ABSTRACT
This chapter explains some of the more significant of the various proposed extensions to Lambek calculus (L) - atomic categories, connectives, rules of all sorts and finally the superficially very different incarnation of the essential categorial enterprise in Unification Categorial Grammars. Most extend the set of atomic categories, at least to some extent; a few extend the set of connectives; the focus of debate is on extensions to the set of rules- what rules can be added, what formal and what descriptive power they add to a grammar, how excessive power might be constrained, which is the best trade-off between binary and unary rules, or between generality and restriction, or between formal purity and linguistic accuracy and so on. Recursion underlies the 'generalized composition' with which Ades and Steedman treat unbounded dependencies. Directional variants have been proposed for most combination rules, as have new rules of permutation or 'wrapping', to handle other discontinuities and word order variations.
