scholarly journals Very true operators on MTL-algebras

2016 ◽  
Vol 14 (1) ◽  
pp. 955-969 ◽  
Author(s):  
Jun Tao Wang ◽  
Xiao Long Xin ◽  
Arsham Borumand Saeid
Keyword(s):  
Representation Theorem ◽  
Subdirectly Irreducible ◽  
Mv Algebra ◽  
Left And Right ◽  
Soundness And Completeness ◽  
Gödel Algebra

AbstractThe main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

On idempotent modifications of generalized MV-algebras

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Ján Jakubík
Keyword(s):  
Present Note ◽  
Subdirectly Irreducible ◽  
Mv Algebra ◽  
Mv Algebras

AbstractThe notion of idempotent modification of an algebra was introduced by Ježek; he proved that the idempotent modification of a group is always subdirectly irreducible. In the present note we show that the idempotent modification of a generalized MV -algebra having more than two elements is directly irreducible if and only if there exists an element in A which fails to be boolean. Some further results on idempotent modifications are also proved.

scholarly journals Loomis-sikorski theorem for σ-complete MV-algebras and ℓ-groups

2000 ◽  
Vol 68 (2) ◽  
pp. 261-277 ◽  
Author(s):  
Anatolij Dvurečenskij
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Representation Theorem ◽  
Strong Unit ◽  
Direct Generalization ◽  
Mv Algebra ◽  
Mv Algebras

AbstractWe show that every σ-complete MV-algebra is an MV-σ-homomorphic image of some σ-complete MV- algebra of fuzzy sets, called a tribe, which is a system of fuzzy sets of a crisp set Ω containing 1Ω and closed under fuzzy complementation and formation of min {∑nfn, 1}. Since a tribe is a direct generalization of a σ-algebra of crisp subsets, the representation theorem is an analogue of the Loomis-Sikorski theorem for MV-algebras. In addition, this result will be extended also for Dedekind σ-complete ℓ-groups with strong unit.

Monadic NM-algebras

2019 ◽  
Vol 27 (6) ◽  
pp. 812-835
Author(s):  
Juntao Wang ◽  
Pengfei He ◽  
Yanhong She
Keyword(s):  
Representation Theorem ◽  
Predicate Logic ◽  
Algebraic Semantics ◽  
Subdirectly Irreducible ◽  
Approximation Spaces ◽  
Rough Approximation ◽  
Subdirect Representation ◽  
Algebraic Foundation ◽  
The Relationship ◽  
Monadic Filters

Abstract In this paper, we investigate universal and existential quantifiers on NM-algebras. The resulting class of algebras will be called monadic NM-algebras. First, we show that the variety of monadic NM-algebras is algebraic semantics of the monadic NM-predicate logic. Moreover, we discuss the relationship among monadic NM-algebras, modal NM-algebras and rough approximation spaces. Second, we introduce and investigate monadic filters in monadic NM-algebras. Using them, we prove the subdirect representation theorem of monadic NM-algebras, and characterize simple and subdirectly irreducible monadic NM-algebras. Finally, we present the monadic NM-logic and prove its (chain) completeness with respect to (strong) monadic NM-algebras. These results constitute a crucial first step for providing an algebraic foundation for the monadic NM-predicate logic.

scholarly journals An elementary proof of the completeness of the Lukasiewicz axioms

10.29007/s5h9 ◽  
2018 ◽  
Author(s):  
Michal Botur ◽  
Jan Paseka
Keyword(s):  
Representation Theorem ◽  
Elementary Proof ◽  
Direct Proof ◽  
Rational Numbers ◽  
Farkas Lemma ◽  
Mv Algebra ◽  
Long Time ◽  
Mv Algebras

The main aim of this talk is twofold. Firstly, to present an elementarymethod based on Farkas' lemma for rationals how to embed any finite partial subalgebraof a linearly ordered MV-algebra into Q \ [0; 1] and then to establish a new elementaryproof of the completeness of the Lukasiewicz axioms for which the MV-algebras communityhas been looking for a long time. Secondly, to present a direct proof of Di Nola'srepresentation Theorem for MV-algebras and to extend his results to the restriction ofthe standard MV-algebra on rational numbers.

scholarly journals Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras

2003 ◽  
Vol 74 (1) ◽  
pp. 121-144 ◽  
Author(s):  
Anatolij Dvurečenskij
Keyword(s):  
Effect Algebras ◽  
Riesz Decomposition Property ◽  
Bernstein Theorem ◽  
Riesz Decomposition ◽  
Mv Algebra ◽  
Central Elements ◽  
Partial Algebras ◽  
Left And Right ◽  
The Riesz Decomposition Property ◽  
Mv Algebras

