Skip to main content
Log in

Adaptive Logic as a Modal Logic

  • Published:
Studia Logica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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.

  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.

  3. Batens D.: Paraconsistent extensional propositional logics. Logique & Analyse 23(90–91), 195–234 (1980)

    Google Scholar 

  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.

  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.

  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.

  7. Batens D.: Minimally abnormal models in some adaptive logics. Synthese 125(1), 5–18 (2000)

    Article  Google Scholar 

  8. Batens, D., A universal logic approach to adaptive logics, Logica Universalis 1(1):221–242, 2007.

    Google Scholar 

  9. Batens, D., Adaptive Logics and Dynamic Proofs. Mastering the Dynamics of Reasoning, with Special Attention to Handling Inconsistency, 2012 (manuscript).

  10. Blackburn, P., M. De Rijke, and Y. Venema, Modal Logic, Cambridge University Press, Cambridge, 2001.

  11. Boutilier C.: Conditional logics of normality: a modal approach. Artificial Intelligence 68, 87–154 (1990)

    Article  Google Scholar 

  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.

  13. Hughes, G. E., and M. J. Cresswell, A New Introduction to Modal Logic, Routledge, London, 1996.

  14. Makinson D.: Five faces of minimality. Studia Logica 52(3), 339–379 (1993)

    Article  Google Scholar 

  15. Makinson, D., Bridges between classical and nonmonotonic logic, Logic Journal of the IGPL 11(1):69–96, 2003.

    Google Scholar 

  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.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Patrick Allo.

Additional information

Presented by Heinrich Wansing

Rights and permissions

Reprints and permissions

About this article

Cite this article

Allo, P. Adaptive Logic as a Modal Logic. Stud Logica 101, 933–958 (2013). https://doi.org/10.1007/s11225-012-9403-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-012-9403-1

Keywords

Navigation