Skip to main content
Log in

Some Embedding Theorems for Conditional Logic

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

We prove some embedding theorems for classical conditional logic, covering ‘finitely cumulative’ logics, ‘preferential’ logics and what we call ‘semi-monotonic’ logics. Technical tools called ‘partial frames’ and ‘frame morphisms’ in the context of neighborhood semantics are used in the proof.

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

  • Asher, N. and Morreau, M. (1991): Common Sense Entailment: A Modal Theory of Nonmonotonic Reasoning, Proceedings of the 12th IJCAI, Morgan Kaufmann, Los Altos, CA, pp. 387–392.

    Google Scholar 

  • Ben-David, S. and Ben-Eliyahu-Zohary, R. (2000): A Modal Logic For Subjective Default Reasoning, Artif. Intell. 116, 217–236.

    Article  Google Scholar 

  • Boutilier, C. (1994): Conditional Logics of Normality: A Modal Approach, Artif. Intell. 68, 87–154.

    Article  Google Scholar 

  • Bull, R. A. and Segerberg, K. (1984): Basic modal logic, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic, Vol. 2, D. Reidel Publishing Company, Dordrecht, pp. 1–88.

    Google Scholar 

  • Chellas, B. (1975): Basic Conditional Logic, J. Philos. Logic 4, 133–153.

    Article  Google Scholar 

  • Chellas, B. (1980): Modal Logic: An Introduction, Cambridge University Press.

  • Delgrande, J. P. (1987): A First-Order Conditional Logic for Prototypical Properties, Artif. Intell. 33, 105–130.

    Article  Google Scholar 

  • Fine, K. (1974): Logics Containing K4, Part I, J. Symb. Log. 39, 31–42.

    Article  Google Scholar 

  • Gabbay, D. M. (1985): Theoretical foundations for non-monotonic reasoning in expert systems, in K. R. Apt (ed.), Logics and Models of Concurrent Systems, Springer, Berlin Heidelberg New York, pp. 439–459.

    Google Scholar 

  • Harper, W. L., Stalnaker, R. and Pearce, G. (eds.) (1981): Ifs, D. Reidel Publishing Company, Dordrecht, Boston, London.

    Google Scholar 

  • Lewis, D. (1971): Completeness and Decidability of Three Logics of Counterfactual Conditionals, Theoria 37, 74–85.

    Article  Google Scholar 

  • Lewis, D. (1973a): Counterfactuals, Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

  • Lewis, D. (1973b): Counterfactuals and Comparative Possibility, J. Philos. Logic 2, 418–446. Reprinted in Harper et al., (1981).

    Article  Google Scholar 

  • Lewis, D. (1974): Intensional Logics Without Iterative Axioms, J. Philos. Logic 3, 457–466.

    Article  Google Scholar 

  • Makinson, D. (1971): Some Embedding Theorems in Modal Logic, Notre Dame J. Form. Log. 12, 252–254.

    Article  Google Scholar 

  • Makinson, D. (1988): General Theory of Cumulative Inference, in M. Reinfrank, J. de Kleer, M. L. Ginsberg and E. Sandewall (eds.), Non-Monotonic Reasoning, 2nd International Workshop, Grassau, FRG, June 13–15, 1988, Proceedings, Lecture Notes in Artificial Intelligence 346, Springer, Berlin, Heidelberg, New York pp. 1–18.

    Google Scholar 

  • Makinson, D. (1994): General patterns in nonmonotonic reasoning, in D. M. Gabbay, C. J. Hogger and J. A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3, Oxford University Press, Oxford, pp. 35–110.

    Google Scholar 

  • Montague, R. (1968): Pragmatics, in R. Klibansky (ed.) Comtemporary Philosophy: A Survey, Vol. 1, La Nuova Editrice, Florence, pp. 102–122. Reprinted in Montague (1974).

    Google Scholar 

  • Montague, R. (1974): Formal Philosophy: Selected Papers of Richard Montague edited with an introduction by Richmond H. Thomason, Yale University Press, New Heavens, London.

    Google Scholar 

  • Nute, D. (1980): Topics in Conditional Logic, Vol. 20 of Philosophical Studies Series in Philosophy, Reidel Publishing Company, Dordrecht.

    Google Scholar 

  • Pelletier, F. J. and Asher, N. (1997): Generics and defaults, in J. van Benthem and A. ter Meulen (eds), Handbook of Logic and Language, MIT, Cambridge, Massachusetts, pp. 1125–1177.

    Chapter  Google Scholar 

  • Scott, D. (1970): Advice on modal logic, in K. Lambert (ed.), Philosophical Problems in Logic, Reidel Publishing Company, Dordrecht, pp. 143–173.

    Google Scholar 

  • Segerberg, K. (1971): An Essay in Classical Modal Logic, Philosophical Studies published by the Philosophical Society and the Department of Philosophy, University of Uppsala, Uppsala.

  • Segerberg, K. (1972): Post Completeness in Modal Logic, J. Symb. Log. 37(4), 711–715.

    Article  Google Scholar 

  • Stalnaker, R. (1968): A theory of conditionals, in N. Rescher (ed.), Studies in Logical Theory, Basil Blackwell, Oxford, pp. 98–112. Reprinted in Harper et al., (1981).

    Google Scholar 

  • Stalnaker, R. (1981): A Defense of Conditional Excluded Middle, in Harper et al., (1981), pp. 87–104.

  • Stalnaker, R. and Thomason, R. H. (1970): A Semantic Analysis of Conditional Logic, Theoria 36, 23–42.

    Article  Google Scholar 

  • Thomason, S. K. (1972): Semantic Analysis of Tense Logic, J. Symb. Log. 37, 150–158.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ming Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, M. Some Embedding Theorems for Conditional Logic. J Philos Logic 35, 599–619 (2006). https://doi.org/10.1007/s10992-005-9021-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-005-9021-8

Key Words

Navigation