Abstract
In [1,2] a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded semantics can formally be understood as a stratified version of the Fitting (or Kripke-Kleene) semantics. The constructions leading to this result, however, show a certain asymmetry which is not readily understood. We will study this situation here with the result that we will obtain a coherent picture of relations between different semantics.
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Hitzler, P., Wendt, M.: The well-founded semantics is a stratified Fitting semantics. In: Jarke, M., Koehler, J., Lakemeyer, G. (eds.) KI 2002. LNCS (LNAI), vol. 2479, pp. 205–221. Springer, Heidelberg (2002)
Hitzler, P., Wendt, M.: A uniform approach to logic rogramming semantics. Technical Report WV–02–14, Knowledge Representation and Reasoning Group, Artificial Intelligence Institute, Department of Computer Science, Dresden University of Technology, Dresden, Germany (2002) (submitted)
Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)
Lloyd, J.W.: Foundations of Logic Programming. Springer, Berlin (1988)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Logic Programming, Proceedings of the 5th International Conference and Symposium on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)
van Gelder, A., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38, 620–650 (1991)
Fitting, M.: A Kripke-Kleene-semantics for general logic programs. The Journal of Logic Programming 2, 295–312 (1985)
Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann, Los Altos (1988)
Przymusinski, T.C.: On the declarative semantics of deductive databases and logic programs. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 193–216. Morgan Kaufmann, Los Altos (1988)
Fitting, M.: Fixpoint semantics for logic programming — A survey. Theoretical Computer Science 278, 25–51 (2002)
Denecker, M., Marek, V.W., Truszczynski, M.: Approximating operators, stable operators, well-founded fixpoints and applications in non-monotonic reasoning. In: Minker, J. (ed.) Logic-based Artificial Intelligence, pp. 127–144. Kluwer Academic Publishers, Boston (2000)
Przymusinski, T.C.: Well-founded semantics coincides with three-valued stable semantics. Fundamenta Informaticae 13, 445–464 (1989)
van Gelder, A.: The alternating fixpoint of logic programs with negation. In: Proceedings of the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Philadelphia, Pennsylvania, pp. 1–10. ACM Press, New York (1989)
Dung, P.M., Kanchanasut, K.: A fixpoint approach to declarative semantics of logic programs. In: Lusk, E.L., Overbeek, R.A. (eds.) Logic Programming, Proceedings of the North American Conference 1989, NACLP 1989, Cleveland, Ohio, pp. 604–625. MIT Press, Cambridge (1989)
Fages, F.: Consistency of Clark’s completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60 (1994)
Wendt, M.: Unfolding the well-founded semantics. Journal of Electrical Engineering, Slovak Academy of Sciences 53, 56–59 (2002); Proceedings of the 4th Slovakian Student Conference in Applied Mathematics, Bratislava (April 2002)
Hitzler, P.: Circular belief in logic programming semantics. Technical Report WV– 02–13, Knowledge Representation and Reasoning Group, Artificial Intelligence Institute, Department of Computer Science, Dresden University of Technology, Dresden, Germany (2002)
Jachymski, J.: Order-theoretic aspects of metric fixed-point theory. In: Kirk, W.A., Sims, B. (eds.) Handbook of Metric Fixed Point Theory, pp. 613–641. Kluwer Academic Publishers, Dordrecht (2001)
Fitting, M.: Bilattices and the semantics of logic programming. The Journal of Logic Programming 11, 91–116 (1991)
Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D., Maibaum, T.S. (eds.) Handbook of Logic in Computer Science, vol. 3. Clarendon, Oxford (1994)
Przymusinska, H., Przymusinski, T.C.: Weakly stratified logic programs. Fundamenta Informaticae 13, 51–65 (1990)
Wang, K.: A comparative study of well-founded semantics for disjunctive logic programs. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 133–146. Springer, Heidelberg (2001)
Mateis, C.: Quantitative disjunctive logic programming: Semantics and computation. AI communications 13, 225–248 (2000)
Leite, J.A.: Evolving Knowledge Bases. Frontiers of Artificial Intelligence and Applications, vol. 81. IOS Press, Amsterdam (2003)
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Hitzler, P. (2003). Towards a Systematic Account of Different Logic Programming Semantics. In: Günter, A., Kruse, R., Neumann, B. (eds) KI 2003: Advances in Artificial Intelligence. KI 2003. Lecture Notes in Computer Science(), vol 2821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39451-8_9
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