  Leśniewski himself never gave an explicit formulation of the theory of semantic categories, being content to work with them in practice. The first formulation was by his contemporary Kazimierz Ajdukiewicz, in the 1935 article ‘Syntactic Connection’. Ajdukiewicz’s essay became the fountainhead of the subsequent subdiscipline of categorial grammar. Modifying Ajdukiewicz’s notation, we may explain semantic categories as Leśniewski used them. Leśniewski thought that the theory applies only to his logical systems, not to ordinary language, about which he became rather sceptical as to its ability to be unambiguously precise. Subsequently it has been shown that categorial grammar can be applied quite successfully to the syntax of natural languages.