Abstract
We give an introduction to default logic, one of the most prominent nonmonotonic logics. Emphasis is given to providing an operational interpretation for the semantics of default logic that is usually defined by fixed-point concepts (extensions). We introduce a process model that allows to exactly calculate the extensions of a default theory in a quite easy way. We give a prototypical implementation of processes in Prolog able to handle the examples that can be found in literature. Finally, we develop some theoretical results about default logic and give new simple proofs using the process model as a theoretical tool.
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Antoniou, G. & Langetepe, E. (1994). Relating Some Classes of Default Logic to Normal Logical Programs with Standard Semantics.Journal of Automated Reasoning (submitted).
Besnard, P. (1989).An Introduction to Default Logic. Springer.
Bibel, W. (1984). Knowledge Representation from a Deductive Point of View.Proc. IFAC Symposium Artificial Intelligence. Pergamon Press: Oxford.
Brewka, G. (1991a).Nonmonotonic Reasoning: Logical Foundations of Commonsense. Cambridge University Press 1991.
Brewka, G. (1991b). Cumulative Default Logic — In Defence of Nonmonotonic Inference Relations.Artificial Intelligence 51: 183–205.
Brewka, G. (1992).A Framework for Cumulative Default Logics. Technical Report TR-92-042, International Computer Science Institute, Berkeley.
Dimopoulos, Y. & Magirou, V. (1994). A Graph Theoretic Approach to Default Logic.Information and Computation (forthcoming).
Etherington, D. W. (1987). Formalizing Nonmonotonic Reasoning Systems.Artificial Intelligence 31: 41–85.
Froidevaux, C. & Menjin, J. (1992).A Framework for Default Logics. Technical Report 755, Universite de Paris-Sud.
Gelfond, M., Przymusinska, H., Lifschitz, V. & Truszczynski, M. (1991). Disjunctive Defaults.Proc. 2nd International Conference on Knowledge Representation and Reasoning. Morgan Kaufmann.
Hopkins, M. S. (1993). Default Logic: Orderings and Extensions. InProc. European Conference on Symbolic and Quantitative Approaches to Uncertainty, Springer LNCS 747.
Junker, U. & Konolige, K. (1990). Computing the Extensions of Autoepistemic and Default Logics with a TMS. InProc. AAAI-90, 278–283.
Levy, F. (1991). Computing Extensions of Default Theories. InProc. European Conference on Symbolic and Quantitative Approaches to Uncertainty, Springer LNCS 548.
Lucaszewicz, W. (1990).Non-Monotonic Reasoning. Ellis Horwood.
Makinson, D. (1989). General Theory of Cumulative Inference. InProc. 2nd International Workshop on Nonmonotonic Reasoning, LNCS 346, Springer.
Marek, V. W. & Truszczynski, M. (1993).Nonmonotonic Logic. Springer 1993.
Mendelson, E. (1978).Introduction to Mathematical Logic. 2. ed., Van Nostrand: New York.
Moore, R. C. (1982). The Role of Logic in Knowledge Representation and Commonsense Reasoning.Proc. AAAI-82.
Nilsson, N. J. (1991). Logic and Artificial Intelligence.Artificial 47: 31–56.
Poole, D. (1988). A Logical Framework for Default Reasoning.Artificial Intelligence 36.
Reiter, R. (1980). A Logic for Default Reasoning.Artificial Intelligence 13: 81–132.
Schwind, C. (1990). A Tableau-Based Theorem Prover for a Decidable Subset of Default Logic. InProc. 10th International Conference on Automated Deduction. Springer LNC 449.
Sperschneider, V. & Antoniou, G. (1991).Logic: A Foundation for Computer Science. Addison-Wesley.
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Antoniou, G., Sperschneider, V. Operational concepts of nonmonotonic logics part 1: Default logic. Artif Intell Rev 8, 3–16 (1994). https://doi.org/10.1007/BF00851348
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DOI: https://doi.org/10.1007/BF00851348