Expressing Disjunctive and Negative Feature Constraints With Classical First-Order Logic.

EXPRESSING DISJUNCTIVE AND NEGATIVE FEATURE CONSTRAINTS WITH CLASSICAL FIRST-ORDER LOGIC. Mark Johnson, Cognitive and Linguistic Sciences, Box 1978, Brown University, Providence, RI 02912. mj@cs.brown.edu ABSTRACT In contrast to the "designer logic" approach, this paper shows how the attribute-value feature structures of unification grammar and constraints on them can be axiomatized in classical first-order logic, which can express disjunctive and negative constraints. Because only quantifier-free formulae are used in the axiomatization, the satisfiability problem is NP- complete. INTRODUCTION. Many modern linguistic theories, such as Lexical-Functional Grammar [1], Functional Unification Grammar [12] Generalized Phrase- Structure Grammar [6], Categorial Unification Grammar [20] and Head-driven Phrase- Structure Grammar [18], replace the atomic categories of a context-free grammar with a "feature structure" that represents the.syntactic and semantic properties of the phrase. These feature structures are specified in terms of constraints that they must satisfy. Lexical entries constrain the feature structures that can be associated with terminal nodes of the syntactic tree, and phrase structure rules simultaneously constrain the feature structures that can be associated with a parents and its immediate descendants. The tree is well-formed if and only if all of these constraints are simultaneously satisfiable. Thus for the purposes of recognition a method for determining the satisfiability of such constraints is required: the nature of the satisfying feature structures is of secondary importance. Most work on unification-based grammar (including the references cited above) has adopted a type of feature structure called an attribute-value structure. The elements in an attribute-value structure come in two kinds: constant elements and complex elements. Constant elements are atomic entities with no internal structure: i.e. they have no attributes. Complex elements have zero or more attributes, whose 173 values may be any other element in the structure (including a complex element) and ally element can be the value of zero, one or several attributes. Attributes are partial: it need not be the case that every attribute is d ef!ned for every complex element. The set of attribute-value structures partially ordered by the subsumption relation (together with all additional entity T that every attribute-value structure subsumes) forms a lattice, and the join operation on this lattice is called the unification operati(m 119]. Example: (from [16]). The attribute-value structure (1) has six complex elements labelled el ... e6 and two corastant elements, singular and third. The complex element el has two attributes, subj and pred, the value of which are the complex elements e 2 and e 3 respectively. (1) e2 e2¢ r number singular el subj~pred "~e 3 verb agr 'e6 person third e 7 (2) )ubi ~pred ""5 e,) verb e8 )el() agr.. ell The unification of elements el of(l) and e7 of(2) results in the attribute-value structure (3), the minimal structure in the subsumption lattice which subsumes both (1)and (2). ¢1 ¢7 (3) ~pred ~ ubj "~e3 e9 e2 e8 verb ...~e 5 el0 a g r ~ a g r number person singular third If constraints on attribute-value structures are restricted to conjunctions of equality constraints (i.e. requirements …

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