Abstract
We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ben-Yelles, C.B.: Type Assignment in the Lambda Calculus. Syntax and Semantics. Thesis, Mathematics Department, University of Wales Swansea, Swansea, UK (1979)
de Groote, P.: Strong Normalization of Classical Natural Deduction with Disjunction. Lecture Notes in Computer Science, vol. 2044, pp. 182–196. Springer, Berlin (2001)
Hindley, J.R.: Basic Simple Type Theory. Cambridge Tracts in Theoretical Computer Science, vol. 42. Cambridge University Press, Cambridge (1997)
Hirokawa S.: Infiniteness of proof(α) is P-space complete. Theor. Comput. Sci. 206(1–2), 331–339 (1998)
Parigot, M.: λμ-Calculus: An Algorithmic Interpretation of Classical Natural Deduction. Lecture Notes in Computer Science, vol. 624, pp. 190–201. Springer, Berlin (1992)
Troelstra A.S., Schwichtenberg H.: Basic Proof Theory. Cambridge University Press, Cambridge (1996)
Van Dalen D.: Logic and Structure. Springer, Berlin (1997)
Wells, J.B., Yakobowski, B.: Graph Based Proof Counting and Enumeration with Applications for Program Fragment Synthesis. Lecture Notes in Computer Science, vol. 3573, pp. 262–277. Springer, Berlin (2005)
Author information
Authors and Affiliations
Corresponding author
Additional information
Research described in this paper is supported by Polish Ministry of Science and Higher Education grant NN206 356236.
Rights and permissions
About this article
Cite this article
David, R., Zaionc, M. Counting proofs in propositional logic. Arch. Math. Logic 48, 185–199 (2009). https://doi.org/10.1007/s00153-009-0119-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-009-0119-5