Yuichi Goto
ABSTRACT
Classical mathematical logic includes a lot of "implicational paradoxes" as its logic theorems. On the other hand, relevant logics and strong relevant logics have rejected those implicational paradoxes as their logical theorems. This paper uses the property of strong relevance as the criterion to identify implicational paradoxes in logical theorems of classical mathematical logic, and count the number of logical theorem schemata of classical mathematical logic that do not satisfy the strong relevance. Our results quantitatively shows that classical mathematical logic is by far not a suitable logical basis for automated forward deduction.
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- A quantitative analysis of implicational paradoxes in classical mathematical logic
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