praeclarum theorema

So named by G.W. Leibniz in his unpublished papers of 1690 (later published as Leibniz: Logical Papers in 1966), meaning "splendid theorem" in Latin.

praeclarum theorema

1. (logic) The following theorem of propositional calculus: (A → B) ∧ (C → D) → (A ∧ C → B ∧ D). ^{[1] [2] [3] [4]}

   The praeclarum theorema can be seen to correspond with the rule ${\displaystyle R\otimes }$ of linear logic; given two sequents ${\displaystyle A\vdash B}$ and ${\displaystyle C\vdash D}$ one may infer (through the said rule) that ${\displaystyle A,C\vdash B\otimes D}$. Then one may further infer, through the rule ${\displaystyle L\otimes }$, that ${\displaystyle A\otimes C\vdash B\otimes D}$.

• constructive dilemma