45
Views
0
CrossRef citations to date
0
Altmetric
Articles

Fuzzy logics – quantitatively

& ORCID Icon
Pages 97-132 | Received 10 Jul 2022, Accepted 23 Aug 2023, Published online: 26 Oct 2023

References

  • Chagrov, A., & Zakharyaschev, M. (1997). Modal logic. Oxford Logic Guides.
  • Chauvin, B., Flajolet, P., Gardy, D., & Gittenberger, B. (1999). And/Or trees revisited. Combinatorics, Probability and Computing, 13(4-5), 475–497. https://doi.org/10.1017/S0963548304006273
  • Esteva, F., & Godo, L. (2001). Monoidal t-Norm based logic: Towards a logic for left-continuous t-Norms. Fuzzy Set and Systems, 124(3), 271–288. https://doi.org/10.1016/S0165-0114(01)00098-7
  • Flajolet, P., & Odlyzko, A. M. (1990). Singularity analysis of generating functions. SIAM Journal on Discrete Mathematics, 3(2), 216–240. https://doi.org/10.1137/0403019
  • Flajolet, P., & Sedgewick, R. (2009). Analitic combinatorics. Cambridge University Press.
  • Fournier, H., Gardy, D. , Genitrini, A., & Zaionc, M. (2007). Classical and intuitionistic logic are asymptotically identical. Lecture Notes in Computer Science, 4646, 177–193. https://doi.org/10.1007/978-3-540-74915-8
  • Gardy, D. (2006). Random boolean expressions. In colloquium on computational logic and applications, chambéry (France), proceedings in discrete mathematics and theoretical computer science, AF (pp. 1–36).
  • Gardy, D., & Woods, A. R. (2005). And/or tree probabilities of boolean functions. discrete mathematics and theoretical computer science (pp. 139–146).
  • Genitrini, A., & Kozik, J. (2012). In the full propositional logic, 5/8 of classical tautologies are intuitionistically valid. Annals of Pure and Applied Logic, 163(7), 875–887. https://doi.org/10.1016/j.apal.2011.09.011
  • Genitrini, A., Kozik, J., & Zaionc, M. (2008). Intuitionistic vs. classical tautologies, quantitative comparison. In TYPES 2007 Proceedings, Lecture Notes in Computer Science Vol. 4941, (pp. 100–109).
  • Glivenko, V. (1929). Sur quelques points de la logique de M. Brouwer. Bulletin Scientifique De La France Et De La Belgique, vol. 15, 183–188.
  • Hájek, P. (1998). Metamathematics of Fuzzy Logic. Vol. 4, of Trends in Logic, Kluwer, Dordercht.
  • Hájek, P. (1999). Ten questions and one problem on fuzzy logic. Annals of Pure and Applied Logic, 96(1-3), 157–165. https://doi.org/10.1016/S0168-0072(98)00037-2
  • Hájek, P. (2006). What is mathematical fuzzy logic. Fuzzy Sets and Systems, Elseviere, 157(5), 597–603. https://doi.org/10.1016/j.fss.2005.10.004
  • Kostrzycka, Z. (2003). On the density of implicational parts of intuitionistic and classical logics. Journal of Applied Non-Classical Logics, 13(3), 295–325.
  • Kostrzycka, Z. (2009). On the density of truth of locally finite logics. Journal of Logic and Computation, 19(6), 1114–1125.
  • Kostrzycka, Z., & Zaionc, M. (2003). On the density of truth in Dummett's logic. Bulletin of the Section of Logic, 32(1/2), 43–55.
  • Kostrzycka, Z., & Zaionc, M. (2004). Statistics of intuitionistic versus classical logics. Studia Logica, 76(3), 307–328. https://doi.org/10.1023/B:STUD.0000032101.88511.93
  • Kostrzycka, Z., & Zaionc, M. (2008). Asymptotic densities in logic and type theory. Studia Logica, 88(3), 385–403. https://doi.org/10.1007/s11225-008-9110-0
  • Kostrzycka, Z., & Zaionc, M. (2020). Quantitative Study of Fuzzy Logics. In IEEE international conference on fuzzy systems (FUZZ-IEEE) (pp. 1–8).
  • Lefmann, H., & Savický, P. (1997). Some typical properties of large and/or boolean formulas. Random Structures and Algorithms, 10, 337–351. https://doi.org/10.1002/(ISSN)1098-2418
  • McNaughton, R. (1951). A Theorem About Infinite-Valued Sentential Logic. The Journal of Symbolic Logic, 16(1), 1–13. Published also online by Cambridge University Press: 12 March 2014.
  • Moczurad, M., Tyszkiewicz, J., & Zaionc, M. (2000). Statistical properties of simple types. Mathematical Structures in Computer Science, 10(5), 575–594. https://doi.org/10.1017/S0960129599002959
  • Novák, V. (2006). What logic is a real fuzzy logic. Fuzzy Sets and Systems, Elseviere, 157(5), 635–641. https://doi.org/10.1016/j.fss.2005.10.010
  • Rasiowa, H. (1974). An algebraic approach to non-classical logics, PWN, Warszawa .
  • Statman, R. (1980). On the existence of closed terms in the typed λ-calculus. In Hindley, J. R. and Seldin, J. (Eds.), Combinatory logic, lambda calculus and formalism Academic Press.
  • Szegö, G. (1975). Orthogonal polynomials, Fourth edition. AMS, Colloquium Publications, Vol. 23.
  • Wilf, H. S. (1994). Generatingfunctionology. Academic Press.
  • Woods, A. R. (1997). Coloring rules for finite trees and probabilities of monadic second order sentences. Random Structures Algorithms, 10(4), 453–485. https://doi.org/10.1002/(ISSN)1098-2418
  • Zaionc, M. (2005). On the asymptotic density of tautologies in logic of implication and negation. Reports on Mathematical Logic, Vol. 39, 67–87.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.