Author: Bob Coecke
Publisher: Springer Science & Business Media
ISBN: 3642128203
Category : Computers
Languages : en
Pages : 1034
Book Description
This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.
New Structures for Physics
Author: Bob Coecke
Publisher: Springer Science & Business Media
ISBN: 3642128203
Category : Computers
Languages : en
Pages : 1034
Book Description
This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.
Publisher: Springer Science & Business Media
ISBN: 3642128203
Category : Computers
Languages : en
Pages : 1034
Book Description
This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.
*- Autonomous Categories
Author: M. Barr
Publisher: Springer
ISBN: 3540348506
Category : Mathematics
Languages : en
Pages : 145
Book Description
Publisher: Springer
ISBN: 3540348506
Category : Mathematics
Languages : en
Pages : 145
Book Description
Handbook of Algebra
Author: M. Hazewinkel
Publisher: Elsevier
ISBN: 0080532969
Category : Mathematics
Languages : en
Pages : 899
Book Description
Handbook of Algebra
Publisher: Elsevier
ISBN: 0080532969
Category : Mathematics
Languages : en
Pages : 899
Book Description
Handbook of Algebra
Category Theory and Computer Science
Author: Eugenio Moggi
Publisher: Springer Science & Business Media
ISBN: 9783540634553
Category : Computers
Languages : en
Pages : 328
Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.
Publisher: Springer Science & Business Media
ISBN: 9783540634553
Category : Computers
Languages : en
Pages : 328
Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.
Categorical Topology
Author: Eraldo Giuli
Publisher: Springer Science & Business Media
ISBN: 9780792340492
Category : Mathematics
Languages : en
Pages : 294
Book Description
This volume contains selected papers presented at the International Workshop on Categorical Topology, held at the University of L'Aquila, L'Aquila, Italy from August 31 to September 4, 1994. The collection should be of interest to mathematicians whose work involves category theory.
Publisher: Springer Science & Business Media
ISBN: 9780792340492
Category : Mathematics
Languages : en
Pages : 294
Book Description
This volume contains selected papers presented at the International Workshop on Categorical Topology, held at the University of L'Aquila, L'Aquila, Italy from August 31 to September 4, 1994. The collection should be of interest to mathematicians whose work involves category theory.
The Theory of Quantaloids
Author: K I Rosenthal
Publisher: CRC Press
ISBN: 1498710409
Category : Mathematics
Languages : en
Pages : 160
Book Description
This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.
Publisher: CRC Press
ISBN: 1498710409
Category : Mathematics
Languages : en
Pages : 160
Book Description
This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.
Theory And Formal Methods Of Computing 94: Proceedings Of The Second Imperial College Workshop
Author: Chris Hankin
Publisher: Imperial College Press
ISBN: 178326358X
Category :
Languages : en
Pages : 446
Book Description
The focus of this workshop was the development of mathematically-based techniques of formal specification of system behaviour, and the systematic development of implementations. The aim is to produce correct, efficient implementations in a reliable fashion. Topics covered at the workshop include category theory, logic, domain theory, semantics, concurrency, specification and verification. The papers published here range from the purely theoretical to practical applications.
Publisher: Imperial College Press
ISBN: 178326358X
Category :
Languages : en
Pages : 446
Book Description
The focus of this workshop was the development of mathematically-based techniques of formal specification of system behaviour, and the systematic development of implementations. The aim is to produce correct, efficient implementations in a reliable fashion. Topics covered at the workshop include category theory, logic, domain theory, semantics, concurrency, specification and verification. The papers published here range from the purely theoretical to practical applications.
The Blind Spot
Author: Jean-Yves Girard
Publisher: European Mathematical Society
ISBN: 9783037190883
Category : Mathematics
Languages : en
Pages : 554
Book Description
These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting with Godel's paradox (1931)--so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way.
Publisher: European Mathematical Society
ISBN: 9783037190883
Category : Mathematics
Languages : en
Pages : 554
Book Description
These lectures on logic, more specifically proof theory, are basically intended for postgraduate students and researchers in logic. The question at stake is the nature of mathematical knowledge and the difference between a question and an answer, i.e., the implicit and the explicit. The problem is delicate mathematically and philosophically as well: the relation between a question and its answer is a sort of equality where one side is ``more equal than the other'': one thus discovers essentialist blind spots. Starting with Godel's paradox (1931)--so to speak, the incompleteness of answers with respect to questions--the book proceeds with paradigms inherited from Gentzen's cut-elimination (1935). Various settings are studied: sequent calculus, natural deduction, lambda calculi, category-theoretic composition, up to geometry of interaction (GoI), all devoted to explicitation, which eventually amounts to inverting an operator in a von Neumann algebra. Mathematical language is usually described as referring to a preexisting reality. Logical operations can be given an alternative procedural meaning: typically, the operators involved in GoI are invertible, not because they are constructed according to the book, but because logical rules are those ensuring invertibility. Similarly, the durability of truth should not be taken for granted: one should distinguish between imperfect (perennial) and perfect modes. The procedural explanation of the infinite thus identifies it with the unfinished, i.e., the perennial. But is perenniality perennial? This questioning yields a possible logical explanation for algorithmic complexity. This highly original course on logic by one of the world's leading proof theorists challenges mathematicians, computer scientists, physicists, and philosophers to rethink their views and concepts on the nature of mathematical knowledge in an exceptionally profound way.
Advanced Systems-Level Problem Solving, Volume 1
Author: Otto Laske
Publisher: Springer Nature
ISBN: 3031403320
Category : Psychology
Languages : en
Pages : 215
Book Description
This three-volume set introduces the practice of advanced, ‘dialectical’ systems-level problem solving in both the social and natural sciences. In social science, it opens new vistas regarding organizational, strategy, and work design. In the natural sciences, it provides heretofore missing conceptions of physical systems in peril due to the climate crisis. In addition, the author draws conclusions that are important for advancing generative AI. The monograph presents novel conceptual tools that directly impact the internal structure of a systems analyst’s mental processing in real time. While the first volume lays the theoretical groundwork for dialectical systems analysis, the second, focusing on the nature of work, lays bare the structure of complex thinking in terms of the ‘thought forms’ it requires. In order to facilitate better understanding of the principles taught in the first two volumes, the third volume provides a Manual of Dialectical Thought Forms, which is the only one in existence today.
Publisher: Springer Nature
ISBN: 3031403320
Category : Psychology
Languages : en
Pages : 215
Book Description
This three-volume set introduces the practice of advanced, ‘dialectical’ systems-level problem solving in both the social and natural sciences. In social science, it opens new vistas regarding organizational, strategy, and work design. In the natural sciences, it provides heretofore missing conceptions of physical systems in peril due to the climate crisis. In addition, the author draws conclusions that are important for advancing generative AI. The monograph presents novel conceptual tools that directly impact the internal structure of a systems analyst’s mental processing in real time. While the first volume lays the theoretical groundwork for dialectical systems analysis, the second, focusing on the nature of work, lays bare the structure of complex thinking in terms of the ‘thought forms’ it requires. In order to facilitate better understanding of the principles taught in the first two volumes, the third volume provides a Manual of Dialectical Thought Forms, which is the only one in existence today.
Linear Logic in Computer Science
Author: Thomas Ehrhard
Publisher: Cambridge University Press
ISBN: 0521608570
Category : Computers
Languages : en
Pages : 393
Book Description
This book illustrates linear logic in the application of proof theory to computer science.
Publisher: Cambridge University Press
ISBN: 0521608570
Category : Computers
Languages : en
Pages : 393
Book Description
This book illustrates linear logic in the application of proof theory to computer science.