Long-Distance Dependencies and Applicative Universal Grammar

To deal with long-distance dependencies, Applicative Universal Grammar (AUG) proposes a new type of categorial rides, called superposition rules. We compare the AUG rules with the alternative rules of Steedman's Combinatery Categorial Grammar (CCG) (Steedman, 1987, 1988, 1990; Szabolcsi, 1987; Ades and Steedman, 1982). In contrast to Steedtmm's rules, the AUG rules are free from inconsistencies in their semantic interpretation, fi'ee from spurious ambiguity. "lhe superposition rules arc based on the Theory of Type Supetposition, established independently of the problem of long-distance dependencies and having a broad unifying power. I. Characterization of Applicative Universal Grammar Applicative Universal Grmnmar (AUG) is a linguistic theory that uses the lormalism of catcgorial g~unmar ,as a means for representing the structure of language. AUG has two levElS: 1) lhe study of the grammatical slructurc in itsclt (genotype grammar), ~md 2) the study of the linear representation of the grammatical structure (phenotype grammar). AUG includes a system of combinators (Curry and Feys, 1958) ,'rod fi)nnulates semiotic concepts, principles, and laws that dctcnninc tile fimctioning of natur~d languages ,as sign systems (for a complete description of AUG, see Shaumyan, 1974, 1977, 1987; Dcsci6s, 1990; Scgond, 1990a; some applications of AI ]G arc discussed in Shaumyan 1989, 1991). AUG is based on the relation operator-operand, which corresponds to the relation fi~nction-argument in categorial grmnmar. We prefer the terms operator-operand for reasons similar to those given by l l indley and Seldin (1986, pp. 44-45). In AI IG categories are generated rccursively by the type-forming operator O, and are called O-types. AUG recognizes two primit ive typeste rms (nouns and noun-phrases) and sentences, denoted by t mid s, respectively. The rule for generating O-types is: 1) The primitive types t and s are O-types. 2) If x and y m'e O-types, then Oxy is an O-lype. (1) For the sake of brevity, we use the term type in the sense of the O-type. Taking t and s as primitives, wc generate the inductive class of types: t, s, Ott, Oss, Ots, Ost, OtOts, OOtsOts, and so on. In representing the types we u ~ the parentheses-free Polish notation, which is more convenient than Curry's nolation with internal parentheses. The basic rule of combination of phrases is the Rule of Phrase Application, which is defined as follows: Phrase A of type Oxy, called an operator, combines with phrase B of type x, called its operand, to form phrase AB of type y, called its resultant: