Journal of Logic, Language and Information

, Volume 18, Issue 4, pp 515–539

Hybrid Counterfactual Logics

David Lewis Meets Arthur Prior Again


The purpose of this paper is to argue that the hybrid formalism fits naturally in the context of David Lewis’s counterfactual logic and that its introduction into this framework is desirable. This hybridization enables us to regard the inference “The pig is Mary; Mary is pregnant; therefore the pig is pregnant” as a process of updating local information (which depends on the given situation) by using global information (independent of the situation). Our hybridization also has the following technical advantages: (i) it preserves the completeness and decidability of Lewis’s logic; (ii) it allows us to characterize the Limit Assumption as a proof-rule with some side-conditions; and (iii) it enables us to establish a general Kripke completeness result by using the proof-rule corresponding to the Limit Assumption.


Counterfactual logic David Lewis Contextually definite description Hybrid logic Arthur Prior The limit assumption Strong completeness Decidability Bisimulation Pure completeness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Areces C., ten Cate B. (2007) Hybrid logics. In: Blackburn P., Benthem J., Wolter F.(eds) Handbook of modal logic.. Elsevier, Amsterdam, pp 821–868CrossRefGoogle Scholar
  2. Blackburn, P. (1990). Nominal tense logic and other sorted intensional frameworks. PhD thesis, Centre for Cognitive Science, University of Edinburgh.Google Scholar
  3. Blackburn P. (1993) Nominal tense logic. Notre Dame Journal of Formal Logic 34: 56–83CrossRefGoogle Scholar
  4. Blackburn P. (1994) Tense, temporal reference and tense logic. Journal of Semantics 11: 83–101CrossRefGoogle Scholar
  5. Blackburn P. (2006) Arthur Prior and hybrid logic. Synthese 150(3): 329–372CrossRefGoogle Scholar
  6. Blackburn P., de Rijke M., Venema Y. (2001) Modal logic. Cambridge tracts in theoretical computer science. Cambridge University Press, CambridgeGoogle Scholar
  7. Blackburn, P., & van Benthem, J. (2007). Modal logic: A semantic perspective. In P. Blackburn, J. van Benthem, & F. Wolter (Eds.), Handbook of modal logic (pp. 1–84). Amsterdam: Elsevier.Google Scholar
  8. Blackburn P., ten Cate B. (2006) Pure extensions, proof rules, and hybrid axiomatics. Studia Logica 84: 277–322CrossRefGoogle Scholar
  9. Grahne G. (1998) Updates and counterfactuals. Journal of Logic and Computation 8(1): 87–117CrossRefGoogle Scholar
  10. Lewis D. (1973) Counterfactuals. Blackwell Publishing, OxfordGoogle Scholar
  11. Nute, D., & Cross, C. B. (2001). Conditional logic. In Gabbay, D.M., & Guenthner, F. (Eds)., Handbook of philosophical logic (2nd ed., Vol. 4, pp. 1–98). Dordrecht: Kluwer Academic Publishers.Google Scholar
  12. Stalnaker, R. (1968). A theory of conditionals. In N. Rescher (Ed.), Studies in logical theory, American Philosophical Quarterly Monograph Series (Vol. 2, pp. 98–112). Oxford: Blackwell.Google Scholar
  13. ten Cate B., Litak T. (2007) Topological perspective on the hybrid proof rules. Electronic Notes in Theoretical Computer Science 174(6): 79–94CrossRefGoogle Scholar
  14. ten Cate B., Marx M., Viana P. (2005) Hybrid logics with Sahlqvist axioms. Logic Journal of the IGPL 13(3): 293–300CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Humanistic Informatics, Graduate School of LettersKyoto UniversityKyotoJapan

Personalised recommendations