Studia Logica 106 (4):675-690 (2018)

Abstract
An l-hemi-implicative semilattice is an algebra $$\mathbf {A} = $$ A= such that $$$$ is a semilattice with a greatest element 1 and satisfies: for every $$a,b,c\in A$$ a,b,c∈A, $$a\le b\rightarrow c$$ a≤b→c implies $$a\wedge b \le c$$ a∧b≤c and $$a\rightarrow a = 1$$ a→a=1. An l-hemi-implicative semilattice is commutative if if it satisfies that $$a\rightarrow b = b\rightarrow a$$ a→b=b→a for every $$a,b\in A$$ a,b∈A. It is shown that the class of l-hemi-implicative semilattices is a variety. These algebras provide a general framework for the study of different algebras of interest in algebraic logic. In any l-hemi-implicative semilattice it is possible to define an derived operation by $$a \sim b := \wedge $$ a∼b:=∧. Endowing $$$$ with the binary operation $$\sim $$ ∼ the algebra $$$$ results an l-hemi-implicative semilattice, which also satisfies the identity $$a \sim b = b \sim a$$ a∼b=b∼a. In this article, we characterize the commutative l-hemi-implicative semilattices. We also provide many new examples of l-hemi-implicative semilattice on any semillatice with greatest element. Finally, we characterize congruences on the classes of l-hemi-implicative semilattices introduced earlier and we characterize the principal congruences of l-hemi-implicative semilattices.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11225-017-9759-3
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 56,999
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

On a Weak Conditional.José Luis Castiglioni & Rodolfo C. Ertola-Biraben - forthcoming - Logic Journal of the IGPL.

Add more citations

Similar books and articles

On Special Implicative Filters.Josep Maria Font - 1999 - Mathematical Logic Quarterly 45 (1):117-126.
N -Fold Filters in BL-Algebras.Masoud Haveshki & Esfandiar Eslami - 2008 - Mathematical Logic Quarterly 54 (2):176-186.
On (∈, ∈ ∨ Q)‐Fuzzy Filters of R0‐Algebras.Xueling Ma, Jianming Zhan & Young B. Jun - 2009 - Mathematical Logic Quarterly 55 (5):493-508.
Ideals in BCK-Algebras Which Are Lower Semilattices.Marek Palasinski - 1981 - Bulletin of the Section of Logic 10 (1):48-50.
Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.
Some Results in BL ‐Algebras.Arsham Borumand Saeid & Somayeh Motamed - 2009 - Mathematical Logic Quarterly 55 (6):649-658.
On Closure Endomorphisms of Implicative Semilattices.Janis Cirulis - 1985 - Bulletin of the Section of Logic 14 (2):52-55.
Multipliers in Implicative Algebras.Janis Cirulis - 1986 - Bulletin of the Section of Logic 15 (4):152-157.
Boolean Deductive Systems of BL-Algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.

Analytics

Added to PP index
2019-01-25

Total views
2 ( #1,372,063 of 2,410,452 )

Recent downloads (6 months)
1 ( #540,320 of 2,410,452 )

How can I increase my downloads?

Downloads

My notes