In sentences like Every teacher laughed we think of every teacher as a unary (=type (1)) quantifier - it expresses a property of one place predicate denotations. In variable binding terms, unary quantifiers bind one variable. Two applications of unary quantifiers, as in the interpretation of No student likes every teacher, determine a binary (= type (2)) quantifier; they express properties of two place predicate denotations. In variable binding terms they bind two variables. We call a binary quantifier Fregean (or (...) reducible) if it can in principle be expressed by the iterated application of unary quantifiers. In this paper we present two mathematical properties which distinguish non-Fregean quantifiers from Fregean ones. Our results extend those of van Benthem (1989) and Keenan (1987a). We use them to show that English presents a large variety of non-Fregean quantifi ers. Some are new here, others are familiar (though the proofs that they are non-Fregean are not). The main point of our empirical work is to inform us regarding the types of quantification natural language presents - in particular (van Benthem, 1989) that it goes beyond the usual (Fregean) analysis which treats it as mere iterated application of unary quantifiers. Secondarily, our results challenge linguistic approaches to "Logical Form" which constrain variable binding operators to "locally" bind just one occurrence of a variable, e.g., the Bijection Principle (BP) of Koopman and Sportiche (1983). The BP (correctly) blocks analyses like For which x, x's mother kissed x? for Who did his mother kiss? since For which x would locally bind two occurrences of x. But some of our irreducible binary quantifiers are naturally represented by operators which do locally bind two variables. This paper is organized as follows: Section 1 provides an explicit formulation of our questions of concern. Section 2 classifies the English constructions which we show to be non-Fregean. Section 3 presents the mathematical properties which test for non-Fregean quantification and applies these tests to the constructions in Section 2. Proofs of the mathema tical properties are given in the Appendix. (shrink)
Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 1 we show that English quantifiers of type $ $ are booleanly generated by their generalized universal and generalized existential members. These two classes also constitute the sortally reducible members of this type. Section 2 presents our main result--the Generalized Prefix Theorem (GPT). This theorem characterizes the conditions under which formulas of the form Q1x 1⋯ Qnx nRx 1⋯ xn and q1x 1⋯ qnx nRx (...) 1⋯ xn are logically equivalent for arbitrary generalized quantifiers Qi, qi. GPT generalizes, perhaps in an unexpectedly strong form, the Linear Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973). (shrink)
We consider the logical form of a natural language sentence to be a formal object which determines both the logical properties of the sentence and, more generally, the ways the sentence is logically related to other sentences. Thus if some NL sentence logically entails another, this fact must follow, given the logical forms of the two sentences. The power of a theory of logical forms of natural language then lies first in what logical properties and relations it can define, and (...) second, in which NL sentences it can show to be logically related to which others. (shrink)
avant propos This paper is basically Keenan (1992) augmented by some new types of properly polyadic quantification in natural language drawn from Moltmann (1992), Nam (1991) and Srivastav (1990). In addition I would draw the reader's attention to recent mathematical studies of polyadic quantiicationz Ben-Shalom (1992), Spaan (1992) and Westerstahl (1992). The first and third of these extend and generalize (in some cases considerably) the techniques and results in Keenan (1992). Finally I would like to acknowledge the stimulating and constructive (...) discussions ofthe earlier paper with many scholars, notably Dorit Ben-Shalom, Jaap van der Does, Hans Kamp, Uwe Mormich, Arnim von Stechow, Mats Rooth, and Ede Zimmermann. And I repeat here the acknowledgment in the earlier paper to Jim Lambek, Ed Stabler and two anonymous referees for Linguistics and Philosophy (the latter responsible for substantial improvements in the proofs - see footnote 10). (shrink)
In this chapter we shall examine the characteristic properties of a construction wide-spread in the world’s languages, the passive. In section 1 below we discuss deﬁning characteristics of passives, contrasting them with other foregrounding and backgrounding constructions. In section 2 we present the common syntactic and semantic properties of the most wide-spread types of passives, and in section 3 we consider passives which differ in one or more ways from these. In section 4, we survey a variety of constructions that (...) resemble passive constructions in one way or another. In section 5, we brieﬂy consider differences between languages with regard to the roles passives play in their grammars. Speciﬁcally, we show that passives are a more essential part of the grammars of some languages than of others. (shrink)
A volume of studies in natural language semantics which brings together work by philosophers, logicians and linguists. The main topics treated are: quantification and reference in natural language; the relations between formal logic, programming languages and natural language; pragmatics and discourse meaning; surface syntax and logical meaning. The volume derives from a colloquium organised in 1973 by the Kings College Research Centre, Cambridge and the papers have been edited for publication by Professor Keenan. It is hoped that the collection will (...) make available some of the best work in this fast-moving field and will stimulate further progress by juxtaposing the different approaches and interests represented here. (shrink)
Linguists rely on intuitive conceptions of structure when comparing expressions and languages. In an algebraic presentation of a language, some natural notions of similarity can be rigorously defined (e.g. among elements of a language, equivalence w.r.t. isomorphisms of the language; and among languages, equivalence w.r.t. isomorphisms of symmetry groups), but it tums out that slightly more complex and nonstandard notions are needed to capture the kinds of comparisons linguists want to make. This paper identihes some of the important notions of (...) structural similarity, with attention to similarity claims that are prominent in the current linguistic tradition of transformational grammar. @ 2002 Elsevier Science B.V. All rights reserved. (shrink)
roots In the Lexicon of Malagasy we include an entry whose string part is vidy ('buy'). Its category is 'RT [AG, TH) ', indicating that it is a root and is associated with a two element set of theta roles, AGFNT and THEME. Semantically this entry is interpreted as a binary relation (= a two participant event), noted VIDY'.
