Gottlob Frege's massive undertaking (1879) resulted in a formal calculus of propositions, but his symbolism is so daunting that it had little influence excepting on one person: Bertrand Russell. First as the student of Alfred North Whitehead he studied Frege's work and suggested a (famous and notorious) emendation with respect to it (1904) around the problem of an antinomy that he discovered in Frege's treatment ( cf Russell's paradox ). Russell's work led to a collatoration with Whitehead that, in the year 1912, produced the first volume of "Principia Mathematica" (PM). It is here that what we consider "modern" propositional logic first appeared. In particular, PM introduces NOT and OR and the assertion symbol ⊦ as primitives. In terms of these notions they define IMPLICATION → ( def. *1.01: ~p ∨ q ), then AND (def. *3.01: ~(~p ∨ ~q) ), then EQUIVALENCE p ←→ q (*4.01: (p → q) & ( q → p ) ).