The problem of constructing an explicit theory of inference for DATR was originally addressed in E&G 1989a. In this work, an attempt is made to set out a logic of DATR\ statements. Consider for example the following rule of inference, adapted from E&G 1989a.
The premises are definitional sentences which can be
read: ``the value of path 
at node 
is
(inherited from) the value of path 
at 
'' and ``the value of
path at node is 
'', respectively. Given the
premises, the rule licences the conclusion ``the value of path at
node is ''. Thus, the rule captures a logical
relationship between DATR sentences. For a given DATR theory
, rules of this kind may be used to deduce additional sentences
as theorems of .
In contrast, the system of inference described here characterizes a relationship between DATR expressions (i.e., sequences of descriptors) and the values they may be used to compute. As an example, consider the following (simplified) rule of the operational semantics:
The rule is applicable just in case the theory contains a
definitional sentence 
. It states that if the sequence
of value descriptors 
on the right of the sentence evaluates to
( 
) the sequence of atoms , then it may be concluded
that the node/path pair 
also evaluates to .
Rules of this kind may be used to provide an
inductive definition of an evaluation relation between DATR\
expressions and their values.
Both approaches to inference in DATR aim to provide a system of
deduction that makes it possible to determine formally, for a given
DATR theory , what follows from the statements in
. The primary interest lies in deducing statements about the
values associated with particular node/path pairs defined within the
theory. Unfortunately, the proof rules described in E&G 1989a are not
sufficiently general to support all of the required inferences, and it
is not obvious that the approach can be extended appropriately to cover
all of the available DATR constructs. A particular problem concerns
DATR's notion of non-local or global inheritance. The value
expressed by a global inheritance descriptor depends on more than just
the properties of the nodes specified by the definitional sentences of a
theory. In fact, it only makes sense to talk about the value of a
global descriptor relative to a given context of evaluation, or
global context. Because the proof rules of E&G 1989a
just talk about DATR sentences, which do not make explicit reference
to context, it is not possible to give a satisfactory
account of the global inheritance mechanism
.
The evaluation semantics described in the following sections provides a perspicuous treatment of both local and global inheritance in DATR. The rules capture the essential details of the process of evaluating DATR expressions, and for this reason should prove of use to the language implementer.