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Titlebook: Logica Universalis; Towards a General Th Jean-Yves Beziau Conference proceedings 20051st edition Birkhäuser Basel 2005 Mathematica.abstract

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书目名称Logica Universalis
副标题Towards a General Th
编辑Jean-Yves Beziau
视频video
概述Second, revised edition of the first collection of articles around the topic of universal logic.Starting point of interdisciplinary research in the fields of, e.g., logic, linguistic, philosophy, math
图书封面Titlebook: Logica Universalis; Towards a General Th Jean-Yves Beziau Conference proceedings 20051st edition Birkhäuser Basel 2005 Mathematica.abstract
描述."I find this book extremely useful and important, because it signifies the arrival of a new renaissance in logic, a new revival not only of logic, but of the vision of logic as a unifying tool for science as a whole, including mathematics, physics, cosmology, computer science and AI. The book and the vision behind it give logic, conceived as a scientific study of rationality, new unifying power, new perspectives, and new horizons."...Istvan Németi, Hungarian Academy of Sciences..."Modern logic has been intimately connected with algebra since its origins in figures such as Boole, De Morgan, and Peirce. But while universal algebra is a long recognized field, universal logic has only recently been named as such. This is perhaps because classical logic was until relatively recently taken by many as the "one true logic". But with the proliferation of special purpose non-classical logics in recent years, universal logic is clearly a field whose time has come. This book contains many excellent papers demonstrating the value of this approach."...J. Michael Dunn, Indiana University..."Modern logic is exploding into manifold applications, and its core research agenda is expanding accordingl
出版日期Conference proceedings 20051st edition
关键词Mathematica; abstract model theory; algebraic logic; categorical logic; consequence relations; identity b
版次1
doihttps://doi.org/10.1007/b137041
isbn_ebook978-3-7643-7304-7
copyrightBirkhäuser Basel 2005
The information of publication is updating

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发表于 2025-3-21 21:50:36 | 显示全部楼层
Abstract Model Theory as a Framework for Universal Logic which covers both classical and non-classical logics. This approach aims at unifying model-theoretic results covering as large a variety of examples as possible, in harmony with the general aim of universal logic.
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A Topological Approach to Universal Logic: Model-Theoretical Abstract Logicsing of a set of expressions, a class of interpretations and a satisfaction relation between interpretations (models) and expressions. The main idea is to use the observation that there exist in some sense pre-topological structures on the set of theories and on the class of interpretations. For exam
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Equipollent Logical Systemsen logical systems, bearing in mind the expressive power of their associated spaces of theories, but without neglecting their syntactical dimension. Departing from a categorial analysis of the question, we introduce the new notion of . between logical systems. We use several examples to illustrate o
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What is a Logic? and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalen
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What is a Logic, and What is a Proof? propose a possible notion, which might be considered to be folklore, but which seems to be the right one from the viewpoint of the problem of the identity of proofs. For that problem I will indicate a possible direction of research.
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