C-0018.
Work partially supported by NSF grants DMS-87-02473 and DMS-90-06413.
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Marek, W., Nerode, A. & Remmel, J. A theory of nonmonotonic rule systems II. Ann Math Artif Intell 5, 229–263 (1992). https://doi.org/10.1007/BF01543477
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DOI: https://doi.org/10.1007/BF01543477