... of.^1.1

Clearly this is not necessarily the case: a finite state grammar, which recognizes a superset of English need not be constrained at all, but can be parsed very efficiently ...

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... case)^1.2

This characterization is due to Jim Barnett. It may be possible to understand the things D.Q. says, but one would never want to talk like him.

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... left.^1.3

Note that it usually will be quite clear from the input in which direction the relation is to be computed.

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... constant.^2.1

Note that, unlike in PATR II, the descriptor c l is syntactically allowed, but all constraints containing such descriptors will be unsatisfiable. Such descriptors are allowed because this allows a more elegant definition of the simplification rules defined later.

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.... ^2.2

Note that in fact the variables in the feature graphs do not matter; hence each of f_i represents a class of feature graphs.

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... suitable.^2.3

Some confusion can easily arise here. In the logic programming tradition, the head of a definite clause p :- q₁... q_n is the atom p; in the linguistic tradition the head of a rule is one of the daughters of the rule. Viewing a rule as a definite clause, as I do here, thus gives rise to two notions of head: the `linguistic' head is one of q<sub>i</sub>, whereas the `logical' head is p. In using the term `head' I will refer to the linguistic notion of `head'.

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... goal.^2.4

It is thus assumed that the start goal only contains one atom.

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... form^2.5

Note that this particular instantiation of the problem partly disappears using the sort labels as introduced in the previous section to differentiate between semantic structures of different arity.

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...coherence). ^2.6

Note that this usage of the terms completeness and coherence should not be confused with the usual meaning of these terms in logic. Neither should it be confused with yet another notion of completeness and coherence which is used in LFG to enforce subcategorization requirements.

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... others.^3.1

This generator was originally defined in [97].

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... parser,^4.1

This name is due to Pete Whitelock.

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... prediction.^4.2

In the general case we need to compute the transitive closure of (restrictions of [82]) possible mother-head relationships.

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... `bags',^4.3

Based on the file `bags.pl' of the Quintus library, by Richard O'Keefe.

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