<?xml version="1.0" standalone="yes"?>
<Paper uid="C92-2076">
  <Title>DISJUNCTIVE FEATURE STRUCTURES AS HYPERGRAPHS</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1. INTRODUCTION
</SectionTitle>
    <Paragraph position="0"> It has become common to make a distinction between a language for file description of feature structures and feature structures themselves, which are seeu as directed acyclic graphs (dags) or automata (see, for instance, Kasper and Rounds, 1986). To avoid confusion, file terms of the representation language are often referred to as feature descriptions. Disjunction is a representation tool in the representation language, intended to describe sets of feature structures. In this framework, there are no disjunctive feature structures, but only disjunctive feature descriptions.</Paragraph>
    <Paragraph position="1"> This framework has enabled researchers to explore the compulational complexity of unification. However, it has some drawbacks. First, properties have to be stated (and proofs carried out) at the syntactic level. This implies using a complicated calculus based on formula equivalence rules, rather than using graph-theoretical properties. In addition, unification is not well-defined with respects to disjunction. There is reference in the literature to the &amp;quot;unification of disjunctive feature descriptions&amp;quot;, but, formally, we should instead speak of the unification of the sets of feature structures the descriptions represent.</Paragraph>
    <Paragraph position="2"> For example, unifying the sets of feature structures represented by the disjunctive feature descriptions in Fig. 1 yields a set of four (non-disjunctive) feature structures, which can be described by several equally legitimate formulae: A factored, B factored, disjunctive normal form (DNF), etc. Depending on the algorithm that is used, the description of file result will be one or the other of these formulae. Some algorithms require expansion to DNF and will therefore produce a DNF representation as a result, but other algorithms may produce different representations.</Paragraph>
    <Paragraph position="3"> There is an important body of research concerned with the development of algorithms that avoid the expensive expansion to DNF (e.g., Kasper, 1987).</Paragraph>
    <Paragraph position="4"> Thcse algorithms typically produce descriptions of the unification, in which some of the disjunctions in the original descriptions are retained. However, these descriptions are produced as a computational side-effect (potentially different depending on the algorithm) rather than as a result of the application of a formal definition. Fig. 1. Different descriptions for tile same set of feature structures In this paper, we first consider disjunctive feature structures as objects in themselves, defined in terms of directed acyclic hypergraphs. This enables us to build a mathematical framework based on graph theory in order to study the properties of disjunctive feature structures and specify operations (such as unification) in algebraic rather that syntactic terms. It also enables the specification of algorithms in terms of graph manipulations, and suggests a data structure for implementation.</Paragraph>
    <Paragraph position="5"> We then illustrate the expressive power of this framework by defining a class of disjunctive feature structures with interesting properties (factored normal form or FNF), such as closure under factoring, unfactoring, unification, and generalization. These operations (and the relation of subsumption) are defined in terms of operations on (or relations among) hypergraphs. Unification, in particular, has the intuitive appeal to preserve as much as possible the particular factoring of the disjunctive feature structures to be ratified. We also show that unification in the FNF class can be extremely efficient in practical applications.</Paragraph>
    <Paragraph position="6"> For lack of space, proofs will be omitted or buly suggested.</Paragraph>
    <Paragraph position="7"> Aca~s DE COLING-92, NANa~S, 23-28 Aotrr 1992 4 9 g FROC. OF COLING-92, NANTES, AUG. 23-28, 1992</Paragraph>
  </Section>
class="xml-element"></Paper>