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Scope dominance with monotone quantifiers over finite domains
 Journal of Logic, Language and Information
, 2004
"... We characterize pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations betwe ..."
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We characterize pairs of monotone generalized quantifiers Q1 and Q2 over finite domains that give rise to an entailment relation between their two relative scope construals. This relation between quantifiers, which is referred to as scope dominance, is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP1VNP2. Simple numerical or settheoretical considerations that follow from our main result are used for characterizing such relations. The variety of examples in which they hold are shown to go far beyond the familiar existentialuniversal type. 1
On Scope Dominance With Monotone Quantifiers
, 2003
"... We characterize pairs of monotone generalized quantifiers Q 1 and Q 2 that give rise to an entailment relation between their two relative scope construals. This result is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP 1 VNP 2 ..."
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We characterize pairs of monotone generalized quantifiers Q 1 and Q 2 that give rise to an entailment relation between their two relative scope construals. This result is used for identifying entailment relations between the two scopal interpretations of simple sentences of the form NP 1 VNP 2 . The general characterization that we give turns out to cover more examples of such entailments besides the familiar type where the NPs are headed by some and every.
The Effect of Negative Polarity Items on Inference Verification
"... The scalar approach to negative polarity item (NPI) licensing assumes that NPIs are allowable in contexts in which the introduction of the NPI leads to proposition ..."
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The scalar approach to negative polarity item (NPI) licensing assumes that NPIs are allowable in contexts in which the introduction of the NPI leads to proposition
Scope Dominance with Generalized Quantifiers
, 2009
"... When two quantifiers Q1 and Q2 satisfy the scheme Q1x Q2y φ → Q2y Q1x φ, we say that Q1 is scopally dominant over Q2. This relation is central in analyzing and computing entailment relations between different readings of ambiguous sentences in natural language. This paper reviews the known results o ..."
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When two quantifiers Q1 and Q2 satisfy the scheme Q1x Q2y φ → Q2y Q1x φ, we say that Q1 is scopally dominant over Q2. This relation is central in analyzing and computing entailment relations between different readings of ambiguous sentences in natural language. This paper reviews the known results on scope dominance and mentions some open problems. 1 Basic definitions An arbitrary generalized quantifier of signature 〈n1,..., nk 〉 over a nonempty domain E is a relation f ⊆ ℘(E n1) ×... × ℘(E nk), where k ≥ 1, and ni ≥ 1 for all i ≤ k (e.g. Peters and Westerst˚ahl, 2006, p.65). In short, we say that f is a quantifier when it is of signature 〈1〉, a determiner (relation) when it is of signature 〈1, 1〉, and a dyadic quantifier when it is of signature 〈2〉. When R is a binary relation over some domain E (not necessarily E), we denote for every X, Y ∈ E: (1) a. RX = {Y ∈ E: R(X, Y)} b. R Y = {X ∈ E: R(X, Y)} In theories of natural language semantics, determiner relations are useful in describing the meaning of determiner expressions as in (2). (2) every: every = {〈A, B 〉 ⊆ E 2: A ⊆ B} some: some = {〈A, B 〉 ⊆ E 2: A ∩ B ̸ = ∅} more than half: mth = {〈A, B 〉 ⊆ E 2: A ∩ B > A ∩ B} It is wellknown (Peters and Westerst˚ahl, 2006, p.469) that meanings of natural language determiners – e.g. of the expression more than half – may be beyond what is expressible in first order logic. We assume that nouns denote sets A ⊆ E. Noun phrase meanings are then described as in (3) using a quantifier DA, where the noun denotation is the left 1 argument of the determiner relation D (cf. (1a)). (3) every student: every S = {B ⊆ E: S ⊆ B} some teacher: someT = {B ⊆ E: T ∩ B ̸ = ∅} more than half of the students: mthS = {B ⊆ E: S ∩ B > S ∩ B} Truth values of simple sentences with intransitive verbs are derived as in (4), using the membership statement that the set denotation of the verb is in the quantifier denotation of the subject, or, equivalently, that the pair of sets denoted by the noun and the verb are in the determiner relation. (4) every student smiled: SM ∈ every S ⇔ 〈S, SM 〉 ∈ every ⇔ S ⊆ SM some teacher cried: C ∈ someT ⇔ 〈T, C 〉 ∈ some ⇔
Computing Scope Dominance with Upward Monotone Quantifiers
"... This paper describes an algorithm that characterizes logical relations between different interpretations of scopally ambiguous sentences. The proposed method uses general properties of natural language determiners in order to generate a model which is indicative of such entailment relations. The ..."
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This paper describes an algorithm that characterizes logical relations between different interpretations of scopally ambiguous sentences. The proposed method uses general properties of natural language determiners in order to generate a model which is indicative of such entailment relations. The computation of this model involves information about cardinalities of noun denotations and containment relations between them, which often affect entailment relations with quantifiers. After proving the correctness of the proposed method, the paper briefly describes a demo implementation that illustrates its main results.
of Scope Dominance with Monotone Quantifiers in Natural Language
"... The research thesis was done under the supervision of Dr. Yoad Winter in the Faculty of Computer Science. This research was supported by grant no. 1999210 (”Extensions and Implementations of Natural Logic”) from the United StatesIsrael Binational Science Foundation (BSF), Jerusalem, Israel. The gen ..."
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The research thesis was done under the supervision of Dr. Yoad Winter in the Faculty of Computer Science. This research was supported by grant no. 1999210 (”Extensions and Implementations of Natural Logic”) from the United StatesIsrael Binational Science Foundation (BSF), Jerusalem, Israel. The generous financial help of the Technion is gratefully acknowledged.
Types and Meanings in Intensionality, Selection and Quantifier Scope Gilad BenAviTypes and Meanings in Intensionality, Selection and Quantifier Scope
"... Acknowledgements First and foremost, I am indebted to Yoad Winter. Yoad is everything one would expect to find in an advisor and a teacher, and much more than this. Yoad is the one who introduced me to the field of natural language semantics. His optimism and encouragement, together with the endless ..."
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Acknowledgements First and foremost, I am indebted to Yoad Winter. Yoad is everything one would expect to find in an advisor and a teacher, and much more than this. Yoad is the one who introduced me to the field of natural language semantics. His optimism and encouragement, together with the endless discussions and iterations we had, made the completion of this thesis possible. Special thanks to Nissim Francez for the time and effort he put into Chapter 3, which is based on a conference paper we published together, and for his thorough remarks on the material in the other chapters. Nissim, as a teacher, has initiated my interest in Categorial Grammars and Proof Theory. Thanks also to the other members in my PhD committee, Johann Makowsky and Ariel Cohen, for their illuminating remarks. I am grateful to Shalom Lappin, Ed Keenan, Johann Makowsky, and especially to Ya’acov Peterzil, for their remarks on the material in Chapter 4.