Hájek basic fuzzy logic and Łukasiewicz infinite-valued logic

Archive for Mathematical Logic 42 (4):361-370 (2003)
  Copy   BIBTEX


Using the theory of BL-algebras, it is shown that a propositional formula ϕ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ˜˜ϕ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ→˜φ)) → ψ, then ϕ is derivable in in classical logic if and only if ˜˜ ϕ is derivable in SBL. Axiomatic extensions of Basic Logic are in correspondence with subvarieties of the variety of BL-algebras. It is shown that the MV-algebra of regular elements of a free algebra in a subvariety of BL-algebras is free in the corresponding subvariety of MV-algebras, with the same number of free generators. Similar results are obtained for the generalized BL-algebras of dense elements of free BL-algebras.



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On arithmetic in the Cantor- Łukasiewicz fuzzy set theory.Petr Hájek - 2005 - Archive for Mathematical Logic 44 (6):763-782.
Finiteness in infinite-valued łukasiewicz logic.Stefano Aguzzoli & Agata Ciabattoni - 2000 - Journal of Logic, Language and Information 9 (1):5-29.
Structural Completeness in Fuzzy Logics.Petr Cintula & George Metcalfe - 2009 - Notre Dame Journal of Formal Logic 50 (2):153-182.
Bourne on future contingents and three-valued logic.Daisuke Kachi - 2009 - Logic and Logical Philosophy 18 (1):33-43.
On witnessed models in fuzzy logic II.Petr Hájek - 2007 - Mathematical Logic Quarterly 53 (6):610-615.


Added to PP

20 (#747,345)

6 months
2 (#1,232,442)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Algebraic foundations of many-valued reasoning.Roberto Cignoli - 1999 - Boston: Kluwer Academic Publishers. Edited by Itala M. L. D'Ottaviano & Daniele Mundici.
Distributive Lattices.Raymond Balbes & Philip Dwinger - 1977 - Journal of Symbolic Logic 42 (4):587-588.
Complexity of t-tautologies.Matthias Baaz, Petr Hájek, Franco Montagna & Helmut Veith - 2001 - Annals of Pure and Applied Logic 113 (1-3):3-11.

Add more references