  Historical work inspired logicians of the LWS toward modern interpretations of traditional logical doctrines. The most famous is Łukasiewicz’s formalization of the Aristotelian logic of categorical sentences (the syllogistic plus conversion and other rules of so-called direct inference). Łukasiewicz interpreted this logic as a specific formal theory, not as a fragment of predicate logic, as it was usually done (for example by Frege or Russell). Yet the logic of categorical sentences assumes propositional logic as prior. The logic of assertoric sentences (Łukasiewicz also considered its modal extension) has the following form. Let the formulas (lower-case letters are term variables) Uab, Iab, Yab, Oab stand for the sentences “every a is b”, “some a are b”, “no a is b” and “some a are not b”. We can define Yab as NIab and Oab as NUab. The axioms are as follows: (a) Uaa; (b) Iaa; (c) CKUmbUamUab (the Barbara modus); (d) CKUmbImaIab (the Datisi mode); the rules are: all the rules of propositional calculus, substitution for term variables, the definitional replacement according to the definitions of Yab and Oab.