Computational tractability has been a major concern in the area of terminological knowledge representation and reasoning. However, all analyses of the computational complexity of terminological reasoning are based on the hidden assumption that subsumption in terminologies reduces to subsumption of concept descriptions without a significant increase in computational complexity. In this paper it will be shown that this assumption, which seems to work in the "normal case," is nevertheless wrong. Subsumption in terminologies turns out to be co-NP-complete for a minimal terminological representation language that is a subset of every useful terminological language.

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

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 describes a nethod for finding structural matching between parallel sentences of two lauguages, (such as Japanese and English). Par- allel sentences are analyzed based on unification grammars, and structural matching is performed by making use of a similarity measure of word pairs in the two languages. Syntactic ambiguities are resolved simultaneously in the matching process. The results serve as a useful source for extracting linguistic and lexical knowledge.

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

Current complex-feature based gnunrnars use a single procedureuficafionfor a multitude of put~ poses, among them, enforcing formal agreement between pcuely syntactic features. 32fis paper presents evidence from several natural languages that unification---variable-matching combined with variable substitutionis the wrong mechanism for effecting agreement. The view of grammar developed here is one in which unification is used for semantic interpretation, while purely formal agreement involves only a check for non-distinctnessi.e. variable-matching without variable substitution.

We descrlbe a general parsing method for systemic grammars. Systemic grammars contain a paradigmatic analysis of language in addition to structural information, so a parser must assign a set of grammatical features and functions to each constituent in addition to producing a constituent structure. Our method constructs a parser by compiling systemic grammars into the notation of Functional Unification Grammar. The existing methods for parsing with unification grammars hace been extended to handle a fuller range of paradigmatic descriptions. In particular, the PATR-II system has been extended by using disjunctive and conditional information in functional descriptions that are attached to phrase structure rules. The method has been tested with a large grammar of English w:hich was originally developed for text generation. This testing is the basis for some observations about the bidirectional

This thesis proposes a strongly lexicalist approach to machine translation and applies it to the translation of spatial prepositions and prepositional expressions between English and Spanish. Bilingual contrastive knowledge resides solely in the bilingual lexicon and is structured in the form of correspondences between sets of source and target language lexemes related through indices. The resulting architecture maximizes the independence of the monolingual and bilingual components. This independence is demonstrated by developing a grammar of Spanish which is significantly different in its constructions from its analogous English grammar. In particular, relative clauses are analysed through a single rule that allows gaps in subject position, while clitic climbing and doubling are handled through mechanisms not normally found in grammatical descriptions of English. Bilingual lexical rules, in conjunction with the bilingual lexicon, constitute a single, motivated and well defined mechani...