propositional

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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.
Textbooks generally begin by laying out the main lines of the propositional calculus understood as an unambiguously extensional system.
The first paraconsistent propositional calculus was constructed by S.
In the propositional calculus a simple form of resolution is expressed by the inference rule: