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Nonmonotonic theories and their axiomatic varieties

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Abstract

The properties of monotonic inference systems and the properties of their theories are strongly linked. These links, however, are much weaker in nonmonotonic inference systems. In this paper we introduce the notion of anaxiomatic variety for a theory and show how this notion, instead of the notion of a theory, can be used for the syntactic and semantic analysis of nonmonotonic inferences.

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References

  • Brown, A. L. and Shoham, Y., 1988, “New Results on Semantical Nonmonotonic Reasoning,” pp. 19–26 inProceedings of the Second International Workshop on Non-Monotonie Reasoning, Springer-Verlag,Lecture Notes in Computer Science 346.

  • Fialkowska, D. and Fialkowski, J., 1990, “On Theories of Non-Monotonie Consequence Operations II,”Bulletin of the Section of Logic PAN 19, 79–83.

    Google Scholar 

  • Gabbay, D. M., 1985, “Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems,” pp. 439–457 inLogics and Models of Concurrent Systems, K. Apt ed., Springer-Verlag.

  • Kraus, S., Lehmann, D. and Magidor, M., 1990, “Nonmonotonic Reasoning, Preferential Models and Cumulative Logics,”Artificial Intelligence 44, 167–207.

    Google Scholar 

  • Makinson, D., 1988, “General Theory of Cumulative Inference,” pp. 1–18 inProceedings of the Second International Workshop on Non-Monotonie Reasoning, Springer-Verlag,Lecture Notes in Artificial Intelligence 346.

  • Makinson, D., 1994, “General Patterns in Nonmonotonic Reasoning,” inHandbook of Logic in Artificial Intelligence and Logic Programming Vol 3:Nonmonotonic Reasoning and Uncertain Reasoning, Gabbay, D. M., Hogger, C. J. and Robinson J. A., eds., Oxford University Press.

  • Malinowski, G., 1993,Many-Valued Logics, Oxford University Press.

  • Piochi, B., 1983, “Logical Matrices and Non-Structural Consequence Operations,”Studia Logica 42, 33–42.

    Google Scholar 

  • Stachniak, Z., 1988, “Two Theorems on Many-Valued Logics,”Journal of Philosophical Logic 17, 171–179.

    Google Scholar 

  • Stachniak, Z., 1993, “Algebraic Semantics for Cumulative Inference Operations,” pp. 444–449 inProceedings of the Eleventh National Conference on Artificial Intelligence, AAAI/MIT Press.

  • Wójcicki, R., 1988,Theory of Logical Calculi: Basic Theory of Consequence Operations, Kluwer.

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Stachniak, Z. Nonmonotonic theories and their axiomatic varieties. J Logic Lang Inf 4, 317–334 (1995). https://doi.org/10.1007/BF01049473

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  • DOI: https://doi.org/10.1007/BF01049473

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