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).

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 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

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

This paper shows how these structures can be axiomatized in a decidable class of first-order logic, which can also be used to express constraints on these structures. Desirable properties, such as compactness and decidability, follow directly. Moreover, additional types of feature values, such as "set-valued" features, can be incorporated into the system simply by axiomatizing their properties

We sketch an axiomatic reformalization of Generalized Phrase Structure Grammar (GPSG)---a definition purely within the language of mathematical logic of the theory GPSG embodies. While this treatment raises a number of theoretical issues for GPSG, our focus is not the reformalization itself but rather the method we employ. The model-theoretic approach it exemplifies can be seen as a natural step in the evolution of constraint-based theories from their grammar-based antecedents. One goal of this paper is to introduce this approach to a broader audience and to demonstrate its application to an existing theory. As such, it joins a growing literature of similar studies. Prior studies, however, have had a number of weaknesses---they generally offer little in the way of concrete examples of the advantages the approach has to offer, they typically ignore significant portions of the theories they address, and, by fully abstracting away from the notion of grammar mechanism, they largely abandon...