Partial algebras for Łukasiewicz logics and its extensions

Archive for Mathematical Logic 44 (7):913-933 (2005)
  Copy   BIBTEX


It is a well-known fact that MV-algebras, the algebraic counterpart of Łukasiewicz logic, correspond to a certain type of partial algebras: lattice-ordered effect algebras fulfilling the Riesz decomposition property. The latter are based on a partial, but cancellative addition, and we may construct from them the representing ℓ-groups in a straightforward manner. In this paper, we consider several logics differing from Łukasiewicz logics in that they contain further connectives: the PŁ-, PŁ'-, PŁ'△-, and ŁΠ-logics. For all their algebraic counterparts, we characterise the corresponding type of partial algebras. We moreover consider the representing f-rings. All in all, we get three-fold correspondences: the total algebras - the partial algebras - the representing rings



    Upload a copy of this work     Papers currently archived: 93,031

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

Free Łukasiewicz implication algebras.José Patricio Díaz Varela - 2008 - Archive for Mathematical Logic 47 (1):25-33.
Free Łukasiewicz implication algebras.José Díaz Varela - 2008 - Archive for Mathematical Logic 47 (1):25-33.
Pavelka-style completeness in expansions of Łukasiewicz logic.Hector Freytes - 2008 - Archive for Mathematical Logic 47 (1):15-23.
Monadic GMV-algebras.Jiří Rachůnek & Dana Šalounová - 2008 - Archive for Mathematical Logic 47 (3):277-297.
Selfextensional logics with a distributive nearlattice term.Luciano J. González - 2019 - Archive for Mathematical Logic 58 (1-2):219-243.
Commutative basic algebras and non-associative fuzzy logics.Michal Botur & Radomír Halaš - 2009 - Archive for Mathematical Logic 48 (3-4):243-255.


Added to PP

42 (#390,194)

6 months
8 (#415,703)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

Add more citations

References found in this work

Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
A complete many-valued logic with product-conjunction.Petr Hájek, Lluis Godo & Francesc Esteva - 1996 - Archive for Mathematical Logic 35 (3):191-208.
An algebraic approach to propositional fuzzy logic.Franco Montagna - 2000 - Journal of Logic, Language and Information 9 (1):91-124.
Product Ł ukasiewicz Logic.Rostislav Horčík & Petr Cintula - 2004 - Archive for Mathematical Logic 43 (4):477-503.

View all 6 references / Add more references