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Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs

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  • © 2022

Overview

Editors:
  1. Ivo Düntsch

    1. Department of Computer Science, Brock University, St. Catharines, Canada

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  2. Edwin Mares

    1. School of History, Philosophy, Political Science and International Relations, Victoria University of Wellington, Wellington, New Zealand

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    You can also search for this editor in PubMed   Google Scholar

  • Celebrates the important work and career of Alasdair Urquhart
  • Brings together authors from Europe and North America
  • Contains original papers and responses

Part of the book series: Outstanding Contributions to Logic (OCTR, volume 22)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xiii
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  2. A Logical Autobiography

    • Alasdair Urquhart
    Pages 1-21

  3. Relevance-Sensitive Truth-Trees

    • David Makinson
    Pages 23-65

  4. Tarskian Classical Relevant Logic

    • Roger D. Maddux
    Pages 67-161

  5. Algorithmic Correspondence for Relevance Logics I. The Algorithm \(\mathsf {PEARL}\)

    • Willem Conradie, Valentin Goranko
    Pages 163-211

  6. Beth Definability in the Logic KR

    • Jacob Garber
    Pages 213-224

  7. Geometric Models for Relevant Logics

    • Greg Restall
    Pages 225-242

  8. Revisiting Semilattice Semantics

    • Shawn Standefer
    Pages 243-259

  9. The Universal Theory Tool Building Toolkit Is Substructural

    • Shay Allen Logan
    Pages 261-285

  10. More on the Power of a Constant

    • Marcus Kracht
    Pages 287-290

  11. Strong Completeness of S4 for the Real Line

    • Philip Kremer
    Pages 291-302

  12. Modal Logics of Some Hereditarily Irresolvable Spaces

    • Robert Goldblatt
    Pages 303-322

  13. St. Alasdair on Lattices Everywhere

    • Katalin Bimbó, J. Michael Dunn
    Pages 323-346

  14. Application of Urquhart’s Representation of Lattices to Some Non–classical Logics

    • Ivo Düntsch, Ewa Orłowska
    Pages 347-366

  15. Ockham Algebras—An Urquhart Legacy

    • T. S. Blyth, H. J. Silva
    Pages 367-387

  16. Temporal Logic of Minkowski Spacetime

    • Robin Hirsch, Brett McLean
    Pages 389-409

  17. Dynamic Contact Algebras with a Predicate of Actual Existence: Snapshot Representation and Topological Duality

    • Dimiter Vakarelov
    Pages 411-475

  18. Substitution and Propositional Proof Complexity

    • Sam Buss
    Pages 477-496

  19. Reflections on Proof Complexity and Counting Principles

    • Noah Fleming, Toniann Pitassi
    Pages 497-520

  20. Satisfiability, Lattices, Temporal Logic and Constraint Logic Programming on Intervals

    • André Vellino
    Pages 521-536
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Keywords

About this book

This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart.


Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, hehas produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.

Editors and Affiliations

  • Department of Computer Science, Brock University, St. Catharines, Canada

    Ivo Düntsch

  • School of History, Philosophy, Political Science and International Relations, Victoria University of Wellington, Wellington, New Zealand

    Edwin Mares

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