Leo Esakia on Duality in Modal and Intuitionistic Logics
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Leo Esakia on Duality in Modal and Intuitionistic Logics

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Description

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia's original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area.

Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Goedel-Loeb provability logic GL. One chapter scrutinizes Esakia's work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.
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Product details

  • Hardback | 334 pages
  • 155 x 235 x 22.86mm | 6,447g
  • Dordrecht, Netherlands
  • English
  • 2014 ed.
  • 44 Illustrations, black and white; XIII, 334 p. 44 illus.
  • 9401788596
  • 9789401788595

Back cover copy

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia's original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics, and to utilize it to obtain some major results in the area.



Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia's work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.
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Table of contents

Preface.- Introduction.- Esakia's Biography.- Canonical extensions, Esakia spaces, and universal models; Mai Gehrke.- Free modal algebras revisited: the step-by-step method; Nick Bezhanishvili, Silvio Ghilardi, and Mamuka Jibladze.- Easkia duality and its extensions; Sergio A. Celani and Ramon Jansana.- On the Blok-Esakia Theorem; Frank Wolter and Michael Zakharyaschev.- Modal logic and the Vietoris functor; Yde Venema and Jacob Vosmaer.- Logic KM: A Biography; Alexei Muravitsky .- Constructive modalities with provability smack; Tadeusz Litak.- Cantor-Bendixson properties of the assembly of a frame; Harold Simmons.- Topological interpretations of provability logic; Lev Beklemishev and David Gabelaia.- Derivational modal logics with the difference modality; Andrey Kudinov and Valentin Shehtman.- Esakia's Bibliography.
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Review Text

From the reviews:
"This is a good book on algebras and set theories of intuitionistic and modal logics. ... This a very good book for logicians and mathematics scholars." (Joseph J. Grenier, Amazon.com, June, 2014)
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Review quote

"All chapters of the collection pay tribute to L.
Esakia's outstanding technical work, which inspired greatly several researchers,
not only in Georgia but also all over the world, to carry out extensive and
deep investigations on modal and intuitionistic logics. For this reason, the
volume under review is necessary reading for anyone interested in Esakia's
contributions, as well as the current state of the large area in which he
conducted his research." (Costas Dimitracopoulos, Metascience, Vol. 24, 2015)

"This is a good book on algebras and set theories of intuitionistic and modal logics. ... This a very good book for logicians and mathematics scholars." (Joseph J. Grenier, Amazon.com, June, 2014)
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