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Mathematics of Modality (Paperback, 2nd Ed.)
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Mathematics of Modality (Paperback, 2nd Ed.)
Series: Center for the Study of Language and Information Publication Lecture Notes, 43
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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.
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