Closure Spaces and Logic PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Closure Spaces and Logic PDF full book. Access full book title Closure Spaces and Logic by N.M. Martin. Download full books in PDF and EPUB format.
Author: N.M. Martin
Publisher: Springer Science & Business Media
ISBN: 147572506X
Category : Mathematics
Languages : en
Pages : 241
Get Book Here
Book Description
This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract, it may find a natural home within several of the more familiar branches of mathematics. This is the case with the theory of closure spaces. It might be considered part of topology, lattice theory, universal algebra or, no doubt, one of several other branches of mathematics as well. In our development we have treated it, conceptually and methodologically, as part of topology, partly because we first thought ofthe basic structure involved (closure space), as a generalization of Frechet's concept V-space. V-spaces have been used in some developments of general topology as a generalization of topological space. Indeed, when in the early '50s, one of us started thinking about closure spaces, we thought ofit as the generalization of Frechet V space which comes from not requiring the null set to be CLOSURE SPACES ANDLOGIC XlI closed(as it is in V-spaces). This generalization has an extreme advantage in connection with application to logic, since the most important closure notion in logic, deductive closure, in most cases does not generate a V-space, since the closure of the null set typically consists of the "logical truths" of the logic being examined.
Author: N.M. Martin
Publisher: Springer Science & Business Media
ISBN: 147572506X
Category : Mathematics
Languages : en
Pages : 241
Get Book Here
Book Description
This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract, it may find a natural home within several of the more familiar branches of mathematics. This is the case with the theory of closure spaces. It might be considered part of topology, lattice theory, universal algebra or, no doubt, one of several other branches of mathematics as well. In our development we have treated it, conceptually and methodologically, as part of topology, partly because we first thought ofthe basic structure involved (closure space), as a generalization of Frechet's concept V-space. V-spaces have been used in some developments of general topology as a generalization of topological space. Indeed, when in the early '50s, one of us started thinking about closure spaces, we thought ofit as the generalization of Frechet V space which comes from not requiring the null set to be CLOSURE SPACES ANDLOGIC XlI closed(as it is in V-spaces). This generalization has an extreme advantage in connection with application to logic, since the most important closure notion in logic, deductive closure, in most cases does not generate a V-space, since the closure of the null set typically consists of the "logical truths" of the logic being examined.
Author: Bob Richardson
Publisher:
ISBN:
Category : Topological spaces
Languages : en
Pages : 76
Get Book Here
Book Description
The first chapter of this thesis expands on the semi-closure operator discussed by Hong in his paper, and in particular how sets behave in a semi-closure space. Hong notes that a semi-closure space is a generalized topological space, and in this thesis, an example of a semi-closure space is shown to not be topological; i.e. semi-closure spaces are less restrictive. In the second chapter, continuity of functions between two semi-closure spaces, separation of points within a semi-closure space, and compactness of semi-closure spaces are established. An example of a T2 semi-closure space is found to not be topological, again showing semi-closure spaces to less restrictive. The third chapter explores how extensions of topologies discussed by Hicks can be applied to semi-closure spaces. By intersecting closed subsets from semi-closure subspaces with arbitrary sets in the larger space, we increase, or extend, the number of closed sets in our space.
Author: Martin Jackson
Publisher:
ISBN: 9781475725070
Category :
Languages : en
Pages : 252
Get Book Here
Book Description
Author: Niels Schwartz
Publisher: American Mathematical Soc.
ISBN: 0821824600
Category : Commutative algebra
Languages : en
Pages : 134
Get Book Here
Book Description
Much in the same way as classical algebraic varieties are generalized by the theory of schemes, locally semi-algebraic spaces are generalized by a class of locally ringed spaces, called real closed spaces. The underlying spaces of affine real closed spaces are real spectra of rings, the structure sheaves are called real closed sheaves. With these spaces a theory can be developed which is very similar to the theory of schemes. There is a natural functor from the category of semi-algebraic spaces to the category of real closed spaces. Via this functor properties of semi-algebraic spaces and their corresponding real closed spaces can be compared.
Author: Stefan Kramer
Publisher: Springer
ISBN: 3540318518
Category : Computers
Languages : en
Pages : 437
Get Book Here
Book Description
1 “Change is inevitable.” Embracing this quote we have tried to carefully exp- iment with the format of this conference, the 15th International Conference on Inductive Logic Programming, hopefully making it even better than it already was. But it will be up to you, the inquisitive reader of this book, to judge our success. The major changes comprised broadening the scope of the conference to include more diverse forms of non-propositional learning, to once again have tutorials on exciting new areas, and, for the ?rst time, to also have a discovery challenge as a platform for collaborative work. This year the conference was co-located with ICML 2005, the 22nd Inter- tional Conference on Machine Learning, and also in close proximity to IJCAI 2005, the 19th International Joint Conference on Arti?cial Intelligence. - location can be tricky, but we greatly bene?ted from the local support provided by Codrina Lauth, Michael May, and others. We were also able to invite all ILP and ICML participants to shared events including a poster session, an invited talk, and a tutorial about the exciting new area of “statistical relational lea- ing”. Two more invited talks were exclusively given to ILP participants and were presented as a kind of stock-taking—?ttingly so for the 15th event in a series—but also tried to provide a recipe for future endeavours.
Author: Enrico G. Beltrametti
Publisher: Cambridge University Press
ISBN: 9780521168496
Category : Mathematics
Languages : en
Pages : 340
Get Book Here
Book Description
This volume examines the logic, theory and mathematics of quantum mechanics in a clear and thorough way.
Author: Bernhard E. von Stengel
Publisher:
ISBN:
Category : Closure operators
Languages : en
Pages : 132
Get Book Here
Book Description
Author: Nina Gierasimczuk
Publisher: Springer Nature
ISBN: 3031517776
Category : Computers
Languages : en
Pages : 147
Get Book Here
Book Description
This book constitutes the revised selected papers of the 5th International Workshop on Dynamic Logic. New Trends and Applications, DaLí 2023, held in Tbilisi, Georgia, during September 15–16, 2023. The 8 full papers in this book were carefully reviewed and selected from 10 submissions. They deal with new trends and applications in the area of Dynamic Logic.
Author: Tai-He Fan
Publisher: Springer
ISBN: 3319462067
Category : Technology & Engineering
Languages : en
Pages : 654
Get Book Here
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: Jyotirmoy Deshmukh
Publisher: Springer Nature
ISBN: 3030605086
Category : Computers
Languages : en
Pages : 538
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 20th International Conference on Runtime Verification, RV 2020, held in Los Angeles, CA, USA, in October 2020. The conference was held virtually due to the COVID-19 pandemic. The 14 regular papers and 2 short papers presented in this book were carefully reviewed and selected from 43 submissions. Also included are an invited paper, 5 tutorial papers, 6 tool papers, and a benchmark paper. The RV conference is concerned with all aspects of monitoring and analysis of hardware, software and more general system executions. The papers are organized in the following topical sections: runtime verification for autonomy; runtime verification for software; runtime verification with temporal logic specifications; stream-based monitoring; and runtime verification for cyber-physical systems.
