Unification-based grammar formalisms use structures containing sets of features to describe linguistic objects. Although computational algo- rithms for unification of feature structures have been worked out in experimental research, these algorithms become quite complicated, and a more precise description of feature structures is desirable. We have developed a model in which descriptions of feature structures can be regarded as logical formulas, and interpreted by sets of directed graphs which satisfy them. These graphs are, in fact, transition graphs for a special type of deterministic finite automaton.

The unification problem and several variants are presented. Various algorithms and data structures are discussed. Research on unification arising in several areas of computer science is surveyed, these areas include theorem proving, logic programming, and natural language processing. Sections of the paper include examples that highlight particular uses

. Though [Pollard and Sag 1994] assumes that an unspecified variant of the formal logic of [Carpenter 1992] will provide a formalism for HPSG, a precise formulation of the envisaged formalism is not immediately obvious, primarily because a principal tenet of [Carpenter 1992], that feature structures represent partial information, seems to conflict with a principal tenet of [Pollard and Sag 1994], that feature structures represent abstract linguistic entities. This has caused many HPSGians to be mistakenly concerned with partial-information specific notions, such as subsumption, that are appropriate for the [Carpenter 1992] logic but inappropriate for the formalism [Pollard and Sag 1994] envisages. This paper hopes to allay this concern and the confusion it engenders by substituting [King 1989] for [Carpenter 1992] as the basis of the envisaged formalism. It demonstrates that the formal logic of [King 1989] provides a formalism for HPSG that meets all [Pollard and Sag 1994] asks of the ...

This paper studies feature description languages that have been developed for use in unification grammars, logic programming and knowledge representation. The distinctive notational primitive of these languages are features that can be understood as unary partial functions on a domain of abstract objects. We show that feature description languages can be captured naturally as sublanguages of first-order predicate logic with equality and show the equivalence of a loose Tarski semantics with a fixed feature graph semantics for quantifier-free constraints. For quantifier-free constraints we give a constraint solving method and show the NP-completeness of satisfiability checking. For general feature constraints with quantifiers satisfiability is shown to be undecidable. Moreover, we investigate an extension of the logic with sort predicates and set-denoting expressions called feature terms.

This paper presents a set description logic with subsorts, feature selection (the inverse of unary function application), agreement, intersection, union and complement. We define a model theoretic open world semantics and show that sorted feature structures constitute a canonical model, that is, without loss of generality subsumption and consistency of set descriptions can be considered with respect to feature structures only. We show that deciding consistency of set descriptions is an NP-complete problem. To appear in: J. Wedekind and C. Rohrer (eds.), Unification in Grammar. The MIT Press, 1992 This text is a minor revision of LILOG Report 33, May 1988, IBM Deutschland, IWBS, Postfach 800880, 7000 Stuttgart 80, Germany. The research reported here has been done while the author was with IBM Deutschland. The author's article [23] is a more recent work on feature logics. 1 1 Introduction This paper presents a set description logic that generalizes and integrates formalisms...

This paper presents the constraint system FT, which we feel is an intriguing alternative to Herbrand both theoretically and practically. As does Herbrand, FT provides a universal data structure based on trees. However, the trees of FT (called feature trees) are more general than the trees of Herbrand (called constructor trees), and the constraints of FT are finer grained and of different expressivity. The basic notion of FT are functional attributes called features, which provide for record-like descriptions of data avoiding the overspecification intrinsic in Herbrand's constructor-based descriptions. The feature tree structure fixes an algebraic semantics for FT. We will also establish a logical semantics, which is given by three axiom schemes fixing the first-order theory FT. FT is a constraint system for logic programming, providing a test for unsatisfiability, and a test for entailment between constraints, which is needed for advanced control mechanisms. The two major technical con...

This thesis presents the foundations for relational logic programming over polymorphically order-sorted data types. This type discipline combines the notion of parametric polymorphism, which has been developed for higher-order functional programming, with the notion of order-sorted typing, which has been developed for equational first-order specification and programming. Polymorphically order-sorted types are obtained as canonical models of a class of specifications in a suitable logic accommodating sort functions. Algorithms for constraint solving, type checking and type inference are given and proven correct.

This paper surveys terminological representation languages and feature-based unification grammars pointing out the similarities and differences between these two families of attributive description formalisms. Emphasis is given to the logical foundations of these formalisms.

Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiablity. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express re-entrancy, the ability to express generalisations, and the ability to express recursive constraints. Two main techniques are used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted. Attribute Value Structures (AVSs) are probably the most widely used means of representing linguistic structure in current computational linguistics, and the process of unifying...

Feature logics are the logical basis for so-called unification grammars studied in computational linguistics. We investigate the expressivity of feature terms with negation and the functional uncertainty construct needed for the description of long-distance dependencies and obtain the following results: satisfiability of feature terms is undecidable, sort equations can be internalized, consistency of sort equations is decidable if there is at least one atom, and consistency of sort equations is undecidable if there is no atom.