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ABSTRACTION IN ALGORITHMIC LOGIC

WAYNE AITKEN and JEFFREY A. BARRETT
Journal of Philosophical Logic
Vol. 37, No. 1 (February 2008), pp. 23-43
Published by: Springer
Stable URL: http://www.jstor.org/stable/41217820
Page Count: 21
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ABSTRACTION IN ALGORITHMIC LOGIC
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Abstract

We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves one no choice but to restrict the use of a certain class of implicational rules including modus ponens.

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