L -effect Algebras

Studia Logica 108 (4):725-750 (2020)
  Copy   BIBTEX

Abstract

L-effect algebras are introduced as a class of L-algebras which specialize to all known generalizations of effect algebras with a \-semilattice structure. Moreover, L-effect algebras X arise in connection with quantum sets and Frobenius algebras. The translates of X in the self-similar closure S form a covering, and the structure of X is shown to be equivalent to the compatibility of overlapping translates. A second characterization represents an L-effect algebra in the spirit of closed categories. As an application, it is proved that every lattice effect algebra is an interval in a right \-group, the structure group of the corresponding L-algebra. A block theory for generalized lattice effect algebras, and the existence of a generalized OML as the subalgebra of sharp elements are derived from this description.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,726

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

Non-commutative logical algebras and algebraic quantales.Wolfgang Rump & Yi Chuan Yang - 2014 - Annals of Pure and Applied Logic 165 (2):759-785.
Hyper-Archimedean BL-algebras are MV-algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
Linear L-Algebras and Prime Factorization.Wolfgang Rump - 2023 - Studia Logica 111 (1):57-82.
Phi-symmetric effect algebras.M. K. Bennett & D. J. Foulis - 1995 - Foundations of Physics 25 (12):1699-1722.
Boolean deductive systems of BL-algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.
Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
D-algebras.Stanley Gudder - 1996 - Foundations of Physics 26 (6):813-822.

Analytics

Added to PP
2019-08-25

Downloads
21 (#747,875)

6 months
4 (#1,051,540)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

L-algebras and three main non-classical logics.Wolfgang Rump - 2022 - Annals of Pure and Applied Logic 173 (7):103121.

Add more citations