A grammar G is specified as a definite clause specification where the
literals of each definite clause are unary relational
atoms. Considering only unary atoms is not a general restriction since
by means of reification (see [Pereira and Shieber1987], [Genesereth and Nilsson1987]) we
can also express an n-ary atom r(X) in terms of constraints of
a unary relation s(Y) using for example the features REL and ARG 
such that the relational symbol r is viewed as a constant bound to the
feature REL and each variable x is bound to the corresponding
feature ARG . Thus r(X) would be represented as follows
Thus the general form of a grammar rule is as follows:
The relational atoms are assumed to denote possible constituents of a grammar, either specifically (using for each possible constituent a specific symbol, like NP, VP, PP) or schematically by only using one symbol, e.g., SIGN. For example, the rule (i.e., the definite clause)
expresses that a verb phrase VP consists of a verb V, a nominal phrase NP and of a prepositional phrase PP and the following rule
expresses
that a phrase is built from two phrases, no matter what they are
(as long as we do not consider the constraint 
). Although the
last rule seems to be useless, since it does not say very much about
the actual structure of an object, this kind of schematic
rule is very prominent in lexicalized
grammars, since they allow the specification of general combinatory
rules, which are independent from individual words (see
[Uszkoreit1986b] for more details of such lexicalized view). In
fact, the grammar that we are going to use in this thesis and which can
be found in appendix A belongs to this kind of
grammars.
Using this notation, we will define lexical entries as unit clauses, and grammar rules as non-unit clauses (defining non empty productions) as well as unit clauses (defining empty productions). In order to distinguish between lexical entries and empty productions we will use the boolean feature LEX.