# The propositional logic of Principia in Coq

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Abstract There have been multiple reconstructions of the propositional logic of *Principia* beginning with the artificial intelligence research of Newell, Simon, and Shaw in the 1950s, including the mechanical validity-checker of Hao Wang (see ''IBM Journal of Research and Development'' 1960), and the proof reconstructions of Daniel O'Leary using Polish notations (see *Russell* 1988). To these results I have added a fully computer-checked reconstruction of the propositional logic of "Principia" following the proof sketches indicated in that work. This talk will discuss what computer-checking *Principia* proofs in Coq tells us about the proof sketches, and also about the development of propositional logic between *Principia* and Russell's 1906 ''The Theory of Implication.''