Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T09:55:14.540Z Has data issue: false hasContentIssue false
  • English
  • Français

SOME (NON)TAUTOLOGIES OF ŁUKASIEWICZ AND PRODUCT LOGIC

Published online by Cambridge University Press:  17 March 2010

PETR HÁJEK
PETR HÁJEK*
Affiliation:
Institute of Computer Science, Academy of Sciences of the Czech Republic
*
*INSTITUTE OF COMPUTER SCIENCE, ACADEMY OF SCIENCES OF THE CZECH REPUBLIC, 182 07 PRAGUE, CZECH REPUBLIC E-mail:hajek@cs.cas.cz
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper presents a particular example of a formula which is a standard tautology of Łukasiewicz but not its general tautology; an example of a model in which the formula is not true is explicitly constructed. Analogous example of a formula and its model is given for product logic.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 2 , June 2010 , pp. 273 - 278
Copyright
Copyright © Association for Symbolic Logic 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Cignoli, R. L. O., D’Ottaviano, I. M. L., & Mundici, D. (2000). Algebraic Foundations of Many-Valued Reasoning. Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar
Hájek, P. (1998). Metamathematics of Fuzzy Logic. Dordrecht, The Netherlands: Kluwer.CrossRefGoogle Scholar
Hájek, P. (2000). Function symbols in fuzzy predicate logic. In Wagenknecht, M. et al. , ed., Proceedings East West Fuzzy Colloquium. Hochschule für Technik, Wirtschaft und Sozialwesen Zittau, Germany, pp. 2–8.Google Scholar
Hájek, P. (2004). A true unprovable formula of fuzzy predicate logic. In Richter, M. and Lenski, W., eds. Logic versus Approximation. Essays Dedicated to Michael M. Richter on the Occasion of His 65th Birthday. Berlin: Springer, s. 1–5.Google Scholar
Hájek, P. (2007). On witnessed models in fuzzy logic. Mathematical Logic Quarterly, 53, 66–77.CrossRefGoogle Scholar
Hájek, P., Godo, L., & Esteva, F. (1996). A complete many-valued logic with product-conjunction. Archive for Mathematical Logic, 35, 191–208.CrossRefGoogle Scholar
Hájek, P., & Pudlák, P. (1993). Metamathematics of First-Order Arithmetic. Berlin, Heidelberg (Germany) Springer Verlag.CrossRefGoogle Scholar
Łukasiewicz, J. (1920). O logice trójwartosciowej (On three-valued logic). Ruch filozoficzny, 5, 170–171.Google Scholar
Łukasiewicz, J., & Tarski, A. (1930). Untersuchungen über den Aussagenkalkül. C.R. de la Societé des Sciences et des Letters de Varsovie cl. iii, 23, 51–77.Google Scholar
Montagna, F. (2001). Three complexity problems in quantified fuzzy logic. Studia Logica, 68, 143–152.CrossRefGoogle Scholar
Ragaz, M. E. (1981). Arithmetische Klassifikation von Formelnmengen der unendlichwertigen Logik. Thesis, ETH Zürich.Google Scholar
Scarpellini, B. (1962). Die Nichtaxiomatisierbarkeit des unendichwertigen Prädikatenkalküls von Łukasiewicz. Journal of Symbolic Logic, 27, 159–170.CrossRefGoogle Scholar