Generalizing the Standard Format

Part of the Trends in Logic book series (TREN, volume 38)


In this chapter we generalize the standard format of adaptive logics and thereby introduce an interesting larger class of adaptive logics that can be characterized in a simple and intuitive way. We demonstrate that the new format overcomes the two shortcomings of the standard format. On the one hand, logics with both qualitative and quantitative rationales can be expressed in it. On the other hand, the format is expressive enough to allow for the handling of priorities in various ways. We show that many adaptive logics that have been considered in the literature fall within this larger class -for instance adaptive logics in the standard format, adaptive logics with counting strategies, lexicographic adaptive logics-and that the characterization of this class offers many possibilities to formulate new logics. One of the advantages of the format studied in this chapter is that a lot of meta-theory comes for free for any logic formulated in it. We show that adaptive logics formulated in it are always sound and complete. Furthermore, many of the meta-theoretic properties that are usually associated with the standard format (such as cumulativity, fixed point property, (strong) reassurance, etc.) also hold for rich subclasses of logics formulated in the new format.



The results presented in this chapter are the product of joint research with Frederik Van De Putte.


  1. 1.
    Primiero, G., Meheus, J.: Majority merging by adaptive counting. Synthese 165, 203–223 (2008)CrossRefGoogle Scholar
  2. 2.
    Primiero, G., Meheus, J.: Quasi-merging and pure-arbitration on information for the family of adaptive logics ADM. In: Proceeding of the Workshop on Logic and Intelligent Interaction, ESSLLI, pp. 21–30. Hamburg (2008)Google Scholar
  3. 3.
    Primiero, G., Meheus, J.: Adaptive arbitration by variant counting on commuatative bases with weights. In: Proceedings of the Fusion 2008 Conference, Köln, 1–3 July, pp. 1374–1380. ISBN 978-3-00-024883-2 (2008)Google Scholar
  4. 4.
    Putte, F.V.D., Straßer, C.: Extending the standard format of adaptive logics to the prioritized case. Logique at Analyse 55(220), 601–641 (2012)Google Scholar
  5. 5.
    Putte, F.V.D., Straßer, C.: A logic for prioritized normative reasoning. J. Logic Comput. 23(3), 568–583 (2013)Google Scholar
  6. 6.
    Putte, F.V.D.: Generic formats for prioritized adaptive logics. with applications in deontic logic, abduction and belief revision. Ph.D. thesis, Ghent University (March 28th, 2012)Google Scholar
  7. 7.
    Verdée, P.: Combining a rich paraconsistent negation with classical negation by means of an infinitely valued logic (in preparation)Google Scholar
  8. 8.
    Shoham, Y.: A semantical approach to nonmonotonic logics. In: Ginsberg, M.L. (ed.) Readings in Non-Monotonic Reasoning, pp. 227–249. Morgan Kaufmann, Los Altos (1987)Google Scholar
  9. 9.
    Shoham, Y.: Reasoning about change: time and causation from the standpoint of artificial intelligence. Cambridge, MIT Press (1988)Google Scholar
  10. 10.
    McCarthy, J.: Circumscription—a form of non-monotonic reasoning. Artif. Intell. 13, 27–29 (1980)CrossRefGoogle Scholar
  11. 11.
    Schlechta, K.: Coherent Systems. Elsevier, Amsterdam (2004)Google Scholar
  12. 12.
    Lindström, S.: A semantic approach to nonmonotonic reasoning: inference operations and choice. Uppsala Prints and Reprints in, Philosophy, no 10, Department of Philosophy, University of Uppsala (1994)Google Scholar
  13. 13.
    Makinson, D.: General patterns in nonmonotonic reasoning. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. III, pp. 35–110. Clarendon Press, Oxford (1994)Google Scholar
  14. 14.
    Rescher, N., Manor, R.: On inference from inconsistent premises. Theor. Decis. 1, 179–217 (1970)CrossRefGoogle Scholar
  15. 15.
    Meheus, J., Straßer, C., Verdée, P.: Which Style of Reasoning to Choose in the Face of Conflicting Information? J. Logic. Comput. (forthcoming)Google Scholar
  16. 16.
    Putte, F.V.D.: Hierarchic adaptive logics. Logic J. IGPL 20(1), 45–72 (2012)CrossRefGoogle Scholar
  17. 17.
    Putte, F.V.D., Straßer, C.: Three formats of prioritized adaptive logics: a comparative study. Logic J. IGPL 2(21), 127–159 (2013)CrossRefGoogle Scholar
  18. 18.
    Batens, D.: Minimally abnormal models in some adaptive logics. Synthese 125, 5–18 (2000)CrossRefGoogle Scholar
  19. 19.
    Bossu, G., Siegel, P.: Saturation, nonmonotonic reasoning and the closed-world assumption. Artif. Intell. 25, 13–63 (1985)CrossRefGoogle Scholar
  20. 20.
    Goldzsmidt, M., Morris, P., Pearl, J.: Amaximumentropy approach to nonmonotonic reasoning. IEEE Trans. Pattern Anal. Mach. Intell. 15(3), 220–232 (1993)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.GhentBelgium

Personalised recommendations