We illustrate a novel conception of linguistic invariant which applies to grammars of different natural languages even though they may use different categories and have difl'erent rules. We illustrate formally how semantically defined notions, such as "is an anaphor" may be invariant in all linguistically motivated grammars, and we show that individual morphemes, such as case markers, may be invariant in grammars that have them in exactly the same sense in which properties, such as "is a Verb Phrase" or relations (...) such as "is a constituent of". (shrink)
This work presents the structure, distribution and semantic interpretation of quantificational expressions in languages from diverse language families and typological profiles. The current volume pays special attention to underrepresented languages of different status and endangerment level. Languages covered include American and Russian Sign Languages, and sixteen spoken languages from Africa, Australia, Papua, the Americas, and different parts of Asia. The articles respond to a questionnaire the editors constructed to enable detailed crosslinguistic comparison of numerous features. They offer comparable information on (...) semantic classes of quantifiers (generalized existential, generalized universal, proportional, partitive), syntactically complex quantifiers (intensive modification, Boolean compounds, exception phrases, et cetera), and several more specific issues such as quantifier scope ambiguities, floating quantifiers, and binary (type 2) quantifiers. The book is intended for semanticists, logicians interested in quantification in natural language, and general linguists as articles are meant to be descriptive and theory independent. The book continues and expands the coverage of the Handbook of Quantifiers in Natural Language (2012) by the same editors, and extends the earlier work in Matthewson (2008), Gil and others (2013) and Bach et al (1995). (shrink)
Grammatical categories of English expressions are shown to differ with regard to the freedom we have in semantically interpreting their lexical (= syntactically simplest) expressions. Section 1 reviews the categories of expression we consider. Section 2 empirically supports that certain of these categories are lexically free, a notion we formally define, in the sense that anything which is denotable by a complex expression in the category is available as a denotation for lexical expressions in the category. Other categories are shown (...) to be not lexically free. Thus for those categories the interpretation of lexical expressions is inherently constrained compared to the interpretation of the full class of expressions in the category. (shrink)
Erratum to: Stanley Peters and Dag Westerståhl: Quantifiers in language and logic Content Type Journal Article Category Erratum Pages 1-1 DOI 10.1007/s10988-011-9094-5 Authors Edward L. Keenan, Department of Linguistics, University of California at Los Angeles, 3125 Campbell Hall, Los Angeles, CA 90095-1543, USA Denis Paperno, Department of Linguistics, University of California at Los Angeles, 3125 Campbell Hall, Los Angeles, CA 90095-1543, USA Journal Linguistics and Philosophy Online ISSN 1573-0549 Print ISSN 0165-0157.
Elements of Formal Semantics has already been reviewed twice :42, 2016; Erlewine in Comput Linguist 42:837–839, 2017). As well, the website for the work is accompanied by evaluative quotes by noted scholars. All are very positive concerning its clarity and its utility as an introduction to formal semantics for natural language. As I agree with these evaluations my interest in reiterating them in slightly different words is limited. So my reviews of the content chapters will be accompanied by a Reflections (...) section consisting of my own reflections on the foundations of model theoretic semantics for natural language as laid out in EFS. The issues I address—alternate ways of accomplishing the tasks Winter treats—should not be included in an introductory work but they may be helpful for those who teach classes for which EFS is an appropriate text. They might also help with queries about the content of the text by those using it. I note that a mark of a clear text is that it allows the reader to reflect on its content not its presentation. (shrink)
Binding relations are fimdamentally semantic in nature. They arise as relations that are established with an interpretation. This is most apparent with dynamic binding, of the kind found in Dynamic Predicate Logic. Here it is the runtime of the evaluation that may permit a binding relation, in..
Pursuing a study begun in (Keenan 2004) this note investigates inference patterns in natural language which proportionality quantifiers enter. We desire to identify such patterns and to isolate any such which are specific to proportionality quantifiers.
Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of QLL we judge (...) to be of specific interest to linguists, and we contribute a few musings of our own, as one mark of a worthy publication is whether it stimulates the reader to seek out new observations, and QLL does. QLL is long and fairly dense, so we make no attempt to cover all the points it makes. But QLL has a topic index, a special symbols index and two tables of contents, a detailed one and an overview one, all of which help make it user friendly. QLL is presented in four parts: I, "The Logical Conception of Quantifiers and Quantification" with an introductory section "Quantification". II, "Quantifiers of Natural Language", the most extensive section in the book and of the most direct interest to linguists. III, "Beginnings of a Theory of Expressiveness, Translation, and Formalization" introduces notions of expressive power and definability, and IV, presents recent work and techniques concerning quantifier definability over finite domains, making accessible to linguists recent work in finite model theory. (shrink)
Within Linguistics the semantic analysis of natural languages (English, Swahili, for example) has drawn extensively on semantical concepts first formulated and studied within classical logic, principally first order logic. Nowhere has this contribution been more substantive than in the domain of quantification and variable binding. As studies of these notions in natural language have developed they have taken on a life of their own, resulting in refinements and generalizations of the classical quantifiers as well as the discovery of new types (...) of quantification which exceed the expressive capacity of the classical quantifiers. We refer the reader to Keenan and Westerståhl (1997) for an overview of results in this area. Here, we focus on one property of quantification in natural language—its inherently sortal nature—which distinguishes it from quantification in classical logic. (shrink)