Inducing implication relations

This paper deals with learning implication relations from some kinds of knowledge (statistical studies, possibilistic information or possible worlds) about truth valuations on a set of propositions. An induction principle is considered in each one of this cases. If only the possible valuations are known, then it is checked when two families of possible valuations produce the same implication. A conditional probability can be deduced when a probabilistic information for each possible valuation is added. In particular, by applying equiprobability when this information is unknown, each preorder can be extended to a "causal" networks which contains it. Changing probability for possibilistic information, conditional possibility and necessity measures are suggested. This conditional measures extend the classical case if the respective information is forgotten. Finally, material implication is studied in Multiple Valued Logic.