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Dualities for Structures of Applied Logics by Ewa Orlowska, Anna Maria Radzikowska, Ingid Rewitzky

Dualities for Structures of Applied Logics

by Ewa Orlowska , Anna Maria Radzikowska , Ingid Rewitzky
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Book cover type: Paperback
  • ISBN13: 9781848901810
  • Binding: Paperback
  • Subject: N/A
  • Publisher: College Publications
  • Publisher Imprint: College Publications
  • Publication Date:
  • Pages: 396
  • Original Price: GBP 16.5
  • Language: English
  • Edition: N/A
  • Item Weight: 554 grams
  • BISAC Subject(s): Logic

This book provides a framework for presenting algebras and frames arising as semantic structures for formal languages and for proving relationships between the structures. For this purpose a discrete framework, referred to as discrete duality, is used rather than a topological framework. Ideas from the classical dualities and representations of Stone, Priestley, and Urquhart are applied in such a way that topology is not part of any of the underlying structures or relationships. A key contribution of the book is the formulation of the concept of duality via truth for expressing that a class of algebras and a class of frames determine equivalent notions of truth for a given formal language. Discrete duality and duality via truth are applied to a wealth of case studies presented in three main parts, namely, classes of Boolean lattices, distributive lattices, and general, that is not necessarily distributive, lattices, respectively. The book is self-contained and all the results are proved in sufficient detail enabling an easy verification.

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