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Mathematics of Modality cover

Mathematics of Modality

Robert Goldblatt

Modal logic is the study of modalities- expressions that qualify assertions about the truth of statements. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades. This volume collects together a number of Goldblatt's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic models, and including two new articles, one on infinitary rules of inference, and the other about recent results on the relationship between modal logic and first-order logic.

Robert Goldblatt is professor of pure mathematics at the Victoria University of Wellington, New Zealand, and is the author of Topoi: The Categorical Analysis of Logic, Axiomatising the Logic of Computer Programming, Orthogonality and Spacetime Geometry, and Logics of Time and Computation.


  • Introduction
  • 1 Metamathematics of Modal Logic
  • 2 Semantic Analysis of Orthologic
  • 3 Orthomodularity is not Elementary
  • 4 Arithmetical Necessity, Provability and Intuitionistic Logic
  • 5 Diodorean Modality in Minkowski Spacetime
  • 6 Grothendieck Topology as Geometric Modality
  • 7 The Semantics of Hoare's Iteration Rule
  • 8 An Abstract Setting for Henken Proofs
  • 9 A Framework for Infinitary Modal Logic
  • 10 The Mckinsey Axiom Is Not Canonical
  • 11 Elementary Logics are Canonical and Psuedo-Equational
  • Bibliography
  • Index


ISBN (Paperback): 1881526232 (9781881526230)
ISBN (Cloth): 1881526240 (9781881526247)
ISBN (Electronic): 1575868016 (9781575868011)

Subject: Mathematics; Modality

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