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In any formula of propositional calculus in any position you may substitute a sentence Q with the formula:
Thus if [proves] [logical not] [open box] [perpendicular to], then both [proves] [logical not] [open box] [logical not] [open box] [perpendicular to], by (11), and [proves] [open box] [logical not] [open box] [perpendicular to], by (i), whence [proves] [perpendicular to], by the propositional calculus. So if [does not prove] [perpendicular to], then [does not prove] [logical not] [open box] [perpendicular to].
My argument about the ambiguity of extensional logic depends upon the achievement of my second purpose, which is to elicit the basis of an intensional propositional calculus from a rigorous attention to the meaning of expressions by virtue of which a logical implication is asserted to exist.
The first paraconsistent propositional calculus was constructed by S.
In the propositional calculus a simple form of resolution is expressed by the inference rule: