Abstract
This chapter discusses induction, a classic proof technique for proving first-order theorems with universal quantifiers. Section 4.1 begins with stepwise induction, which may be familiar to the reader from earlier education. Section 4.2 then introduces complete induction in the context of arithmetic. Complete induction is theoretically equivalent in power to stepwise induction but sometimes produces more concise proofs. Section 4.3 generalizes complete induction to well-founded induction in the context of arithmetic and recursive data structures. Finally, Section 4.4 covers a form of well-founded induction over logical formulae called structural induction. It is useful for reasoning about correctness of decision procedures and properties of logical theories and their interpretations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliographic Remarks
Z. Manna and R. Waldinger. The Deductive Foundations of Computer Programming. Addison-Wesley, 1993.
M. Yadegari. The use of mathematical induction by Abu Kamil Shuja’ Ibn Aslam (850–930). Isis, 69(2):259–262, June 1978.
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2007). Induction. In: The Calculus of Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74113-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-74113-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74112-1
Online ISBN: 978-3-540-74113-8
eBook Packages: Computer ScienceComputer Science (R0)