Journal of Philosophical Logic

, Volume 43, Issue 5, pp 903–942 | Cite as

Preferential Semantics using Non-smooth Preference Relations

  • Frederik Van De PutteEmail author
  • Christian Straßer


This paper studies the properties of eight semantic consequence relations defined from a Tarski-logic L and a preference relation ≺ . They are equivalent to Shoham’s so-called preferential entailment for smooth model structures, but avoid certain problems of the latter in non-smooth configurations. Each of the logics can be characterized in terms of what we call multi-selection semantics. After discussing this type of semantics, we focus on some concrete proposals from the literature, checking a number of meta-theoretic properties and elaborating on their intuitive motivation. As it turns out, many of their meta-properties only hold in case ≺ is transitive. To tackle this problem, we propose slight modifications of each of the systems, showing the resulting logics to behave better at the intuitive level and in metatheoretic terms, for arbitrary ≺ .


Preferential semantics Smoothness Transitivity Selection function 


  1. 1.
    Baader, F., & Schlechta, K. (1993). A semantics for open normal defaults via a modified preferential approach. Technical Report RR-93-13, Deutsches Forschungszentrum fur Kunstliche Intelligenz (DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken, Germany.Google Scholar
  2. 2.
    Batens, D. (2000). Minimally abnormal models in some adaptive logics. Synthese, 125, 5–18.CrossRefGoogle Scholar
  3. 3.
    Bossu, G., & Siegel, P. (1985). Saturation, nonmonotonic reasoning and the closed-world assumption. Artifical Intelligence, 25, 13–63.CrossRefGoogle Scholar
  4. 4.
    Boutilier, C. (1990). Conditional logics of normality as modal systems. In AAAI 90: Proceedings of the eigth national conference on artificial intelligence (pp. 594–599).Google Scholar
  5. 5.
    Hansson, B. (1969). An analysis of some deontic logics. Nous, 3, 373–398.CrossRefGoogle Scholar
  6. 6.
    Hansson, S.O., & Grüne-Yanoff, T. (2012). Preferences In E.N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Winter 2012 edition.
  7. 7.
    Horty, J.F. (2001). Agency and deontic logic. Oxford: Oxford University Press.CrossRefGoogle Scholar
  8. 8.
    Koons, R. (2009). Defeasible reasoning In E.N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford University Press. Winter 2009 edition.Google Scholar
  9. 9.
    Kraus, S., Lehmann, D., Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.CrossRefGoogle Scholar
  10. 10.
    Lewis, D. (1973). Counterfactuals. Cambridge, Mass.: Harvard University Press.Google Scholar
  11. 11.
    Lindström, S. (1994). A semantic approach to nonmonotonic reasoning: inference operations and choice. Uppsala Prints and Reprints in Philosophy, p. 10.Google Scholar
  12. 12.
    Lycke, H. (2011). A formal explication of the search for explanations. The adaptive logics approach to abductive reasoning. Logic Journal of the IGPL, 20(2), 497–516.CrossRefGoogle Scholar
  13. 13.
    Makinson, D. (1994). General patterns in nonmonotonic reasoning. In Handbook of logic in artificial intelligence and logic programming (Vol. III). Clarendon Press.Google Scholar
  14. 14.
    Makinson, D. (2012). Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference. Synthese, 186, 511–529.CrossRefGoogle Scholar
  15. 15.
    Meheus, J., Straßer, C., Verdée, P. Which style of reasoning to choose in the face of conflicting information? Journal of Logic and Computation. In print.Google Scholar
  16. 16.
    Priest, G. (1991). Minimally inconsistent LP. Studia Logica, 50, 321–331.CrossRefGoogle Scholar
  17. 17.
    Schlechta, K. (1996). A two-stage approach to first order default reasoning. Fundamenta Informaticae, 28(3-4), 377–402.Google Scholar
  18. 18.
    Schlechta, K. (2004). Coherent systems. Elsevier.Google Scholar
  19. 19.
    Schumm, G.F. (1987). Transitivity, preference and indifference. Philosophical Studies, 52, 435–437.CrossRefGoogle Scholar
  20. 20.
    Shoham, Y. (1987). A semantical approach to nonmonotonic logics. In M.L. Ginsberg (Ed.), Readings in non-monotonic reasoning (pp. 227–249). Los Altos: Morgan Kaufmann.Google Scholar
  21. 21.
    Straßer, C., & Van De Putte, F. Dynamic proof theories for selection semantics: a generic adaptive logic framework. Unpublished paper.Google Scholar
  22. 22.
    Straßer, C., & Šešelja D. (2010). Towards the proof-theoretic unification of Dung’s argumentation framework: an adaptive logic approach. Journal of Logic and Computation, 21, 133–156. Online access, doi:  10.1093/logcom/exq015.CrossRefGoogle Scholar
  23. 23.
    Van De Putte, F., & Straßer, C. (2012). Extending the standard format of adaptive logics to the prioritized case. Logique et Analyse, 220, 601–641.Google Scholar
  24. 24.
    Voorbraak, F. (1993). Preference-based semantics for nonmonotonic logics. In R. Bajcsy (Ed.), IJCAI (pp. 584–591). Morgan Kaufmann.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceGhent UniversityGentBelgium

Personalised recommendations