Abstract
In this paper a comparative study of many-valued logics, fuzzy logics and the theory of graded consequence has been made focussing on consequence, inconsistency and sorites paradox.
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
Preview
Unable to display preview. Download preview PDF.
References
Bergmann, M.: An Introduction to Many-valued and Fuzzy Logic: Semantics, Algebras and Derivation Systems. Cambridge University Press (2008)
Bertossi, L., Hunter, A., Schaub, T.: Introduction to Inconsistency Tolerance. In: Bertossi, L., Hunter, A., Schaub, T. (eds.) Inconsistency Tolerance. LNCS, vol. 3300, pp. 1–14. Springer, Heidelberg (2005)
Chakraborty, M.K.: Use of fuzzy set theory in introducing graded consequence in multiple valued logic. In: Gupta, M.M., Yamakawa, T. (eds.) Fuzzy Logic in Knowledge-Based Systems, Decision and Control, pp. 247–257. Elsevier Science Publishers, B.V., North Holland (1988)
Chakraborty, M.K.: Graded Consequence: further studies. Journal of Applied Non-Classical Logics 5(2), 127–137 (1995)
Chakraborty, M.K., Basu, S.: Graded Consequence and some Metalogical Notions Generalized. Fundamenta Informaticae 32, 299–311 (1997)
Chakraborty, M.K., Dutta, S.: Graded Consequence Revisited. Fuzzy Sets and Systems 161, 1885–1905 (2010)
Chakraborty, M.K., Dutta, S.: Grade in Metalogical Notions: a Comparative Study of Fuzzy Logics. Mathware and Soft Computing (accepted)
Dunn, P.E., et al.: Inconsistency tolerance in weighted argument systems. In: Decker, Sichman, Sierra, Castelfranchi (eds.) Proc. of 8th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS 2009), Budapest, Hungary, May 10-15, pp. 851–858 (2009)
Edgington, D.: Vagueness by degrees. In: Keefe, R., Smith, P. (eds.) Vagueness: A Reader, pp. 294–316. MIT Press, Massachusetts (1997)
Esteva, E., Godo, L., Noguera, C.: On Completeness results for Predicate Łukasiewicz, Product, G\(\ddot{o}\)del and Nilpotent Minimum Logics expanded with truth constants. Mathware and Soft Computing XIV(3), 233–246 (2007)
Gerla, G.: Fuzzy Logic: Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers (2001)
Goguen, J.A.: The logic of inexact concepts. 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.) IPMU 1994. LNCS, vol. 945, pp. 380–388. Springer, Heidelberg (1995)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers (1998)
Parikh, R.: The Problem of Vague Predicates. In: Cohen, R.S., Wartofsky, M. (eds.) Language, Logic, and Method, pp. 241–261. D. Ridel Publishing Company (1983)
Pavelka, J.: On fuzzy logic I, II, III Zeitscher for Math. Logik und Grundlagen d. Math. 25, 45–52, 119–134, 447–464 (1979)
Pelta, C.: Wide Sets, Deep Many-valuedness and Sorites Arguments. Mathware and Soft Computing 11, 5–11 (2004)
Rescher, N.: A Survey of Many-valued Logic. Mc.Graw-Hill Book Company, New York (1969)
Shoesmith, D.J., Smiley, T.J.: Multiple Conclusion Logic. Cambridge University Press (1978)
Tye, M.: Sorites paradoxes and the semantics of vagueness. In: Tomberlin, J.E. (ed.) Philosophical Perspectives 8: Logic and Language, pp. 189–206. Ridgeview Publishing Co., Atascadero (1994)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dutta, S., Basu, S., Chakraborty, M.K. (2013). Many-Valued Logics, Fuzzy Logics and Graded Consequence: A Comparative Appraisal. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-36039-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36038-1
Online ISBN: 978-3-642-36039-8
eBook Packages: Computer ScienceComputer Science (R0)