In many domains, characterizations of a given attribute are imprecise, uncertain and incomplete in the available learning examples. The definitions of classes may be vague. Learning systems are frequently forced to deal with such uncertainty. Traditional learning systems are designed to work in the domains where imprecision and uncertainty in the data are absent. Those learning systems are limited because of their impossibility to cope with uncertainty--a typical feature of real-world data. In this thesis, we developed a fuzzy learning system which combines inductive learning with a fuzzy approach to solve problems arising in learning tasks in the domains affected by uncertainty and vagueness. Based on Fuzzy Logic, rather than pure First Order Logic used in FOIL, this system extends FOIL with learning fuzzy logic relation from both imprecise examples and background knowledge represented by Fuzzy Prolog. The classification into the positive and negative examples is allowed to be a degree (of positiveness or negativeness) between 0 and 1. The values of a given attribute in examples need not to be the same type. Symbolic and continuous data can exist in the same attribute, allowing for fuzzy unification (inexact matching). An inductive learning problem is formulated as to find a fuzzy logic relation with a degree of truth, in which a fuzzy gain calculation method is used to guide heuristic search. The Fuzzy FOIL's ability of learning the required fuzzy logic relations and dealing with vague data enhances FOIL's usefulness.