  Leśniewski suggested the theory of syntactic categories, later developed by Ajdukiewicz in the early 1930s. This theory takes the categories of sentences and names (for Ajdukiewicz, following Leśniewski, there is no syntactic difference between proper names and common nouns) as fundamental and assigns the pointer s to sentences and n to names. Now functors have fractions as pointers. For example, “is” has s/nn as its categorial index; it says that “is” is a two-placed functor of two nominal arguments which forms a sentence. The conjunction as a propositional connective forming sentences from two other sentences has s/ss as its index. Consider now the expression “p and q”. Write the categorial indexes of its parts. We thus obtain the sequence: s s/ss s. Perform simplifications by divisions similar to dividing algebraic fractions. The letter s is the result. A simple algorithm says that an expression is syntactically coherent if and only if s or n is its index after performing all simplifications. Ajdukiewicz’s quasi-arithmetical notation was the first system of categorial grammar.