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

. 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...

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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.

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.

this article concerns autosegmental representations, and not the rules which are presumed to manipulate them. Due to the expository goals of this paper we have not attempted to carry out a detailed analysis of a large body of phonological data, however we acknowledge that this is an important task and it is one that we intend to undertake in future work. Deriving the No-Crossing Constraint Sagey defines three relations on temporal units: simultaneity, precedence and overlap. Certain facts about the first two relations (and presumably the third also) are taken to be `included in our knowledge of the world' (p.110). We begin with a brief review of these facts. Temporal overlap is a two-place relation which is reflexive, symmetric and nontransitive. If we employ the notation x ffi y for the statement `x overlaps y' then these facts about overlap can be stated as follows: (1) a. For any x, x ffi x overlap is reflexive

Feature logics form a class of specialized logics which have proven especially useful in classifying and constraining the linguistic objects known as feature structures. Linguistically, these structures have their origin in the work of the Prague school of linguistics, followed by the work of Chomsky and Halle in The Sound Pattern of English [16]. Feature structures have been reinvented several times by computer scientists: in the theory of data structures, where they are known as record structures, in artificial intelligence, where they are known as frame or slot-value structures, in the theory of data bases, where they are called "complex objects", and in computati