Two Theories For Computing The Logical Form Of Mass Expressions

Applying the rules of translation is even simpler. In essence, all that is needed is a mechanism for arranging There are various difficulties in accomodating the traditional logical expressions into larger expressions in conformity with mass/count distinction into a grammar for English which the semantic rules. (For examples of parsers see Thompson has a goal the production of "logical form" semantic translations of the initial English sentences, The present paper surveys some of these difficulties. One puzzle is whether the distinction is a syntactic one or a semantic one, i.e., whether it is a well-formedness constraint or whether it is a description of the semantic translations produced. Another puzzle is whether it should be applied to simple words (as they occur in the lexicon) or whether it should apply only to longer units (such as entire NPs). Of the wide variety of possible theories, only two seem to produce the required results (having to do with plausible inferences and intuitively satisfying semantic representations). These two theories are developed and compared. According to Montague (Thomason 1974), Gazdar (Gazdar et al 1984) and a rapidly growing number of linguists, philosophers, and AI researchers, the logical form underlying sentences of a natural language are systematically--and simply--determined by the syntactic form of those sentences. This view is in contrast with a tacit assumption often made in AI, that computation of logical translations requires throngs of more or less arbitrary rules operating upon syntactic forms.* The following are a few grammar rules in approximately the style of Gazdar's Generalized Phrase Structure Grammar (GPSG). They differ from Gazdar's primarily in that they are designed to produce more or less "conventional" logical translations, rather than the intensional ones of Montague and Gazdar (for details see Schubert & Pelletier 1982). Each rule consists of a rule number, a phrase structure rule, and a semantic (logical translation) rule. 1. S . , NP VP, VP'(NP') 2. V P . , [V +be] PRED, PRED' 3. PILED .* N, N' N,={water,wine,food,furniture,...} Parsing and translating in accordance with such rules is a fairly straightforward matter. Since the syntactic rules are context free, standard context-free parsing methods can be employed, except that allowance must be made for the propagation of features, with due regard for concord. 'The work reported herein was partially supported by NSERC grants A5525 (FJP) and A8818 (LKS). We also wish to thank Matthew Dryer, David Justice, Bernard Linsky, and other members of the Univ. Alberta Logical Grammar Study Group for discussions on these topics. 1981, Schubert & Pelletier 1982, Gawron et al 1982, Rosenschein & Shieber 1982). The topic of mass terms and predicates has a substantial literature within both linguistics and philosophical logic, with much of the recent research deriving inspiration from Montague Grammar (e.g., see Pellefier 1979, ter Meulen 1980, Bunt 1981, Chierchia 1982). There are three views on the mass/count distinction, namely that the distinction is (a) syntactic, (b) semantic,, and (c) pragmatic, Orthogonal to these views we have the further possibilities (i) that the mass/count distinction is lexical. and (ii) that it is determined by the context in which the expression occurs. We shall present arguments in the full paper to eliminate position (c), leaving us with four possible kinds of theories. ( i ) a syntactic expression (lexical) approach, (2) a syntactic occurrence approach. (3) a semantic expression approach, and (4) a semantic occurrence approach. This raises the question of what is the difference between syntactic approaches generally and semantic approaches generally. A syntactic approach treats +mass and +count as syntactic classifications or features, that is as features to be used by the syntactic rules in determining whether some longer stretch of words is well-formed. Central to the semantic approach is the claim that +count and +mass are not syntactic features or categories, but rather are a description of the semantic representation of the expression. In this approach, no syntactic rules refer to +count or +mass (since these are not syntactic objects). Rather, in sentences like Mary put apple in the salad vs. Mary put an apple in the. salad, the semantic approaches allow us to say that it was a mass or count semantic representation of apple only after inspecting the kind of thing that apple is true of in the