Incorporating Inheritance and Feature Structures Into a Logic Grammar Formalism

INCORPORATING INHERITANCE AND FEATURE STRUCTURES INTO A LOGIC GRAMMAR FORMALISM Harry H. Porter, III Oregon Graduate Center 19600 N.W. Von Neumann Dr. Beaverton Oregon 97008-1999 ABSTRACT Hassan Ait-Kaci introduced the #/-term, an informational structure resembling feature- based functional structures but which also includes taxonomic inheritance (Ait-Kaci, 1984). We describe e-terms and how they have been incorporated into the Logic Grammar formal- ism. The result, which we call Inheritance Grammar, is a proper superset of DCG and includes many features of PATR-II. Its taxo- nomic reasoning facilitates semantic type-class reasoning during grammatical analysis. INTRODUCTION The Inheritance Grammar (IG) formalism is an extension of Hassan Ait-Kaci's work on #/- terms (Ait-Kaci, 1984; Ait-Kaci and Nasr, 1986). A e-term is an informational structure similar to both the feature structure of PATR-II (Shieber, 1985; Shieber, et al, 1986) and the first-order term of logic, e-terms are ordered by subsumption and form a lattice in which unification of #/-terms amounts to greatest lower bounds (GLB, [-']). In Inheritance Grammar, #/- terms are incorporated into a computational paradigm similar to the Definite Clause Gram- mar (DCG) formalism (Pereira and Warren, 1980). Unlike feature structures and first-order terms, the atomic symbols of #/-terms are ordered in an IS-A taxonomy, a distinction that is useful in performing semantic type-class rea- soning during grammatical analysis. We begin by discussing this ordering. THE IS-A RELATION AMONG FEATURE VALUES Like other grammar formalisms using feature-based functional structures, we will assume a fixed set of symbol8 called the signa- ture. These symbols are atomic values used to represent lexical, syntactic and semantic categories and other feature values. In many formalisms (e.g. DCG and PATR-II), equality is the only operation for symbols; in IG symbols are related in an IS-A hierarchy. These rela- tionships are indicated in the grammar using statements such as1: boy < masculineObject. girl < feminineObject. man < masculineObject. woman < feminineObJect. {boy, girl} < child. {man, woman} < adult. {child, adult} < human. The symbol < can be read as "is a" and the notation {a,,... ,an}<b is an abbreviation for al<b, • • • ,an<b. The grammar writer need not distinguish between instances and classes, or between syntactic and semantic categories when the hierarchy is specified. Such distinctions are only determined by how the symbols are used in the grammar. Note that this example ordering exhibits multiple inheritance: feminineOb- jeers are not necessarily humans and humans are not necessarily feminine0b- Jeers, yet a girl is both a human and a feminineObj ect. Computation of LUB (t_ J) and GLB (['7) in arbitrary partial orders is problematic. In IG, the grammar writer specifies an arbitrary ordering which the rule execution system automatically embeds in a lattice by the addi- tion of newly created symbols (Maier, 1980). Symbols may be thought of as standing for conceptual sets or semantic types and the IS-A relationship can be thought of as set I Symbols appearing in the grammar but not in the 228 inclusion. Finding the GLB-i.e. unification of symbols-then amounts to …

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