and the node of the type A is called an argument. Functor–argument structure Refinements of categorial grammar A variety of changes to categorial grammar have been proposed to improve syntactic coverage. Some of the most common are listed below. Features and subcategories Most systems of categorial grammar subdivide categories. The most common way to do this is by tagging them with features, such as person, gender, number, and tense. Sometimes only atomic categories are tagged in this way. In Montague grammar, it is traditional to subdivide function categories using a multiple slash convention, so A/B and A//B would be two distinct categories of left-applying functions, that took the same arguments but could be distinguished between by other functions taking them as arguments. Function composition Rules of function composition are included in many categorial grammars. An example of such a rule would be one that allowed the concatenation of a constituent of type A/B with one of type B/C to produce a new constituent of type A/C. The semantics of such a rule would simply involve the composition of the functions involved. Function composition is important in categorial accounts of conjunction and extraction, especially as they relate to phenomena like right node raising. The introduction of function composition into a categorial grammar leads to many kinds of derivational ambiguity that are vacuous in the sense that they do not correspond to semantic ambiguities. Conjunction Many categorial grammars include a typical conjunction rule, of the general form X CONJ X → X, where X is a category. Conjunction can generally be applied to nonstandard constituents resulting from type raising or function composition.. Discontinuity The grammar is extended to handle linguistic phenomena such as discontinuous idioms, gapping and extraction. See also Combinatory categorial grammar Link grammar Noncommutative logic Pregroup Grammar Scope Type shifter References Further reading Michael Moortgat, Categorial Type Logics, Chapter 2 in J. van Benthem and A. ter Meulen (eds.) Handbook of Logic and Language. Elsevier, 1997, Wojciech Buszkowski, Mathematical linguistics and proof theory, Chapter 12 in J. van Benthem and A. ter Meulen (eds.) Handbook of Logic and Language. Elsevier, 1997, External links Grammar, categorial at Springer Encyclopaedia of Mathematics http://plato.stanford.edu/entries/typelogical-grammar/ Grammar frameworks Formal languages Computational linguistics Type theory Semantics