Abstraction in Algorithmic Logic

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• 作者：Wayne Aitken and Jeffrey A. Barrett
• 关键词：abstraction ; algorithmic logic ; Curry paradox
• 刊名：Journal of Philosophical Logic
• 出版时间：February, 2008
• 出版年：2008
• 期刊代码：23_00223611
• 类别：law
• 卷：37
• 期：1
• 页码：23-43
• 数据来源：sp

摘要

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.