Abstract
This chapter presents a comparative analysis of the notion of graded consequence with other approaches to consequence in fuzzy logics. We shall first present different systems of fuzzy logics with respect to their proposed notions of consequence and then analyse in order to see how faithful those approaches are in incorporating many-valuedness in the notion of consequence.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bergmann, M.: An Introduction to Many-valued and Fuzzy Logic: Semantics, Algebras and Derivation Systems. Cambridge University Press (2008)
Bou, F., Esteva, F., Font, J.M., Gil, A., Godo, L., Torrens, A., Verdú, V.: Logics preserving degrees of truth from varieties of residuated lattices. J. Logic Comput. 19(6), 1031–1069 (2009)
Church, A.: Introduction to Mathematical Logic, vol. 1. Princeton University Press, N.J. (1956)
Dutta, S., Chakraborty, M.K.: Grade in metalogical notions: a comparative study of fuzzy logics. Mathware Soft Comput. Mag. 21(2), 20–32 (2014)
Esteva, F., Godo, L., Noguera, C.: First order t-norm based fuzzy logics with truth-constants: distinguished semantics and completeness properties. Ann. Pure and Appl. Logic 161(2): Elsevier, 185–202 (2009)
Goguen, J.A.: The logic of inexact concept. Synthese 19, 325–373 (1968)
Gottwald, S.: An approach to handle partially sound rules of inference. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (Eds.) Advances in Intelligent Computing, IPMU’94, Selected papers, Lecture Notes Computer Science, Vol. 945, pp. 380–388. Springer: Berlin etc. (1995)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)
Novak. V.: On syntactico-semantical completeness of first order fuzzy logic, parts I and II. Kybernetica 2, 6(1, 2), 47–154 (1990)
Pavelka, J.: On fuzzy logic I, II, III Zeitscher for Math. Logik und Grundlagen d. Math. 25, 4552, 119134, 447464 (1979)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Chakraborty, M.K., Dutta, S. (2019). Graded Consequence and Consequence in Different Approaches to Fuzzy Logics. In: Theory of Graded Consequence. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-13-8896-5_6
Download citation
DOI: https://doi.org/10.1007/978-981-13-8896-5_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-8894-1
Online ISBN: 978-981-13-8896-5
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)