Default Assumptions and Selection Functions: A Generic Framework for Non-monotonic Logics

  • Frederik Van De Putte
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8265)


We investigate a generalization of so-called default-assumption consequence relations, obtained by replacing the consequence relation of classical logic with an arbitrary supraclassical, compact Tarski-logic, and using arbitrary selection functions on sets of sets of defaults. Both generalizations are inspired by various approaches in non-monotonic logic and belief revision. We establish some meta-theoretic properties of the resulting systems. In addition, we compare them with two other frameworks from the literature on non-monotonic logic, viz. adaptive logics and selection semantics.


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  1. 1.
    Makinson, D.: Bridges from Classical to Nonmonotonic Logic. Texts in Computing, vol. 5. King’s College Publications, London (2005)zbMATHGoogle Scholar
  2. 2.
    Lindström, S.: A semantic approach to nonmonotonic reasoning: inference operations and choice. Uppsala Prints and Reprints in Philosophy 10 (1994)Google Scholar
  3. 3.
    Makinson, D.: General patterns in nonmonotonic reasoning. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. III. Clarendon Press (1994)Google Scholar
  4. 4.
    Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50, 510–530 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gärdenfors, P., Makinson, D.: Nonmonotonic inference based on expectations. Artificial Intelligence 65, 197–245 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Levi, I.: Mild Contraction. Evaluating Loss of Information due to Loss of Belief. Clarendon Press (2004)Google Scholar
  7. 7.
    Rott, H., Pagnucco, M.: Severe withdrawal (and recovery). Journal of Philosophical Logic 29, 501–547 (2000)MathSciNetGoogle Scholar
  8. 8.
    Horty, J.F.: Reasons as Defaults. Oxford University Press (2012)Google Scholar
  9. 9.
    Gabbay, D.M.: Theoretical foundations for nonmonotonic reasoning inexpert systems. In: Apt, K. (ed.) Logics and Models of Concurrent Systems. Springer (1985)Google Scholar
  10. 10.
    Batens, D.: A universal logic approach to adaptive logics. Logica Universalis 1, 221–242 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Straßer, C.: Adaptive Logic and Defeasible Reasoning. Applications in Argumentation, Normative Reasoning and Default Reasoning. Springer (201x)Google Scholar
  12. 12.
    Batens, D.: Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency (in Progress)Google Scholar
  13. 13.
    Horsten, L., Welch, P.: The undecidability of propositional adaptive logic. Synthese 158, 41–60 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Verdée, P.: Adaptive logics using the minimal abnormality strategy are \(\Pi^1_1\)-complex. Synthese 167, 93–104 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Odintsov, S., Speranski, S.: Computability issues for adaptive logics in expanded standard format. Studia Logica (in print, 2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Frederik Van De Putte
    • 1
  1. 1.Centre for Logic and Philosophy of ScienceGhent UniversityBelgium

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