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Author: Lavinia Corina Ciungu
Publisher: Springer
ISBN: 9783319015903
Category : Mathematics
Languages : en
Pages : 276
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Book Description
This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.
Author: Lavinia Corina Ciungu
Publisher: Springer
ISBN: 9783319015903
Category : Mathematics
Languages : en
Pages : 276
Get Book Here
Book Description
This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.
Author: Lavinia Corina Ciungu
Publisher: Springer Science & Business Media
ISBN: 3319015893
Category : Mathematics
Languages : en
Pages : 284
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Book Description
This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.
Author: Linsen Chou
Publisher:
ISBN: 9781681171883
Category :
Languages : en
Pages : 0
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Book Description
A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which xy does not always equal yx; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. The main motivation is to extend the commutative duality between spaces and functions to the noncommutative setting. In mathematics, spaces, which are geometric in nature, can be related to numerical functions on them. In general, such functions will form a commutative ring. For instance, one may take the ring C(X) of continuous complex-valued functions on a topological space X. In many cases, we can recover X from C(X), and therefore it makes some sense to say that X has commutative topology. The dream of noncommutative geometry is to generalize this duality to the duality between noncommutative algebras, or sheaves of noncommutative algebras, or sheaf-like noncommutative algebraic or operator-algebraic structures and geometric entities of certain kind, and interact between the algebraic and geometric description of those via this duality. Regarding that the commutative rings correspond to usual affine schemes, and commutative C*-algebras to usual topological spaces, the extension to noncommutative rings and algebras requires non-trivial generalization of topological spaces, as "non-commutative spaces". This book provides an elementary introduction to noncommutative rings and algebras.
Author: LAVINIA CORINA CIUNGU
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
In this paper we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute.
Author: Matej Brešar
Publisher: Springer
ISBN: 3319086936
Category : Mathematics
Languages : en
Pages : 227
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Book Description
Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.
Author: Afrodita Iorgulescu
Publisher:
ISBN: 9781848904637
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This monograph is devoted mainly to the author's results in her research on non-commutative algebras related to logic started on October 17, 2022, results never published. It would not be written in so little time and with so many important results and examples without the help of the computer program Prover9-Mace4, developed by William W. McCune (1953 - 2011). There exist a frame-work of non-commutative algebras of logic, having in its `center' the pseudo-BCK algebra. In this monograph, the author mainly has generalized to the non-commutative case the m-BCK algebra and its related algebras, as particular cases of unital magmas, thus creating a new frame-work of non-commutative algebras, having in its `center' the new m-pseudo-BCK algebra. The pseudo-MV algebras are particular cases of m-pseudo-BCK algebras, the groups belong to this new frame-work. But, the goal of her research was to define and study the quantum-pseudo-MV algebra, the non-commutative generalization of quantum-MV algebra. She was able to reach her goal only because she has discovered the`principle' that governs the non-commutative algebras, called `transposition' principle (`m-transposition' principle, for magmas). She has also introduced and studied other non-commutative generalizations of quantum algebras: the bounded involutive pseudo-lattices, the pseudo-De Morgan algebras and the ortho-pseudo-lattices. The book has 18 chapters, divided into three parts: Part I (centered on pseudo-BCK algebras: Chapters 1 - 7), Part II (the core of the monograph, centered on m-pseudo-BCK algebras: Chapters 8 - 16) and Part III (`bridge' theorems: Chapters 17, 18).
Author: Tai-He Fan
Publisher: Springer
ISBN: 3319462067
Category : Technology & Engineering
Languages : en
Pages : 654
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Book Description
This book is the proceedings of the Fourth International Conference on Quantitative Logic and Soft Computing (QLSC2016) held 14-17, October, 2016 in Zhejiang Sci-Tech University, Hangzhou, China. It includes 61 papers, of which 5 are plenary talks( 3 abstracts and 2 full length talks). QLSC2016 was the fourth in a series of conferences on Quantitative Logic and Soft Computing. This conference was a major symposium for scientists, engineers and practitioners to present their updated results, ideas, developments and applications in all areas of quantitative logic and soft computing. The book aims to strengthen relations between industry research laboratories and universities in fields such as quantitative logic and soft computing worldwide as follows: (1) Quantitative Logic and Uncertainty Logic; (2) Automata and Quantification of Software; (3) Fuzzy Connectives and Fuzzy Reasoning; (4) Fuzzy Logical Algebras; (5) Artificial Intelligence and Soft Computing; (6) Fuzzy Sets Theory and Applications.
Author: Hepu Deng
Publisher: Springer Science & Business Media
ISBN: 3642238807
Category : Computers
Languages : en
Pages : 717
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Book Description
This three-volume proceedings contains revised selected papers from the Second International Conference on Artificial Intelligence and Computational Intelligence, AICI 2011, held in Taiyuan, China, in September 2011. The total of 265 high-quality papers presented were carefully reviewed and selected from 1073 submissions. The topics of Part I covered are: applications of artificial intelligence; applications of computational intelligence; automated problem solving; biomedical inforamtics and computation; brain models/cognitive science; data mining and knowledge discovering; distributed AI and agents; evolutionary programming; expert and decision support systems; fuzzy computation; fuzzy logic and soft computing; and genetic algorithms.
Author: C.S. Calude
Publisher: Springer Science & Business Media
ISBN: 1447107179
Category : Mathematics
Languages : en
Pages : 254
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Book Description
This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001. The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.
Author: L. C. Ciungu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 18
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Book Description
In this paper, we define the notion of Smarandache pseudo-CI algebras and we investigate their properties. We also define and study the notions of Smarandache filters, pseudo-CI Smarandache homomorphisms and modal Smarandache operators on pseudo-CI algebras. The classes of Smarandache fantastic, implicative and positive implicative filters of Smarandache pseudo-CI algebras are defined and studied by extending some results regarding Smarandache fantastic, fresh and clean ideals in Smarandache BCI-algebras and Smarandache BCH-algebras to the case of Smarandache pseudo-CI algebras. The notion of Smarandache commutative pseudo-CI algebras is defined and a characterization theorem is given. It is proved that in the case of commutative Q-Smarandache pseudo-CI algebras the notions of Smarandache filters and fantastic filters coincide.
