gain is probably the information gain as used in decision trees: entropy before spliting on the rule - entropy after spliting on the rule (
http://en.wikipedia.org/wiki/Information_gain_in_decision_trees). Conviction is well described under Association Rule mining when you use wikipedia. Now laplace, I am not sure, the definition of laplace:
Laplace Criterion: If the probabilities of several chance events are unknown, they should be assumed
equal, and the different actions should be judged according to their payoffs averaged over all the states
of nature. The question is what is the payoff?