System JLZ – rational default reasoning by minimal ranking constructions. (English) Zbl 1076.68076
Summary: We present a powerful quasi-probabilistic default formalism for graded defaults based on a well-motivated canonical ranking construction procedure, System JLZ. It implements the minimal construction paradigm and verifies the major inference principles and inheritance desiderata, including rational monotony for propositions and structured cumulativity for default conditionals. With help from a structured ranking semantics for defaults, it also avoids some drawbacks of semi-qualitative entropy maximization and other competing accounts.
MSC:
| 68T27 | Logic in artificial intelligence |
Keywords:
Default reasoning; Conditionals; Nonmonotonic inference; Belief revision; Ranking measures; Possibility; Non-standard probability; Maximum entropy; System ZReferences:
| [1] | Bacchus, F.; Grove, A. J.; Koller, D.; Halpern, J. Y., Statistical foundations for default reasoning, Artificial Intelligence, 87, 75-143 (1997) · Zbl 1506.68146 |
| [2] | Benferhat, S.; Saffiotti, A.; Smets, P., Belief functions and default reasoning, Artificial Intelligence, 122, 1-69 (2000) · Zbl 0948.68112 |
| [3] | Bourne, R.; Parsons, S., Maximum entropy and variable strength defaults, (Proceedings of IJCAI ’99 (1999), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) · Zbl 1045.68136 |
| [4] | Boutilier, C., Conditional logics of normality: A modal approach, Artificial Intelligence, 68, 87-154 (1994) · Zbl 0811.68114 |
| [5] | Dubois, D.; Prade, H., Possibility theory: Qualitative and quantitative aspects, (Smets, P., Quantified Representation of Uncertainty and Imprecision, Handbook on Defeasible Reasoning and Uncertainty Management Systems, Vol. 1 (1998), Kluwer Academic: Kluwer Academic Dordrecht) · Zbl 0924.68182 |
| [6] | Friedman, N.; Halpern, J., Plausibility measures and default reasoning, J. ACM, 48, 4, 648-685 (2001) · Zbl 1127.68438 |
| [7] | Geffner, H.; Pearl, J., Conditional entailment: Bridging two approaches to default reasoning, Artificial Intelligence, 53, 209-244 (1992) · Zbl 1193.68235 |
| [8] | Goldszmidt, M.; Morris, P.; Pearl, J., A maximum entropy approach to nonmonotonic reasoning, IEEE Trans. Pattern Anal. Mach. Intelligence, 15, 220-232 (1993) |
| [9] | Goldszmidt, M.; Pearl, J., Qualitative probabilities for default reasoning, belief revision, and causal modeling, Artificial Intelligence, 84, 57-112 (1996) · Zbl 1497.68457 |
| [10] | Halpern, J. Y.; Koller, D., Representation dependence in probabilistic inference, (Proceedings of IJCAI ’95 (1995), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) · Zbl 1080.68686 |
| [11] | Hill, L. C.; Paris, J. B., When maximum entropy gives the rational closure, J. Logic Comput., 13, 51-68 (2003) · Zbl 1020.03014 |
| [12] | Jaynes, E. T., Where do we stand on maximum entropy?, (Rosenkrantz, R. D.; Jaynes, E. T., Papers on Probability, Statistics and Statistical Physics (1983), Reidel: Reidel Dordrecht) · Zbl 0501.01026 |
| [13] | Kern-Isberner, G., Handling conditionals adequately in uncertain reasoning, (Proceedings of ECSQARU 2001 (2001), Springer: Springer Berlin) · Zbl 1001.68144 |
| [14] | Kraus, S.; Lehmann, D.; Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, 44, 167-207 (1990) · Zbl 0782.03012 |
| [15] | Lehmann, D., Another perspective on default reasoning, Ann. Math. Artificial Intelligence, 15, 1, 61-82 (1995) · Zbl 0857.68096 |
| [16] | Lehmann, D.; Magidor, M., What does a conditional knowledge base entail?, Artificial Intelligence, 55, 1-60 (1992) · Zbl 0762.68057 |
| [17] | Pearl, J., System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning, (Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge (1990), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) |
| [18] | Paris, J. B.; Vencovska, A., A note on the inevitability of maximum entropy, Internat. J. Approx. Reason., 4, 183-223 (1990) · Zbl 0697.68089 |
| [19] | Spohn, W., Ordinal conditional functions: A dynamic theory of epistemic states, (Harper, W. L.; Skyrms, B., Causation in Decision, Belief Change, and Statistics (1988), Kluwer Academic: Kluwer Academic Dordrecht) |
| [20] | Spohn, W., A general non-probabilistic theory of inductive reasoning, (Uncertainty in Artificial Intelligence, Vol. 4 (1990), North-Holland: North-Holland Amsterdam) |
| [21] | Spohn, W., Ranking Functions, AGM Style, (Hansson, B.; Halldén, S.; Sahlin, N.-E.; Rabinowicz, W., Internet Festschrift for Peter Gärdenfors (1999), Lund) |
| [22] | Shore, J. E.; Johnson, R. W., Axiomatic derivation of the principle of cross-entropy minimization, IEEE Trans. Inform. Theory, IT-26, 1, 26-37 (1980) · Zbl 0429.94011 |
| [23] | van den Dries, L.; Macintyre, A.; Marker, D., The elementary theory of restricted analytic fields with exponentiation, Ann. Math., 140, 182-205 (1994) · Zbl 0837.12006 |
| [24] | Weydert, E., Qualitative magnitude reasoning. Towards a new semantics for default reasoning, (Dix, J.; etal., Nonmonotonic and Inductive Reasoning (1991), Springer: Springer Berlin) · Zbl 0792.68174 |
| [25] | Weydert, E., Plausible inference for default conditionals, (Proceedings of ECSQARU ’93 (1993), Springer: Springer Berlin) |
| [26] | Weydert, E., General belief measures, (Proceedings of UAI ’94 (1994), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) |
| [27] | Weydert, E., Defaults and infinitesimals. Defeasible inference by non-Archimedean entropy maximization, (Proceedings of UAI ’95 (1995), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) |
| [28] | Weydert, E., Default entailment. A preferential construction semantics for defeasible inference, (Nebel, B.; Dreschler-Fischer, L., Proceedings of KI ’95 (1995), Springer: Springer Berlin) |
| [29] | Weydert, E., System J—Revision entailment, (Proceedings of FAPR ’96 (1996), Springer: Springer Berlin) · Zbl 1419.68137 |
| [30] | Weydert, E., System JZ—How to build a canonical ranking model of a default knowledge base, (Proceedings of KR ’98 (1998), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) |
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