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Universal Algebraic Logic - Dedicated to the Unity of Science (Hardcover, 1st ed. 2022)
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Universal Algebraic Logic - Dedicated to the Unity of Science (Hardcover, 1st ed. 2022)
Series: Studies in Universal Logic
Expected to ship within 10 - 15 working days
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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.
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