Abstract
Default logic is one of the principal formalisms for nonmonotonic, reasoning. In this paper, we study algorithms for computing extensions for a class of general propositional default theories. We focus on the problem of partitioning a given set of defaults into a family of its subsets. Then we investigate how the results obtained for these subsets can be put together to achieve the extensions of the original theory. The method we propose is designed to prune the search space and reduce the number of calls to propositional provability procedure. It also constitutes a simple and uniform framework for the design of parallel algorithms for computing extensions.
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References
K. Apt and H.A. Blair. Arithmetical classification of perfect models of stratified programs. Fundamenta Informaticac, 12:1–17, 1990.
K. Apt, H.A. Blair, and A. Walker. Towards a theory of declarative knowledge. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–142, Los Altos, CA, 1987. Morgan Kaufmann.
R. Ben-Eliyahu and R. Dechter. Propositional semantics for disjunctive logic programs. In K. Apt, editor, Proceedings of International Joint Conference and Symposium on Logic Programming, pages 813–827, Cambridge, MA, 1992, MIT Press.
N. Bidoit and Ch. Froidevaux. General logical databases and programs: Default logic semantics and stratification. Information and Computation, 91:15–54, 1991.
P. Gholewiński, W. Marek, A. Mikitiuk and M. Truszczyński. Experimenting with default logic In Proceedings of ICLP-95, MIT Press, to appear.
P. Cholewiński. Seminormal stratified default theories. Technical Report 238-93, University of Kentucky, Lexington, 1993.
P. Cholewiński. Stratified default theories. In Proceedings of CSL-94, Springer Verlag, to appear.
D. W. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.
M. Gelfond. On stratified autoepistemic theories. In Proceedings of AAAI-87, pages 207–211, Los Altos, CA., 1987. American Association for Artificial Intelligence, Morgan Kaufmann.
G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2:397–425, 1992.
H.A. Kautz and B. Selman. Hard problems for simple default logics. In Principles of Knowledge Representation and Reasoning, pages 189–197, San Mateo, CA., 1989. Morgan Kaufmann.
W. Marek and M. Truszczyński. Autoepistemic logic. Journal of the ACM, 38:588–619, 1991.
W. Marek and M. Truszczyński. Nonmonotonic Logics; Context-Dependent Reasoning. Springer-Verlag, 1993.
I. Niemelä. On the decidability and complexity of autoepistemic reasoning. Fundamenta Informaticae, 1992.
R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.
M. Truszczyński. Stratified modal theories and iterative expansions. Technical Report 159-90, Department of Computer Science, University of Kentucky, 1990.
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Cholewiński, P. (1995). Reasoning with stratified default theories. In: Marek, V.W., Nerode, A., Truszczyński, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 1995. Lecture Notes in Computer Science, vol 928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59487-6_20
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DOI: https://doi.org/10.1007/3-540-59487-6_20
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