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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. . | Expressing Disjunctive and Negative Feature Constraints with Classical First-Order Logic. Mark Johnson Cognitive and Linguistic Sciences Box 1978 Brown University Providence RI02912. 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 ÍAỂP-complete. Introduction Many modern linguistic theories such as Lexical-Functional Grammar 1 Functional Unification Grammar 12 Generalized PhraseStructure Grammar 6 Categorial Unification Grammar 20 and Head-driven PhraseStructure 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 values
