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Logic and Logical Philosophy

Counterfactuals and semantic tableaux
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Counterfactuals and semantic tableaux

Authors

  • Daniel Rönnedal Stockholm University

DOI:

https://doi.org/10.12775/LLP.2009.006

Keywords

counterfactuals, subjunctive conditionals, conditional logic, modal logic, semantic tableau, analytic tableau, Robert Stalnaker, David Lewis, Melvin Fitting, Graham Priest

Abstract

The purpose of this paper is to develop a class of semantic tableau systems for some counterfactual logics. All in all I will discuss 1024 systems. Possible world semantics is used to interpret our formal languages. Soundness results are obtained for every tableau system and completeness results for a large subclass of these.

Author Biography

Daniel Rönnedal, Stockholm University

The Department of Philosophy

References

Addison, J.W., L. Henkin, and A. Tarski (eds.), The Theory of Models (Proceedings of the 1963 International Symposium at Berkeley), North-Holland, Amsterdam, 1965.

Bennett, J., A Philosophical Guide to Conditionals, Clarendon Press, Oxford, 2003.

Beth, E.W., “Semantic entailment and formal derivability”, Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afdeling Letterkunde, N.S., vol. 18, no. 13, (1955), Amsterdam, pp. 309–342. Reprinted in [13], pp. 9–41.

Beth, E.W., The Foundations of Mathematics, North-Holland, Amsterdam, 1959.

D’Agostino, M., D.M. Gabbay, R. Hähnle, and J. Posegga (eds.), Handbook of Tableau Methods, Kluwer Academic Publishers, Dordrecht, 1999.

Fitting, M., “Tableau methods of proof for modal logics”, Notre Dame Journal of Formal Logic 13 (1972), 237–247.

Fitting, M., Proof Methods for Modal and Intuitionistic Logic, D. Reidel, Dordrecht, 1983.

Fitting, M., “Introduction”, pages 1–43 in [5].

Gentzen, G., “Untersuchungen über das Logische Shliessen I”, Mathematische Zeitschrift 39 (1935), 176–210. English translation “Investigations into Logical Deduction”, in [27].

Gentzen, G., “Untersuchungen über das Logische Shliessen II”, Mathematische Zeitschrift 39 (1935), 405–431. English translation “Investigations into Logical Deduction”, in [27].

Hanson, W.H., “Semantics for deontic logic”, Logique et Analyse 8 (1965), 177–190.

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Kripke, S.A., “A completeness theorem in modal logic”, The Journal of Symbolic Logic 24 (1959), 1–14.

Kripke, S.A., “Semantical analysis of modal logic I. Normal propositional calculi”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 9 (1963), 67–96.

Kripke, S.A., “Semantical analysis of modal logic II. Non-normal modal propositional calculi”,

pages 206–220 in [1].

Lewis, D., Counterfactuals, Basil Blackwell, Oxford, 1973.

Lis, Z., “Wynikanie semantyczne a wynikanie formalne” (in Polish: “Logical consequence – semantic and formal), Studia Logica 10 (1960), 39–60.

Priest, G., An Introduction to Non-Classical Logic, Cambridge University Press, Cambridge, 2001.

Smullyan, R.M., “A unifying principle in quantificational theory”, Proceedings of the National Academy of Sciences 49, no. 6 (1963), 828–832.

Smullyan, R.M., “Analytic natural deduction”, Journal of Symbolic Logic 30 (1965), 123–139.

Smullyan, R.M., “Trees and nest structures”, Journal of Symbolic Logic 31 (1966), 303–321.

Smullyan, R.M., First-Order Logic, Springer-Verlag, Heidelberg, 1968.

Stalnaker, R.C., “A theory of conditionals”, in: N. Rescher (ed.), Studies in Logical Theory, Blackwell, Oxford, 1968.

Szabo, M.E., (ed.), The Collected Papers of Gerhard Gentzen, North-Holland, Amsterdam, 1969.

Zeman, J.J., Modal Logic. The Lewis-Modal Systems, Clarendon Press, Oxford, 1973.

Åqvist, L., ““Next” and “ought”. Alternative foundations for von Wright’s tense-logic with an application to deontic logic”, Logique et Analyse 9 (1966), 231–251.

Logic and Logical Philosophy

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Published

2009-08-15

How to Cite

1.
RÖNNEDAL, Daniel. Counterfactuals and semantic tableaux. Logic and Logical Philosophy. Online. 15 August 2009. Vol. 18, no. 1, pp. 71-91. [Accessed 19 November 2025]. DOI 10.12775/LLP.2009.006.
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