Which CSL rules hold in Łukasiewicz's 3-valued logic? CSL is classical logic. So I'm talking about the basic introduction and elimination rules (conditional, biconditional, disjunction, conjunction and negation).
I'm not talking about his infinite-valued logical theory, but the 3-valued one where any atomic sentence can be given T,F or I. (See the Wikipedia article here:
http://en.wikipedia.org/wiki/Three-valued_logic

1) I believe that Conditional introduction works: 
     My experience is that the problem lies in getting a getting valid derivation from a set of premises, given the other rules that don't work.
2) Conditional elimination does not.
   This is the chief thing that cripples Lukasiewicz logic as a logic. 
   Modus Ponens and the transitivity of the conditional both fail  for the Lukasiewicz conditional, as they properly should, given that it allows conditionals with a value of I. If your conditionals are doubtful, you should not expect inference using them to be valid. 
    (It is not generally known that this can be remedied: Define Spq as NCCpqNCpq and use that for the conditional)
3) Biconditional introduction works.
4) Biconditional elimination works.
5) Conjunction introduction works.
6) Conjunction elimination works
7) Disjunction introduction works.
8) Disjunction elimination does not work.
9) Negation introduction does not work.
10) Negation elimination does not work. 
    Classically, 9 and 10 depend on the Law of the Excluded Middle, which doesn't hold in Lukasiewicz logic.
