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Classical First Order Logic 1st Edition by Stewart Shapiro, Teresa Kouri Kissel ISBN 9781108987004 1108987001

Name: Classical First Order Logic 1st Edition by Stewart Shapiro, Teresa Kouri Kissel ISBN 9781108987004 1108987001
SKU: EB-48072156
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Classical First Order Logic 1st Edition Stewart Shapiro Digital Instant Download

Author(s): Stewart Shapiro, Teresa Kouri Kissel

ISBN(s): 9781108987004, 1108987001, 25164171

Edition: 1

File Details: PDF, 1.01 MB

Year: 2022

Language: English

SKU: EB-48072156 Category: Mathematics - Logic Tags: Stewart Shapiro, Teresa Kouri Kissel

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Classical First Order Logic 1st Edition by Stewart Shapiro, Teresa Kouri Kissel – Ebook PDF Instant Download/Delivery: 9781108987004 ,1108987001
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Product details:
ISBN 10: 1108987001
ISBN 13: 9781108987004
Author: Stewart Shapiro, Teresa Kouri Kissel

One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. The authors provide theorems about the system they developed, such as unique readability and the Lindenbaum lemma. They also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet.

Classical First Order Logic 1st Edition Table of contents:

1 Introduction
Classical First-Order Logic
2 Formal System
3 Language
3.1 Building Blocks
3.2 Atomic Formulas
3.3 Compound Formulas
3.4 Features of the Syntax
4 Deduction
5 Model-Theoretic Semantics
6 Meta-theory
Alternatives to Classical First-Order Logic
7 Classical Higher-Order Logic
7.1 Languages
7.2 Deductive System
7.3 Model Theory
7.3.1 Standard Semantics
7.3.2 Henkin Semantics
7.3.3 Multi-sorted, First-order Semantics
7.3.4 Plural Quantification
7.4 Meta-theory
7.4.1 Henkin and First-order Semantics
7.4.2 Standard Semantics
8 Intuitionism
8.1 Philosophical background
8.1.1 Brouwer and Heyting on the Nature of Mathematics
8.1.2 Dummett: Considerations on Language
8.1.3 Drawbacks
8.2 Deduction
8.2.1 Heyting Predicate Calculus
8.2.2 Comparison with the Classical System D
8.3 Informal Semantics: The Brouwer, Heyting, Kolmogorov (BHK) Interpretation
8.4 Kripke Frames
9 Paraconsistency: Demurring from ex falso quodlibet
9.1 Relevance
9.1.1 Motivation
9.1.2 Deduction
9.1.3 A Sample Model Theory
9.2 Dialetheism
9.3 Core Logic
9.4 Meta-theoretic Issues
10 Conclusion

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Tags: Stewart Shapiro, Teresa Kouri Kissel, Classical, First Order Logic