Perspectives on Universal Logic PDF Download

Author: J. Y. Beziau
Publisher: Polimetrica s.a.s.
ISBN: 8876990771
Category : Mathematics
Languages : en
Pages : 442

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Book Description

Author: Jean-Yves Beziau
Publisher: Springer Science & Business Media
ISBN: 3764383542
Category : Mathematics
Languages : en
Pages : 247

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Book Description
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.

Author: Julie Brumberg-Chaumont
Publisher: Springer Nature
ISBN: 3030584461
Category : Philosophy
Languages : en
Pages : 172

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Book Description
This contributed volume explores the ways logical skills have been perceived over the course of history. The authors approach the topic from the lenses of philosophy, anthropology, sociology, and history to examine two opposing perceptions of logic: the first as an innate human ability and the second as a skill that can be learned and mastered. Chapters focus on the social and political dynamics of the use of logic throughout history, utilizing case studies and critical analyses. Specific topics covered include: the rise of logical skills problems concerning medieval notions of idiocy and rationality decolonizing natural logic natural logic and the course of time Logical Skills: Social-Historical Perspectives will appeal to undergraduate and graduate students, as well as researchers in the fields of history, sociology, philosophy, and logic. Psychology and colonial studies scholars will also find this volume to be of particular interest.

Author: Arnold Koslow
Publisher: Birkhäuser
ISBN: 3319153684
Category : Mathematics
Languages : en
Pages : 607

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Book Description
This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.

Author: Jean-Yves Béziau
Publisher: Birkhäuser
ISBN: 9783034601443
Category : Mathematics
Languages : en
Pages : 0

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Book Description
A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and influence.

Author: Hajnal Andréka
Publisher: Springer Nature
ISBN: 3031148878
Category : Mathematics
Languages : en
Pages : 337

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Book Description
This book gives a comprehensive introduction to Universal Algebraic Logic. The three main themes are (i) universal logic and the question of what logic is, (ii) duality theories between the world of logics and the world of algebra, and (iii) Tarskian algebraic logic proper including algebras of relations of various ranks, cylindric algebras, relation algebras, polyadic algebras and other kinds of algebras of logic. One of the strengths of our approach is that it is directly applicable to a wide range of logics including not only propositional logics but also e.g. classical first order logic and other quantifier logics. Following the Tarskian tradition, besides the connections between logic and algebra, related logical connections with geometry and eventually spacetime geometry leading up to relativity are also part of the perspective of the book. Besides Tarskian algebraizations of logics, category theoretical perspectives are also touched upon. This book, apart from being a monograph containing state of the art results in algebraic logic, can be used as the basis for a number of different courses intended for both novices and more experienced students of logic, mathematics, or philosophy. For instance, the first two chapters can be used in their own right as a crash course in Universal Algebra.

Author: Jean-Yves Béziau
Publisher: Birkhäuser
ISBN: 9783034601467
Category : Mathematics
Languages : en
Pages : 410

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Book Description
A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and influence.

Author: Jean-Yves Beziau
Publisher: Birkhäuser
ISBN: 9783764383534
Category : Mathematics
Languages : en
Pages : 246

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Book Description
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.

Author: Ross Brady
Publisher: Stanford Univ Center for the Study
ISBN: 9781575862552
Category : Mathematics
Languages : en
Pages : 346

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Book Description
This work conceptualizes a new logic, where the main inference connective is understood as meaning containment. Classical logic plays a restricted role, applying to classical sentences, while the new logic is studied in depth with chapters on semantics, proof theory, and properties. Based on this logic, simple consistency is proved for naive class theory, also in conjunction with classical theories such as a Z-F-style set theory. This book shows how the main set-theoretic and semantic paradoxes can be solved in a systematic way, which is conceptualized independently of the paradoxes themselves.

Author: Paolo Rossi
Publisher: University of Chicago Press
ISBN: 0226728269
Category : Philosophy
Languages : en
Pages : 361

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Book Description
The mnemonic arts and the idea of a universal language that would capture the essence of all things were originally associated with cryptology, mysticism, and other occult practices. And it is commonly held that these enigmatic efforts were abandoned with the development of formal logic in the seventeenth century and the beginning of the modern era. In his distinguished book, Logic and the Art of Memory Italian philosopher and historian Paolo Rossi argues that this view is belied by an examination of the history of the idea of a universal language. Based on comprehensive analyses of original texts, Rossi traces the development of this idea from late medieval thinkers such as Ramon Lull through Bruno, Bacon, Descartes, and finally Leibniz in the seventeenth century. The search for a symbolic mode of communication that would be intelligible to everyone was not a mere vestige of magical thinking and occult sciences, but a fundamental component of Renaissance and Enlightenment thought. Seen from this perspective, modern science and combinatorial logic represent not a break from the past but rather its full maturity. Available for the first time in English, this book (originally titled Clavis Universalis) remains one of the most important contributions to the history of ideas ever written. In addition to his eagerly anticipated translation, Steven Clucas offers a substantial introduction that places this book in the context of other recent works on this fascinating subject. A rich history and valuable sourcebook, Logic and the Art of Memory documents an essential chapter in the development of human reason.