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CSLI Lecture Notes #43: Mathematics of Modality

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CSLI Lecture Notes #43: Mathematics of Modality Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

Modal logic is the study of modalities—expressions that qualify assertions about the truth of statements—like some ordinary language phrases and mathematically motivated expressions. 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 Golblatt'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.

Table of Contents

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

Product Details

ISBN:
9781881526230
Author:
Goldblaff, Robert
Publisher:
Center for the Study of Language and Informat
Author:
Goldblatt, Robert
Subject:
Logic
Subject:
Modality (logic)
Subject:
Mathematics-Logic and Philosophy
Edition Description:
1
Series:
Center for the Study of Language and Information - Lecture Notes
Series Volume:
43
Publication Date:
19940131
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Pages:
274
Dimensions:
9 x 6 in

Related Subjects

History and Social Science » Linguistics » Specific Languages and Groups
Reference » Words Phrases and Language
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Logic and Philosophy

CSLI Lecture Notes #43: Mathematics of Modality New Trade Paper
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Product details 274 pages University of Chicago Press - English 9781881526230 Reviews:
"Synopsis" by ,
Modal logic is the study of modalities—expressions that qualify assertions about the truth of statements—like some ordinary language phrases and mathematically motivated expressions. 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 Golblatt'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.
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