Barbara H. Partee

Quantificational Structures and Compositionality

In the course of a recent project on cross-linguistic quantification and semantic typology (in collaboration with Emmon Bach and Angelika Kratzer), it has become increasingly apparent that there are significant differences between languages, and also between constructions within languages, in the extent to which the semantic interpretation of various kinds of sentences or constructions whose interpretation is in some sense “quantificational” is explicitly signaled by or encoded in the surface syntax. Leaving aside issues concerning scope ambiguity in sentences containing multiple quantifiers and concentrating on sentences with a single quantificational operator of some sort, one can find examples of two or three different kinds. In some cases, the semantic structure seems to be completely determined by the overt phrase structure; in some cases it seems to be determined by a combination of phrase structure and topic and/or focus structures, and in some cases it may be underdetermined by both of those and may result in sentences that are linguistically ambiguous (unless one can find arguments for calling them nonspecific or indeterminate instead) and only disambiguated, if at all, by the non-linguistic context.

Some Transformational Extensions of Montague Grammar

Richard Montague’s work on English, as represented in Montague (1970a), (1970b), (1972), represents the first systematic attempt to apply the logician’s methods of formal syntax and semantics to natural language. With few exceptions,1 linguists and logicians had previously been agreed, although for different reasons, that the apparatus developed by logicians for treating the syntax and semantics of artificially constructed formal languages, while obviously fruitful within its restricted domain, was not in any direct way applicable to the analysis of natural languages. Logicians seem to have felt that natural languages were too unsystematic, too full of vagueness and ambiguity, to be amenable to their rigorous methods, or if susceptible to formal treatment, only at great cost.2 Linguists, on the other hand, emphasize their own concern for psychological reality, and the logicians’ lack of it, in eschewing the logicians’ approach: linguists, at least those of the Chomskyan school, are searching for a characterization of the class of possible human languages, hoping to gain thereby some insight into the structure of the mind, and the formal languages constructed by logicians appear to depart radically from the structures common to actual natural languages.

EXISTENTIAL SENTENCES, BE, AND THE GENITIVE OF NEGATION IN RUSSIAN

The Genitive of Negation (Gen Neg) in Russian involves alternation of Genitive with Nominative or Accusative under conditions which have been debated for many decades. What gives the construction its name is that Gen Neg occurs only under sentential negation; other allegedly crucial factors include topic–focus structure, unaccusativity, perspectival structure, the lexical semantics of the verb, and the referential status of the NP. Here we focus on Subject Gen Neg sentences, which on our account (following Babby and many Russian scholars) are normally Existential sentences. We address the problem raised by certain Gen Neg sentences with the copula byt’ and referential subjects which appear to be negations of Locative rather than Existential sentences. We review why Babby exempted some sentences with byt’ from his analysis, and present challenges raised by the two present tense forms of the verb. These problems lead to a re-examination of the distinction between Existential and Locative sentences, and of the distinction between sentential and constituent negation. We identify three distinct approaches to these issues, exploring their strengths and weaknesses. We do not argue conclusively for one approach but identify open questions which we believe need answers before the issues can be resolved.

The Semantics of Belief-Sentences

Bar-Hillel in 1954 suggested that formal semantics as developed by such logicians as Tarski and Camap had achieved insights and developed approaches which linguists might profitably make use of for the analysis of natural language. The long delay in taking up Bar-Hillel’s suggestion has stemmed in part from the rejection by some linguists (notably Chomsky, 1955) of the claimed relevance of formal to natural semantics, and in part from the preoccupation of linguists with the more tractable syntax and phonology of natural language to the almost total exclusion of serious attention to semantics. Within the last few years, however, linguists have begun to be more concerned with semantics, and to give more than lip service to the principle that semantic considerations should have equal weight with syntactic ones in evaluating competing theories of grammars.1 The present study is a preliminary investigation into the mutual relevance of some formal semantical notions developed by Carnap and the natural-language syntactic theory developed by Chomsky.

A mathematical model of transformational grammars

A mathematical model of transformational grammars is presented which incorporates most current versions. Among other things, the model has a formal definition of transformations and a general scheme for ordering them. Numerous examples are given to illustrate the theory.

