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In the paper, concentrated on the historical analysis of Bolzano’s Wissenschaftslebre the author makes it his aim to given an interpretation and formal reconstruction of some basic characteristics of Bolzano’s theory of inference. He first sums up conceptual starting points of Bolzano’s conception where he critically re-values Aristotelian and traditional 'theories of syllogism and at the same time he develops his specific theory of deduction which is in many cases very near to the ideas of the algebra of logic. The author then analyzes i;n detail ten chosen syllogistic moods. Many of them appear to be founded on the laws of logic of classes, which were not known in Bolzano’s days. Validity of the syllogistic moods are proved by Bolzano by means of direct and indirect proof, in one case even by means of direct proof, founded on additional presuppositions. Bolzano, however, does not give all steps in the proof (procedure as he considers some of them intuitively evident, e.g. the use of the rule of introducing or eliminating conjunction. Proof procedures that are done by Bolzano show well enough that he anticipated the method of natural deduction to a great degree, systematically worked out as late as in the thirties of our century.