Incompleteness, Undecidability and Automated Proofs

(Invited Talk)
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9890)

Abstract

Incompleteness and undecidability have been used for many years as arguments against automatising the practice of mathematics. The advent of powerful computers and proof-assistants – programs that assist the development of formal proofs by human-machine collaboration – has revived the interest in formal proofs and diminished considerably the value of these arguments.

In this paper we discuss some challenges proof-assistants face in handling undecidable problems – the very results cited above – using for illustrations the generic proof-assistant Isabelle.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.Department of PhilosophyStanford UniversityStanfordUSA

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