Algebraic Methods In Philosophical Logic
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Algebraic Methods In Philosophical Logic
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Author : J. Michael Dunn
language : en
Publisher:
Release Date : 2001
Algebraic Methods In Philosophical Logic written by J. Michael Dunn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Algebraic Methods In Philosophical Logic
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Author : J. Michael Dunn
language : en
Publisher: OUP Oxford
Release Date : 2001-06-28
Algebraic Methods In Philosophical Logic written by J. Michael Dunn and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-28 with Common law categories.
This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translate into standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.
Protoalgebraic Logics
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Author : Janusz Czelakowski
language : en
Publisher: Boom Koninklijke Uitgevers
Release Date : 2001-04-30
Protoalgebraic Logics written by Janusz Czelakowski and has been published by Boom Koninklijke Uitgevers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-30 with Language Arts & Disciplines categories.
The main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, where the focus is on the algebraic forms of specific deductive systems, abstract algebraic logic is concerned with the process of algebraization itself. This book presents in a systematic way recent ideas in abstract algebraic logic centered around the notion of the Leibniz operator. The stress is put on the taxonomy of deductive systems. Isolating a list of plausible properties of the Leibniz operator serves as a basis for distinguishing certain natural classes of sentential logics. The hierarchy of deductive systems presented in the book comprises, among others, the following classes: protoalgebraic logics, equivalential logics, algebraizable logics, and Fregean logics. Because of the intimate connection between algebraic and logical structures, the book also provides a uniform treatment of various topics concerning deduction theorems and quasivarieties of algebras. The presentation of the above classes of logics is accompanied by a wealth of examples illustrating the general theory. An essential part of the book is formed by the numerous exercises integrated into the text. This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and as a reference work for the expert.
Algebraic Theory Of Machines Languages And Semi Groups
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Author : Kenneth Krohn
language : en
Publisher:
Release Date : 1968
Algebraic Theory Of Machines Languages And Semi Groups written by Kenneth Krohn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Computers categories.
The book is an integrated exposition of the algebraic, and especially semigroup-theoretic, approach to machines and languages. It is designed to carry the reader from the elementary theory all the way to hitherto unpublished research results.
The Logic Of Real Arguments
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Author : Alec Fisher
language : en
Publisher: Cambridge University Press
Release Date : 2004-09-23
The Logic Of Real Arguments written by Alec Fisher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-23 with Philosophy categories.
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Algebraic Set Theory
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Author : André Joyal
language : en
Publisher: Cambridge University Press
Release Date : 1995-09-14
Algebraic Set Theory written by André Joyal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-14 with Mathematics categories.
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
An Algebraic Introduction To Mathematical Logic
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Author : D.W. Barnes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
An Algebraic Introduction To Mathematical Logic written by D.W. Barnes 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 2013-06-29 with Mathematics categories.
This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a substantial course on abstract algebra. Consequently, our treatment of the subject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.
A Structuralist Theory Of Logic
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Author : Arnold Koslow
language : en
Publisher: Cambridge University Press
Release Date : 1992-03-27
A Structuralist Theory Of Logic written by Arnold Koslow and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-27 with Mathematics categories.
Professor Koslow advances a new account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general concept of an implication structure and its forms are illustrated and explained. Part 3 defines the various logical operations and systematically explores their properties. A generalized account of extensionality and dual implication is given, and the extensionality of each of the operators, as well as the relation of negation and its dual are given substantial treatment because of the novel results they yield. Part 4 considers modal operators and studies their interaction with logical operators. By obtaining the usual results without the usual assumptions this new approach allows one to give a very simple account of modal logic minus the excess baggage of possible world semantics.
Handbook Of Philosophical Logic
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Handbook Of Philosophical Logic written by Dov M. Gabbay 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 2013-03-09 with Philosophy categories.
It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
Proof Theory And Algebra In Logic
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Author : Hiroakira Ono
language : en
Publisher: Springer
Release Date : 2019-08-02
Proof Theory And Algebra In Logic written by Hiroakira Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-02 with Philosophy categories.
This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.