In the logical literature, Discursive (or Discussive) Logic introduced by Stanis law Ja´skowski is seen as one of the earliest examples of the so-called paraconsistent logic. Nevertheless, there is some confusion over what discursive logic actually is. One of the possible sources of the confusion may be easily discerned; it comes from the fact that Ja´skowski published his two papers in Polish and their English translations appeared many years later.1 Up till 1999, no one but a Polish reader was able to read Ja´skowskis paper on the discursive conjunction and, consequently some authors took discursive logic to be a foremost example of a non-adjunctive logic. The situation became even more complicated when da Costa, Dubikajtis and Kotas presented an axiomatization with discursive connectives as primitive symbols. It turned out that a connective of the discursive conjunction they considered did not correspond to any of Ja´skowskis connectives. Thus, their axiomatization contained some axiom schemata that were not generally valid in Ja´skowskis logic. The purpose of this paper is to clarify the confusion surrounding the discursive logic. We will present a direct semantics and axiomatization of Ja´skowskis adjunctive discursive logic and show how to define and axiomatize two additional connectives of negation.

VL - 37 SP - 143–160 ER -