Alain Badiou is speaking at Law and Event, Benjamin N. Cardozo School of Law, Nov 11 & Nov 12. It's a public event. [link].
I went to Badiou's keynote this morning. He produced a handout entitled "A formalized presentation of the three meanings of negation", with the following symbols:
~ : negation ^ : and v : or  : it is possible that... P: a sentence
And this table
|Classical||~(P ^ ~P)||(P v ~P)|
|Intuonistic||~(P ^ ~P)|| ~(P v ~P)|
|Para-consistent||(P ^ ~P)||(P v ~P)|