# On sets, types, fixed points, and checkerboards

Invited Lectures

First Online:

## Abstract

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.

## Keywords

Type Theory Automate Reasoning Proof Tree Automate Theorem Prove Order Binary Decision Diagram
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1996