scholarly journals Hilbert Implication Algebra and Some Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Dejen Gerima Tefera
Keyword(s):  
Comparison Theorem ◽  
Implication Algebras ◽  
Implication Algebra

The concepts of Hilbert implication algebra and generalized Hilbert implication algebra are introduced. The comparison theorem of Hilbert implication algebra and generalized Hilbert implication algebra is proved. In addition, the idea of groupoid and commutative Hilbert implication algebras is investigated. Ideals and filters in Hilbert implication algebras are also discussed. In general, different theorems which show different properties are proved.

scholarly journals Vague Congruences and Quotient Lattice Implication Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoyan Qin ◽  
Yi Liu ◽  
Yang Xu
Keyword(s):  
Lattice Implication Algebra ◽  
Implication Algebras ◽  
Homomorphism Theorem ◽  
Similarity Relations ◽  
Implication Algebra ◽  
Congruence Theory ◽  
Congruence Relations

The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given.

scholarly journals Q-Filters of Quantum B-Algebras and Basic Implication Algebras

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 573 ◽  
Author(s):  
Xiaohong Zhang ◽  
Rajab Borzooei ◽  
Young Jun
Keyword(s):  
Algebraic Semantics ◽  
Fuzzy Logics ◽  
Quantum Logics ◽  
Filter Theory ◽  
Implication Algebras ◽  
Implication Algebra

The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.

Algebraic functions in Łukasiewicz implication algebras

2016 ◽  
Vol 26 (02) ◽  
pp. 223-247 ◽  
Author(s):  
Miguel Campercholi ◽  
Diego Castaño ◽  
José Patricio Díaz Varela
Keyword(s):  
Main Tool ◽  
Algebraic Functions ◽  
Implication Algebras ◽  
Implication Algebra ◽  
Tarski Algebras ◽  
Łukasiewicz Implication Algebras ◽  
Finitely Generated Variety ◽  
Element Chain ◽  
Global Representation ◽  
Partial Description

In this article we study algebraic functions in [Formula: see text]-subreducts of MV-algebras, also known as Łukasiewicz implication algebras. A function is algebraic on an algebra [Formula: see text] if it is definable by a conjunction of equations on [Formula: see text]. We fully characterize algebraic functions on every Łukasiewicz implication algebra belonging to a finitely generated variety. The main tool to accomplish this is a factorization result describing algebraic functions in a subproduct in terms of the algebraic functions of the factors. We prove a global representation theorem for finite Łukasiewicz implication algebras which extends a similar one already known for Tarski algebras. This result together with the knowledge of algebraic functions allowed us to give a partial description of the lattice of classes axiomatized by sentences of the form [Formula: see text] within the variety generated by the 3-element chain.

scholarly journals Fantastic filters of lattice implication algebras

2000 ◽  
Vol 24 (4) ◽  
pp. 277-281 ◽  
Author(s):  
Young Bae Jun
Keyword(s):  
Extension Property ◽  
Equivalent Condition ◽  
Lattice Implication Algebra ◽  
Implication Algebras ◽  
Implication Algebra ◽  
Fantastic Filter ◽  
Positive Implicative Filter

The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.

scholarly journals Topological representation for monadic implication algebras

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Manuel Abad ◽  
Cecilia Cimadamore ◽  
José Díaz Varela
Keyword(s):  
Boolean Algebra ◽  
Topological Representation ◽  
Implication Algebras ◽  
Implication Algebra ◽  
Monadic Boolean Algebra ◽  
Dual Equivalence ◽  
Implication Spaces ◽  
Monadic Filters

AbstractIn this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.

scholarly journals A comparison theorem

1985 ◽  
Vol 106 (1) ◽  
pp. 188-195
Author(s):  
Walter Leighton
Keyword(s):  
Comparison Theorem

scholarly journals IFI–ideals of lattice implication algebras

2013 ◽  
Vol 6 (6) ◽  
pp. 1002-1011 ◽  
Author(s):  
Hua Zhu ◽  
Jianbin Zhao ◽  
Yang Xu
Keyword(s):  
Implication Algebras

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

scholarly journals Cohomological comparison theorem

2015 ◽  
Vol 219 (12) ◽  
pp. 5573-5589
Author(s):  
Edward L. Green ◽  
Dag Oskar Madsen ◽  
Eduardo Marcos
Keyword(s):  
Comparison Theorem
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