  Independently of either of these traditions, Joachim Lambek considered mathematical models of language and syntax (Lambek 1958, 1961). The idea here is that premise combination corresponds to composition of strings or other linguistic units. Here \(X,X\) differs in content from \(X\), but in addition, \(X,Y\) differs from Y,X. Not only does the number of premises used count but so does their order. Good introductions to the Lambek calculus (also called categorial grammar) can be found in books by Moortgat (1988) and Morrill (1994).