In DATR, values may be associated with particular node/path pairs
either explicitly, in terms of local or global inheritance, or
implicitly (by default). The basic idea underlying DATR's
default mechanism is as follows: any definitional sentence is applicable
not only to the path specified on its left-hand side, but also for any
rightward extension of that path for which no more specific definitional
sentence exists. Making use of defaults, the 
theory given
above can be expressed more succinctly as shown below:
NOUN:
<cat> == noun
<suff> == s.
<sing> == "<root>"
<plur> == "<root>" <suff>.
Llama:
<> == NOUN
<root> == llama.
Here, the relationship between the nodes Llama and NOUN
has effectively been collapsed into just a single statement
Llama:<> == NOUN. This is possible because the
sentence now corresponds to a whole class of implicit definitional
sentences, each of which is obtained by extending the paths found on the
left- and right-hand sides in the same way. Accordingly, the value of
Llama:<cat> is specified implicitly as the value of
NOUN:<cat>, and similarly for Llama:<sing> and
Llama:<suff>. In contrast, the specification
Llama:<root> == NOUN:<root> does
not follow by default from the definition of Llama,
even though it can be obtained by extending left and right paths in the
required manner. The reason is that the theory already contains an
explicit statement about the value of Llama:<root>.
The evaluation relation is now defined as
a mapping from elements of 
(i.e., context/descriptor sequence/path extension triples) to
. We write:
to mean that 
evaluates to 
in context C given
path extension 
. When 
is the empty path
extension, we will continue to write
.
Figure 5: The evaluation semantics for DATR
A complete set of inference rules for DATR is shown in
Figure 5. The rules for Values, Sequences
and Evaluable Paths require only slight modification as the path
extension is simply passed through from premises to consequent. The
rules for Quoted Descriptors are also much as before. Here,
however, the path extension appears as part of the global
context in the premise of each rule. This means that when a global
descriptor is encountered, any path extension present is treated
globally rather than locally. The main change in the
Definitions rule lies in the conditions under which it is applicable.
The amended rule just captures the ``most specific sentence wins'' default
mechanism. Finally, the new rule for Path Extensions serves as
a way of making any path extension explicit. For example, if
Llama:<cat> evaluates to noun, then Llama:<>
also evaluates to noun given the (explicit) path extension
cat.
An example proof showing that Llama:<plur> evaluates to llama s given the DATR theory presented above is shown in Figure 6.
Figure 6: Proof utilising defaults
