On sets, types, fixed points, and checkerboards (1996) [6 citations — 2 self]
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by Peter B. Andrews, Matthew Bishop
In Pierangelo Miglioli, Ugo Moscato, Daniele Mundici, and Mario Ornaghi, editors, Theorem Proving with Analytic
http://gtps.math.cmu.edu/tw96.ps.Z
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@INPROCEEDINGS{Andrews96onsets,,author = {Peter B. Andrews and Matthew Bishop},
title = {On sets, types, fixed points, and checkerboards},
booktitle = {In Pierangelo Miglioli, Ugo Moscato, Daniele Mundici, and Mario Ornaghi, editors, Theorem Proving with Analytic},
year = {1996},
pages = {1--15},
publisher = {Springer}
}
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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. 1.
