Multiple inheritance, in inheritance network terminology, describes any situation where a node in an inheritance network inherits information from more than one other node in the network. Wherever this phenomenon occurs there is the potential for conflicting inheritance, i.e., when the information inherited from one node is inconsistent with that inherited from another. Because of this, the handling of multiple inheritance is an issue which is central to the design of any formalism for representing inheritance networks.
For the formalism to be coherent, it must provide a way of avoiding or resolving any conflict which might arise. This might be by banning multiple inheritance altogether, restricting it so that conflicts are avoided, providing some mechanism for conflict resolution as part of the formalism itself, or providing the user of the formalism with the means to specify how the conflict should be resolved. Putting aside considerations of functionality for the moment, we see that, in DATR, both the second and third of these options are employed. The ``longest-defined-subpath-wins'' principle amounts to conflict resolution built into the formalism; however, it does not deal with every case: definitions such as
Node3: <> == Node1 <> == Node2.may result in unresolvable conflicts. Such conflicts could, of course, just be ruled out by appealing to their inconsistency, which, following a logical tradition, is grounds for ruling the description to be ``improper''.
Touretzky (1986, p70ff) provides a formal description of a number of properties that an inheritance network may have, and discusses their significance with respect to the problem of multiple inheritance. Tree-structured networks, as their name suggests, allow any node to inherit from at most one other node, so multiple inheritance conflicts cannot arise. Orthogonal networks allow a node to inherit from more than one other node, but the properties it inherits from each must be disjoint, so that again, no conflict can possibly arise.
The basic descriptive features of DATR allow the specification of simple orthogonal networks similar to Touretzky's. For example, if we write:
A: <a> == true. B: <b> == false. C: <a> == A <b> == B.then we are specifying a network of three nodes (A B, and C), and two ``predicates'' (boolean-valued attributes coded as DATR paths <a> and <b>), with C inheriting a value for <a> from A, and for <b> from B. The network is orthogonal, since <a> and <b> represent distinct (sets of) predicates.
Orthogonal multiple inheritance (OMI) is a desirable property of lexical representation systems. Consider an analysis in which we put the common properties of verbs at a VERB node and the (disjoint) common properties of words that take noun phrase complements at an NP_ARG node. A transitive verb (TR_VERB) is both a verb and a word that takes an NP complement, thus it should inherit from both VERB and NP_ARG in this analysis. In DATR, this might be expressed as follows:
VERB: <cat> == verb. NP_ARG: <arg cat> == np <arg case> == acc. TR_VERB: <cat> == VERB <arg> == NP_ARG.Here TR_VERB inherits from both VERB and NP_ARG but the path prefixes cat and arg ensure that the inheritance is orthogonal and that no conflict (e.g., in respect of <cat> values) can arise.
More generally, OMI is invaluable for partitioning the various different, and largely independent, aspects of lexical description conventionally associated with such initial path prefixes as phn (phonology), mor (morphology), syn (syntax), and sem (semantics). In the English verbal system, for example, most morphological subregularities (such as having a past participle form in -en) operate entirely independently of most syntactic subregularities (such as having a ditransitive subcategorisation frame). Within the semantic domain, Pustejovsky & Boguraev (1993, 214) introduce the expression typed inheritance for OMI and argue for its advantages in connection with the consistent assembly of the different facets of meaning associated with a lexical item.
The above examples of OMI are in fact instances of a more general phenomenon in DATR. We have already noted that the combination of the longest-defined-subpath-wins and logical consistency are the basis of DATR's support for coherent multiple inheritance. It turns out that functionality (which of course implies consistency) ensures orthogonality, so that OMI falls out as the most normal, natural mode of definition using DATR.
Finally here, we note that a number of recent lexical theories have invoked a form of inheritance in which multiple parents with overlapping domains are specified, and a priority ordering imposed to resolve potential inheritance conflicts (e.g., Flickinger 1987; Russell et al. 1992). In this prioritised multiple inheritance (PMI), precedence is given to nodes that come earlier in the ordering, so that the inherited value for a property comes from the first parent node in the ordering that defines that property, regardless of whether other later nodes also define it (possibly differently).
Surprisingly perhaps, DATR's version of OMI can be used to reconstruct PMI without making syntactic and semantic additions to the language. In fact, we have described elsewhere no fewer than three different techniques for capturing PMI in DATR (Evans et al. 1993). But DATR was primarily designed to facilitate OMI analyses of natural language lexicons and we do not believe that PMI treatments of the lexicon offer significant analytical or descriptive advantages.