Found searching Blogonia for “propositional calculus”:

• Alain Badiou - Course on Logic - Part I
• Alain Badiou - Course on Logic - Part II
• Alain Badiou - Course on Logic - Part III

“A translation of lecture notes from a course on Logic delivered by Alain Badiou in 1980 - 81. It is rather short and deals specifically with Gödel and his theorem of incompleteness.”