Lexical Rules as Binary Predicates

For concreteness we will assume that our grammar is a Definite Clause Grammar, in which lexical entries are introduced with the special predicate lexicon(Word,Cat). This predicate in turn is defined as follows ¹:

$$\mbox{\em lexicon(Word,Cat) :- stem(Word,Cat0), lexical\_rules(Cat0,Cat). }$$

The lexical_rules predicate is true if the underlying category, Cat0, can be related to the surface category, Cat, by the lexical rules machinery.

Lexical rules themselves are thought of as binary predicates that relate an `incoming' category with an `outgoing' category. Given that lexical rules supposedly can apply freely, the lexical_rules/2 predicate thus reflects the reflexive and transitive closure of these lexical rules:²

$$\mbox{\em lexical\_rules(C,C). }$$

$$\mbox{\em lexical\_rules(Lex,Surf) :- lr(Mid,Surf), lexical\_rules(Lex,Mid). }$$