Mathematics of Modality
Robert Goldblatt(Author)
The Center for the Study of Language and Information Publications (Publisher)
Published on 1. October 1993
Book
Paperback/Softback
288 pages
978-1-881526-23-0 (ISBN)
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Description
Modal logic is the study of modalities - expressions that qualify assertions about the truth of statements - like the ordinary language phrases necessarily, possibly, it is known/believed/ought to be, etc., and computationally or mathematically motivated expressions like provably, at the next state, or after the computation terminates. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades, since the introduction of the methods of Kripke semantics, and now impacts on a wide range of disciplines, including the philosophy of language and linguistics ('possible words' semantics for natural language), constructive mathematics (intuitionistic logic), theoretical computer science (dynamic logic, temporal and other logics for concurrency), and category theory (sheaf semantics). This volume collects together a number of the author's papers on modal logic, beginning with his work on the duality between algebraic and set-theoretic modals, 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. Another paper on the 'Henkin method' in completeness proofs has been substantially extended to give new applications. Additional articles are concerned with quantum logic, provability logic, the temporal logic of relativistic spacetime, modalities in topos theory, and the logic of programs.
More details
Series
Language
English
Place of publication
New York
United States
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 228 mm
Width: 152 mm
Thickness: 18 mm
Weight
474 gr
ISBN-13
978-1-881526-23-0 (9781881526230)
Schweitzer Classification
Content
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 Henkin proofs; 9. A framework for infinitary modal logic; 10. The McKinsey axiom is not canonical; 11. Elementary logics are canonical and pseudo-equational; Bibliography; Index.