A Treatment Of Negative Descriptions Of Typed Feature Structures

A formal treatment of typed feature structures (TFSs) is developed to augment TFSs, so that negative descriptions of them can be treated. Negative descriptions of TFSs can make linguistic descriptions compact and thus easy to understand. Negative descriptions can be classified into three primitive negative descriptions: (1) negations of type symbols, (2) negations of feature existences, and (3) negations of feature-address value agreements. The formalization proposed in this paper is based on A'it-Kaci's complex terms. The first description is treated by extending type symbol lattices to include complement type symbols. The second and third are treated by aug-meriting term structures with structures representing these negations. Algorithrrts for augmented-TFS unification have been developed using graph unification, and programs using these algorithms have been written in Conmaon Lisp. 1 Introduction In unification-based or information:based linguistic frameworks, the most important objects are structures called 'feature structures' (FSs), which are used to describe linguistic objects and phenomena. A feature structure is either atomic or complex: an atomic FS is denoted by an atomic symbol; a complex FS consists of a set of feature-value pairs each of which describes an aspect of an object. Partial information on aJ~ object is merged by applying the unification operation to FSs. ILeseareh on unification-based linguistic theories has been accompanied by research on FSs themselves. Several extensions on FSs or on feature descriptions and formal treatments of the extensions have been proposed. Disjunctive and negative descriptions on FSs help make the linguistic descriptions simple, compact, and thus easy to understand. For disjunctive feature de-acrq)tions, Kay[14] introduces them into FUG (lqlnc-tmnal Unification Grammar) and gives the procedural semantics. Karttunen[ll] also proposes procedural treatments of disjunctions in conjunction with relatively simple negations. ILounds and Ka.sper[19, 13] propose a logic-based formalism-feature logic-which uses automata to model FSs and can treat dis-Junctive feature descriptions, and they obtain important results. For negative descriptions of PSs, one of the most. fundamental properties of FSs, the partiality of information they carry, makes its insufficient to adopt relatively simple treatments. Classical interpretation of negation, for example, does not, allow evaluation of negations to be freely interleaved with unification. Moshier and Rounds[17] propose a formal framework which treats negative feature descriptions on the b`a~is of intuitionistic logic. Ilowever, their |bHnalism has trouble treating double negations. Dawar[5] l)rOl)OSeS a formal treatment b~ed on three-valued logic. In order to treat feature domains of complex FSs and to treat taxonomic hierarchies …