On sets, types, fixed points, and checkerboards

  • Peter B. Andrews
  • Matthew Bishop
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1071)


Most current research on automated theorem proving is concerned with proving theorems of first-order logic. We discuss two examples which illustrate the advantages of using higher-order logic in certain contexts. For some purposes type theory is a much more convenient vehicle for formalizing mathematics than axiomatic set theory. Even theorems of first-order logic can sometimes be proven more expeditiously in higher-order logic than in first-order logic. We also note the need to develop automatic theorem-proving methods which may produce proofs which do not have the subformula property.


Type Theory Automate Reasoning Proof Tree Automate Theorem Prove Order Binary Decision Diagram 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter B. Andrews
    • 1
  • Matthew Bishop
    • 1
  1. 1.Mathematics DepartmentCarnegie Mellon UniversityPittsburghUSA

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