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The Proof Theory and Semantics of Intuitionistic Modal Logic [PhD Thesis] by Alex K. Simpson is a nonfiction available to read on EtoBox.

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1. Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2. Intuitionistic logic 9 2.1 Natural deduction for intuitionistic logic . . . . . . . . . . . . . . . 9 2.1.1 The natural deduction system . . . . . . . . . . . . . . . . . 9 2.1.2 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 The semantics of intuitionistic logic . . . . . . . . . . . . . . . . . . 20 2.3 Geometric theories in intuitionistic logic . . . . . . . . . . . . . . . 24 3. Intuitionistic modal logic 32 3.1 Modal logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.2 What is intuitionistic modal logic? . . . . . . . . . . . . . . . . . . 38 3.3 Previous approaches to intuitionistic modal logic . . . . . . . . . . . 41 3.4 Our approach to intuitionistic modal logic . . . . . . . . . . . . . . 58 4. Natural deduction for intuitionistic modal logics 65 4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2 The basic modal natural deduction system . . . . . . . . . . . . . . 70 4.3 Conditions on the visibility relation .

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Author

Alex K. Simpson

Publisher

University of Edinburgh

Published

1994

Language

EN

Category

nonfiction

Subjects

Mathematics, Logic, Stem