Belief-Sentences and the Limits of Semantics

One of the goals of the conference of which this paper is a part is to compare the enterprise of formal semantics with that of procedure-oriented psychological semantics. The former has traditionally been the domain of logicians and philosophers, the latter the domain of psychologists and computer scientists, with some linguists on each side. The problem that is evident at the outset is that semantics is treated very differently within these two enterprises, each side seemingly committed to assumptions that lead to inadequacies by the other’s criteria. A fruitful comparison could lead to either of two outcomes, which we might characterize roughly as the “Separatist” position and the “Common Goals” position.

Montague Grammar, Mental Representations, and Reality

Over the past ten years or so, there has been a notable convergence of interest between linguists and philosophers on issues in semantic theory and the semantic description of natural languages. Within the line of development in which Montague’s work is an important milestone, a key feature has been the influence of the formal semantic theories of logicians on the semantic analysis of natural languages, and the equally important influence of natural language semantic description on the elaboration and enrichment of formal semantic theories. Although this development is in many ways similar to the development of syntax under Chomsky and other generative grammarians in the past two decades, a development marked at least at the outset by the mutual influence of progressively refined formal syntactic theories and progressively formalized syntactic descriptions of natural language phenomena, nevertheless there remains considerable skepticism among some linguists toward the applicability of formal logical models to natural language semantics. In my own previous work I have argued for the appropriateness of a suitably constrained Montague-type possible worlds semantics as a candidate for a linguistic theory of semantics; in this paper I wish to raise what I perceive to be certain fundamental problems in the application of Montague’s theory to the goals of linguistics.

Genitive Modifiers, Sorts, and Metonymy

Our long-term goal is to contribute to the integration of formal and lexical semantics. Our more immediate theoretical starting point is the idea of text as theory, within a model-theoretic semantic framework. We describe a set of empirical problems in the domain of genitive modifiers that offers a challenge to theories of the integration of lexical, compositional, and contextual information. After sketching a solution, we raise the issue of metonymy in the interpretation of genitives, and examine the role of sortal information in the specification of underspecified meanings and in processes of type-shifting and sort-shifting, including metonymy.

Russian Genitive of Negation Alternations: The Role of Verb Semantics

Genitive-nominative and genitive-accusative alternations exist to various degrees in Slavic and Baltic languages. In Russian the alternation of Gen-Nom and Gen-Acc in negative sentences is conditioned by a combination of syntactic, semantic, and morphological factors. A series of papers by Borschev and Partee and by the present set of authors has studied the semantic factors involved in the genitive of negation. Our recent work builds on the intuition that genitive NPs are “less referential” than their nominative or accusative counterparts; both we and Olga Kagan take that decreased referentiality to involve a “demotion”. We have formalized this demotion in terms of semantic types, arguing that Gen NPs in these alternations are of property type rather than entity type e. In this article we address how verb meanings shift along with the types of their arguments. We review the treatment of Borschev and Partee (1998) of the “bleaching” of the open class of intransitive verbs that appear in existential sentences with Subject Gen Neg, and compare it to the more heterogeneous class of shifts in verb meaning that occurs with Object Gen Neg. The resulting analysis helps to explain both the similarities and the differences between Subject Gen Neg and Object Gen Neg.

How Non-Context Free is Variable Binding?

Within and across theoretical frameworks, linguists have debated whether various phenomena related to variable binding should be handled within syntax, as part of a syntax-to-semantics mapping, or possibly by one or more separate levels of rules or principles specifically dedicated to such phenomena. Relevant phenomena include the interpretation of pronouns and reflexives as bound variables and the binding of gaps or traces by WH-phrases or other operators. Given current interest in the generative capacity of alternative syntactic theories, it is important to note that whatever level of grammatical description deals with variable binding must involve some non-context-freeness if certain natural restrictions on well-formedness (spelled out below) are taken to belong to grammar at all. In this paper we investigate the formal properties of variable binding via an investigation of two restricted versions of predicate logic. We first review the familiar fact that the set L of formulas of first-order predicate logic (FOPL) (allowing free variables and vacuous quantifiers) is a context free (CF) language. We then consider two restricted sublanguages of L, the set S of Sentences of FOPL (formulas with no free variables), and the set U of formulas of FOPL with no vacuous quantifiers. Both S and U can be shown by established methods to be non-CF.