The Query is reasonable (First Order) Predicate Logic (PL:) is a ”Universal Grammar" for the languages of Elementary Arithmetic, Euclidean Geometry, Set Theory, Boolean Algebra, .... It defines their expressions, their semantic interpretations, and texts, called proofs, that syntactically characterize the boolean semantic entailment relation: P entails Q iff Q is true whenever P is.
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..
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)
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.
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)
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'.
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)
We illustrate a novel conception of linguistic invariant which applies to grammars of different natural languages (English, Korean,...) 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 (the issue is an empirical one), 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)
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)
In this note I provide an answer to an apparently technical query by van Benthem (1986; 67) concerning denotations of English expressions. The answer turns out to be revealing of some systematic semantic differences associated with certain categories of expression. The categories of interest to us are illustrated in (1a) and given an extensional type theoretic analysis in (1b).
Voice: Malagasy presents morphologically distinct verbs built from the same root which assign different grammatical cases to DPs with given theta roles, yielding Ss that are theta equivalent, and, with appropriate choice of DPs, logically equivalent, much like active and agented passive Ss in English. The problem is to derive and interpret such Ss so as to yield these judgments of semantic equivalence as theorems. Our solution, which is purely structural, invoking no notion of ‘subject’, ‘topic’, ‘pivot’, ‘trigger’, etc., is (...) simply an explicit syntactic and semantic interpretation of voice affixes. Deriving Ss built from verbs in different voices involves no A movement of DPs. Voice morphology determines the distinctive syntactic and semantic properties of nuclear clauses. This supports that “Variation of language is essentially morphological ...” (Chomsky 1995:7). (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)
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.
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)
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)
In sentences likeEvery teacher laughed we think ofevery teacher as aunary (=type ) quantifier — it expresses a property ofone place predicate denotations. In variable binding terms, unary quantifiers bind one variable. Two applications of unary quantifiers, as in the interpretation ofNo student likes every teacher, determine abinary (= (type ) quantifier; they express properties oftwo place predicate denotations. In variable binding terms they bind two variables. We call a binary quantifierFregean (orreducible) 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 quantifiers. Some are new here, others are familiar (though the proofs that they are non-Fregean are not). (shrink)