Studia Logica

, Volume 101, Issue 5, pp 933–958 | Cite as

Adaptive Logic as a Modal Logic

Article

Abstract

Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, this aim is achieved at the level of the model-theory. By proposing formulae that express the consequence relation of adaptive logic in the object-language, the same aim is also partially achieved at the syntactical level.

Keywords

Adaptive logic Modal logic Preference logic Nonmonotonic inference 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Avron, A., and I. Lev, A formula-preferential base for paraconsistent and plausible reasoning systems, Workshop on Inconsistency in Data and Knowledge (KRR-4) Int. Joint Conf. on AI (IJCAI 2001), 2001.Google Scholar
  2. 2.
    Baltag, A., and S. Smets, A qualitative theory of dynamic interactive belief revision, in G. Bonanno, W. van der Hoek, and M. Woolridge (eds.), Logic and the Foundations of Decision Theory, Amsterdam University Press, Amsterdam, 2008, pp. 11–58.Google Scholar
  3. 3.
    Batens D.: Paraconsistent extensional propositional logics. Logique & Analyse 23(90–91), 195–234 (1980)Google Scholar
  4. 4.
    Batens, D., Dynamic dialectical logics, in G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic—Essays on the inconsistent, Philosophia Verlag, München, 1989, pp. 187–217.Google Scholar
  5. 5.
    Batens, D., Inconsistency-adaptive logics, in E. Orlowska (ed.), Logic at Work—Essays dedicated to the Memory of Helena Rasiowa, Springer, Heidelberg, 1999, pp. 445–472.Google Scholar
  6. 6.
    Batens, D., A survey of inconsistency-adaptive logics, in D. Batens, C. Mortensen, G. Priest, and J. P. Van Bendegem (eds.), Frontiers of Paraconsistent Logic, Research-Studies Press, Baldock, 2000, pp. 49–73.Google Scholar
  7. 7.
    Batens D.: Minimally abnormal models in some adaptive logics. Synthese 125(1), 5–18 (2000)CrossRefGoogle Scholar
  8. 8.
    Batens, D., A universal logic approach to adaptive logics, Logica Universalis 1(1):221–242, 2007.Google Scholar
  9. 9.
    Batens, D., Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency, 2012 (manuscript).Google Scholar
  10. 10.
    Blackburn, P., M. De Rijke, and Y. Venema, Modal Logic, Cambridge University Press, Cambridge, 2001.Google Scholar
  11. 11.
    Boutilier C.: Conditional logics of normality: a modal approach. Artificial Intelligence 68, 87–154 (1990)CrossRefGoogle Scholar
  12. 12.
    Girard, P., Modal logic for belief and preference change, PhD thesis, Department of Philosophy, Stanford University, Stanford. ILLC Dissertation Series DS-2008-04, 2008.Google Scholar
  13. 13.
    Hughes, G. E., and M. J. Cresswell, A New Introduction to Modal Logic, Routledge, London, 1996.Google Scholar
  14. 14.
    Makinson D.: Five faces of minimality. Studia Logica 52(3), 339–379 (1993)CrossRefGoogle Scholar
  15. 15.
    Makinson, D., Bridges between classical and nonmonotonic logic, Logic Journal of the IGPL 11(1):69–96, 2003.Google Scholar
  16. 16.
    van Benthem, J., S. van Otterloo, and O. Roy, Preference logic, conditionals and solution concepts in games, in H. Lagerlund, S. Lindström, and R. Sliwinski (eds.), Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg, Uppsala Philosophical Studies, Uppsala, 2006, pp. 61–77.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceVrije Universiteit BrusselBrusselsBelgium

Personalised recommendations