Feature Structures and Path Congruences. The discussion of abstract feature structures raises a historical difficulty. While I do not dispute that the full theoretical investigation of feature structures modulo renaming is correctly attributed to Moshier, the idea of representing renaming classes by equivalence relations over paths seems an obvious variant of the representation of such classes as deductively closed sets of path equations in Pereira and Shieber's account (1984) of the semantics of PATR-II, which is further explored in Shieber's dissertation (1989).

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.

A distinctive propertyofmanycurrent grammatical formalisms is their use of feature equality constraints to express a wide variety of grammatical dependencies. Lexical-Functional Grammar[6], Head-Driven Phrase-Structure Grammar[14], PATR[8], FUG[12, 13], and the various forms of categorial uni cation grammar[9,15,16] all require an analysis of a sentence

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 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.

The thesis describes novel techniques and algorithms for the practical parsing of realistic Natural Language (NL) texts with a wide-coverage unification-based grammar of English. The thesis tackles two of the major problems in this area: firstly, the fact that parsing realistic inputs with such grammars can be computationally very expensive, and secondly, the observation that many analyses are often assigned to an input, only one of which usually forms the basis of the correct interpretation. The thesis starts by presenting a new unification algorithm, justifies why it is well-suited to practical NL parsing, and describes a bottom-up active chart parser which employs this unification algorithm together with several other novel processing and optimisation techniques. Empirical results demonstrate that an implementation of this parser has significantly better practical

This paper outlines a simple and general notion of syntactic category on a metatheoretical level, independent of the notations and substantive claims of any particular grammatical framework. We define a class of formal objects called "category structures" where each such object provides a constructive definition for a space of syntactic categories. A unification operation and subsumption and identity relations are defined for arbitrary syntactic categories. In addition, a formal language for the statement of constraints on categories is provided. By combining a category structure with a set of constraints, we show that one can define the category systems of several well-known grammatical frameworks: phrase structure grammar, tagmemics, augmented phrase structure grammar, relational grammar, transformational grammar, generalized phrase structure grammar, systemic grammar, categorial grammar, and indexed grammar. The problem' of checking a category for conformity to constraints is shown to be soivable in linear time. This work provides in effect a unitary class of data structures for the representation of syntactic categories in a range of diverse grammatical frameworks. Using such data structures should make it possible for various pseudo-issues in natural language processing research to be avoided. We conclude by examining the questions posed by set-valued features and sharing of values between distinct feature specifications, both of which fall outside the scope of the formal system developed in this paper

The paper describes a new implementation of feature structures containing disjunctive values, which can be characterized by the following main points: Local representation of embedded dis-junctions, avoidance of expansion to disjunctive normal form and of repeated test-unifications for checking consistence. The method is based on a modification of Kasper and Rounds ' calculus of feature descriptions and its correctness therefore is easy to see. It can handle cyclic structures and has been incorporated successfully into an envi-ronment for grammar development. 1

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