AbstractPseudo-effect algebras are partial algebras (E; +, 0, 1) with a partially defined addition + which is not necessary commutative and with two complements, left and right ones. We define central elements of a pseudo-effect algebra and the centre, which in the case of MV-algebras coincides with the set of Boolean elements and in the case of effect algebras with the Riesz decomposition property central elements are only characteristic elements. If E satisfies general comparability, then E is a pseudo MV-algebra. Finally, we apply central elements to obtain a variation of the Cantor-Bernstein theorem for pseudo-effect algebras.

scholarly journals A note on commutative Baer rings

1972 ◽  
Vol 13 (1) ◽  
pp. 1-6 ◽  
Author(s):  
T. P. Speed ◽  
M. W. Evans
Keyword(s):  
Representation Theorem ◽  
Commutative Rings ◽  
Subdirectly Irreducible ◽  
Binary Operations ◽  
Boolean Rings ◽  
Nullary Operation ◽  
Baer Rings

The class of commutative rings known as Baer rings was first discussed by J. Kist [4], where many interesting properties of these rings were established. Not necessarily commutative Baer rings had previously been studied by I. Kaplansky [3], and by R. Baer himself [1]. In this note we show that commutative Baer rings, which generalize Boolean rings and p-rings, satisfy the Birkhoff conditions for a variety. Next we give a set of equations characterising this variety involving + and * as binary operations, – and as unary operations, and 0 as nullary operation. Finally we describe Baer-subdirectly irreducible commutative Baer rings and state the appropriate representation theorem.

scholarly journals A New Model of Fuzzy Logic: Monadic Monoidal T-Norm Based Logic

2022 ◽  
Author(s):  
Saeide Zahiri ◽  
Arsham Borumand Saeid
Keyword(s):  
Fuzzy Logic ◽  
Representation Theorem ◽  
Completeness Theorem ◽  
Subdirectly Irreducible ◽  
New Model ◽  
Basic Properties ◽  
Subdirect Representation ◽  
Ams Classification ◽  
Monadic Filters

Abstract In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.

The three-dimensional structure of frozen-hydrated left- and right-handed forms of bacterial flagellar filaments from an identical serotype

1986 ◽  
Vol 44 ◽  
pp. 298-299
Author(s):  
S. Trachtenberg ◽  
D. J. DeRosier
Keyword(s):  
Ionic Strength ◽  
Basal Body ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Protein Species ◽  
Liquid Environment ◽  
Bacterial Flagellum ◽  
Left And Right ◽  
Rotary Motor ◽  
Helical Parameters

The bacterial cell is propelled through the liquid environment by means of one or more rotating flagella. The bacterial flagellum is composed of a basal body (rotary motor), hook (universal coupler), and filament (propellor). The filament is a rigid helical assembly of only one protein species — flagellin. The filament can adopt different morphologies and change, reversibly, its helical parameters (pitch and hand) as a function of mechanical stress and chemical changes (pH, ionic strength) in the environment.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

Histological evaluation of cochlear hair cell damage from noise-induced hearing loss in chinchillas

1990 ◽  
Vol 48 (3) ◽  
pp. 332-333
Author(s):  
R.V. Harrison ◽  
R.J. Mount ◽  
P. White ◽  
N. Fukushima
Keyword(s):  
Hair Cell ◽  
Evoked Potential ◽  
Cell Damage ◽  
Acoustic Trauma ◽  
Histological Evaluation ◽  
Cell Integrity ◽  
Functional Changes ◽  
Cochlear Hair Cell ◽  
Left And Right ◽  
Contralateral Ear

In studies which attempt to define the influence of various factors on recovery of hair cell integrity after acoustic trauma, an experimental and a control ear which initially have equal degrees of damage are required. With in a group of animals receiving an identical level of acoustic trauma there is more symmetry between the ears of each individual, in respect to function, than between animals. Figure 1 illustrates this, left and right cochlear evoked potential (CAP) audiograms are shown for two chinchillas receiving identical trauma. For this reason the contralateral ear is used as control.To compliment such functional evaluations we have devised a scoring system, based on the condition of hair cell stereocilia as revealed by scanning electron microscopy, which permits total stereociliar damage to be expressed numerically. This quantification permits correlation of the degree of structural pathology with functional changes. In this paper wereport experiments to verify the symmetry of stereociliar integrity between two ears, both for normal (non-exposed) animals and chinchillas in which each ear has received identical noise trauma.

Sign in / Sign up

Export Citation Format

Share Document