An Algebraic Approach To Non Classical Logics
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An Algebraic Approach To Non Classical Logics
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Author : Helena Rasiowa
language : en
Publisher:
Release Date : 1974
An Algebraic Approach To Non Classical Logics written by Helena Rasiowa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Algebraic logic categories.
Sheaves Games And Model Completions
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Author : Silvio Ghilardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Sheaves Games And Model Completions written by Silvio Ghilardi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
This book is an example of fruitful interaction between (non-classical) propo sitionallogics and (classical) model theory which was made possible due to categorical logic. Its main aim consists in investigating the existence of model completions for equational theories arising from propositional logics (such as the theory of Heyting algebras and various kinds of theories related to proposi tional modal logic ). The existence of model-completions turns out to be related to proof-theoretic facts concerning interpretability of second order propositional logic into ordinary propositional logic through the so-called 'Pitts' quantifiers' or 'bisimulation quantifiers'. On the other hand, the book develops a large number of topics concerning the categorical structure of finitely presented al gebras, with related applications to propositional logics, both standard (like Beth's theorems) and new (like effectiveness of internal equivalence relations, projectivity and definability of dual connectives such as difference). A special emphasis is put on sheaf representation, showing that much of the nice categor ical structure of finitely presented algebras is in fact only a restriction of natural structure in sheaves. Applications to the theory of classifying toposes are also covered, yielding new examples. The book has to be considered mainly as a research book, reporting recent and often completely new results in the field; we believe it can also be fruitfully used as a complementary book for graduate courses in categorical and algebraic logic, universal algebra, model theory, and non-classical logics. 1.
An Algebraic Approach To Non Classical Logics
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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01
An Algebraic Approach To Non Classical Logics written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
An Algebraic Approach to Non-Classical Logics
V A Yankov On Non Classical Logics History And Philosophy Of Mathematics
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Author : Alex Citkin
language : en
Publisher: Springer Nature
Release Date : 2022-11-08
V A Yankov On Non Classical Logics History And Philosophy Of Mathematics written by Alex Citkin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-08 with Mathematics categories.
This book is dedicated to V.A. Yankov’s seminal contributions to the theory of propositional logics. His papers, published in the 1960s, are highly cited even today. The Yankov characteristic formulas have become a very useful tool in propositional, modal and algebraic logic. The papers contributed to this book provide the new results on different generalizations and applications of characteristic formulas in propositional, modal and algebraic logics. In particular, an exposition of Yankov’s results and their applications in algebraic logic, the theory of admissible rules and refutation systems is included in the book. In addition, the reader can find the studies on splitting and join-splitting in intermediate propositional logics that are based on Yankov-type formulas which are closely related to canonical formulas, and the study of properties of predicate extensions of non-classical propositional logics. The book also contains an exposition of Yankov’s revolutionary approach to constructive proof theory. The editors also include Yankov’s contributions to history and philosophy of mathematics and foundations of mathematics, as well as an examination of his original interpretation of history of Greek philosophy and mathematics.
An Algebraic Approach To Non Classical Logics
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Author : Helena Rasiowa
language : en
Publisher:
Release Date : 1974
An Algebraic Approach To Non Classical Logics written by Helena Rasiowa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Algebraic logic categories.
The main aim of this book is to formulate an algebraic approach to a carefully selected widest possible class of logics and to prove fundamental theorems for it, which previously have usually been proved for each of those logics separately. The second aim of this book has been to give a number of examples of logics which belong to the class above.
Abstract Algebraic Logic An Introductory Textbook
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Author : Josep Maria Font
language : en
Publisher:
Release Date : 2016-04-11
Abstract Algebraic Logic An Introductory Textbook written by Josep Maria Font and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-11 with Computers categories.
Abstract algebraic logic is the more general and abstract side of algebraic logic, the branch of mathematics that studies the connections between logics and their algebra-based semantics. This emerging subfield of mathematical logic consolidated since the 1980s, and is considered as the algebraic logic of the twenty-first century; as such it is increasingly becoming an indispensable tool to approach the algebraic study of any (mainly sentential) logic in a systematic way. This book is an introductory textbook on abstract algebraic logic, and takes a bottom-up approach, treating first logics with a simpler algebraic study, such as Rasiowa's implicative logics, and then guides readers, by means of successive steps of generalization and abstraction, to meet more and more complicated algebra-based semantics. An entire chapter is devoted to Blok and Pigozzi's theory of algebraizable logics, proving the main theorems and incorporating later developments by other scholars. After a chapter with the basics of the classical theory of matrices, one chapter is devoted to an in-depth exposition of the semantics of generalized matrices. There are also two more avanced chapters providing introductions to the two hierachies that organize the logical landscape according to the criteria of abstract algebraic logic, the Leibniz hierarchy and the Frege hierarchy. All throughout the book, particular care is devoted to the presentation and classification of dozens of examples of particular logics. The book is addressed to mathematicians and logicians with little or no previous exposure to algebraic logic. Some acquaintance with examples of non-classical logics is desirable in order to appreciate the extremely general theory. The book is written with students (or beginners in the field) in mind, and combines a textbook style in its main sections, including more than 400 carefully graded exercises, with a survey style in the exposition of some research directions. The book includes scattered historical notes and numerous bibliographic references.
Alasdair Urquhart On Nonclassical And Algebraic Logic And Complexity Of Proofs
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Author : Ivo Düntsch
language : en
Publisher: Springer Nature
Release Date : 2021-09-24
Alasdair Urquhart On Nonclassical And Algebraic Logic And Complexity Of Proofs written by Ivo Düntsch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-24 with Philosophy categories.
This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.
Consequence Relations
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Author : Alex Citkin
language : en
Publisher: Oxford University Press
Release Date : 2022-06-30
Consequence Relations written by Alex Citkin and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-30 with Young Adult Nonfiction categories.
The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The work also includes helpful exercises to aid the reader's assimilation of the book's material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.
Classical And Nonclassical Logics
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Author : Eric Schechter
language : en
Publisher: Princeton University Press
Release Date : 2005-08-28
Classical And Nonclassical Logics written by Eric Schechter and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-28 with Mathematics categories.
Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).
Logica Universalis
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Author : Jean-Yves Beziau
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-06
Logica Universalis written by Jean-Yves Beziau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-06 with Mathematics categories.
Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic. It was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. The present book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. It will help those who are lost in the jungle of heterogeneous logical systems to find a way. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.