Elsevier

Journal of Applied Logic

Volume 6, Issue 3, September 2008, Pages 267-286
Journal of Applied Logic

The seven virtues of simple type theory

https://doi.org/10.1016/j.jal.2007.11.001Get rights and content
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Abstract

Simple type theory, also known as higher-order logic, is a natural extension of first-order logic which is simple, elegant, highly expressive, and practical. This paper surveys the virtues of simple type theory and attempts to show that simple type theory is an attractive alternative to first-order logic for practical-minded scientists, engineers, and mathematicians. It recommends that simple type theory be incorporated into introductory logic courses offered by mathematics departments and into the undergraduate curricula for computer science and software engineering students.

Keywords

Higher-order logic
Type theory
Practical logics
Nonstandard models
Peano arithmetic
Complete ordered field

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