As a feature-based formalism with a syntax modelled on `PATR`, it would
be reasonable to expect that `DATR` can be used to describe directed
acyclic graphs (DAGs) in a `PATR`-like fashion. Consider an example such
as the following:

DAG1: <vp agr> == <v agr> <v agr per> == 3 <vp agr gen> == masc.This looks like simple reentrancy from which we would expect to be able to infer:

DAG1: <vp agr per> = 3.And, indeed, this turns out to be valid. But matters are not as simple as the example makes them appear: if

DAG1: <v agr gen> = masc.But this is not valid, in fact

DAG1: <vp agr> == <v agr>.taken in isolation is very similar to the semantics of the corresponding

Another difference lies in the fact that `DATR` subpaths and superpaths
can have values of their own:

DAG2: <v agr> == sing <v agr per> == 3.From this little description we can derive the following statements, inter alia:

DAG2: <v agr> = sing <v agr num> = sing <v agr per> = 3 <v agr per num> = 3.From the perspective of a standard untyped DAG-encoding language like

As these examples clearly show, `DATR` descriptions do not map **
trivially** into (sets of) standard DAGs (although neither are they
entirely dissimilar). But that does not mean that `DATR` descriptions
cannot **describe** standard DAGs. Indeed, there are a variety of
ways in which this can be done. An especially simple approach is
possible when the DAGs one is interested are all built out of a set of
paths whose identity is known in advance (Kilbury et
al. 1991). In this case, we can use `DATR` paths as DAG
paths, more or less directly:

PRONOUN2: <referent> == '<' 'NP' referent '>'. She2: <> == PRONOUN2 <case> == nominative <person> == third <number> == singular.From this description, we can derive the following theorems:

She2: <case> = nominative <person> = third <number> = singular <referent> = < NP referent >.We can also derive the following un-DAG-like consequences, of course:

She2: <case person> = nominative <person number> = third <referent referent referent> = < NP referent >.But these nonsensical theorems will be of no concern to a

A more sophisticated approach uses `DATR` itself to construct a DAG
description (in the notation of your choice) as a value. This
approach is due to recent unpublished work by Jim
Kilbury
. He has
shown that the **same** `DATR` theorems can have their values
realised as conventional attribute-value matrix representations,
Prolog terms, or expressions of a feature logic, simply by changing
the fine detail of the transducer employed.

IDEM: <> == <$atom> == $atom <>. PATH: <> == '<' IDEM '>'. LHS_EQ: <> == PATH '='. LHS_EQ_RHS: <> == LHS_EQ "<>". PRONOUN1: <dag> == [ LHS_EQ_RHS:<case> LHS_EQ_RHS:<person> LHS_EQ_RHS:<number> LHS_EQ:<referent> PATH:<'NP' referent> ]. She1: <> == PRONOUN1 <case> == nominative <person> == third <number> == singular.From this description, we can derive the following theorem:

She1: <dag> = [ < case > = nominative < person > = third < number > = singular < referent > = < NP referent > ].The sequence of atoms on the right hand side of this equation is