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15
Incremental Interpretation
 Artificial Intelligence
, 1991
"... We present a system for the incremental interpretation of naturallanguage utterances in context. The main goal of the work is to account for the influences of context on interpretation, while preserving compositionality to the extent possible. To achieve this goal, we introduce a representational d ..."
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We present a system for the incremental interpretation of naturallanguage utterances in context. The main goal of the work is to account for the influences of context on interpretation, while preserving compositionality to the extent possible. To achieve this goal, we introduce a representational device, conditional interpretations, and a rule system for constructing them. Conditional interpretations represent the potential contributions of phrases to the interpretation of an utterance. The rules specify how phrase interpretations are combined and how they are elaborated with respect to context. The control structure defined by the rules determines the points in the interpretation process at which sufficient information becomes available to carry out specific inferential interpretation steps, such as determining the plausibility of particular referential connections or modifier attachments. We have implemented these ideas in Candide, a system for interactive acquisition of procedural ...
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
Normal Forms for Characteristic Functions on nary Relations Abstract
, 2004
"... Functions of type 〈n 〉 are characteristic functions on nary relations. Keenan [5] established their importance for natural language semantics, by showing that natural language has many examples of irreducible type 〈n 〉 functions, i.e., functions of type 〈n 〉 that cannot be represented as compositio ..."
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Functions of type 〈n 〉 are characteristic functions on nary relations. Keenan [5] established their importance for natural language semantics, by showing that natural language has many examples of irreducible type 〈n 〉 functions, i.e., functions of type 〈n 〉 that cannot be represented as compositions of unary functions. Keenan proposed some tests for reducibility, and Dekker [3] improved on these by proposing an invariance condition that characterizes the functions with a reducible counterpart with the same behaviour on product relations. The present paper generalizes the notion of reducibility (a quantifier is reducible if it can be represented as a composition of quantifiers of lesser, but not necessarily unary, types), proposes a direct criterion for reducibility, and establishes a diamond theorem and a normal form theorem for reduction. These results are then used to show that every positive 〈n〉 function has a unique representation as a composition of positive irreducible functions, and to give an algorithm for finding this representation. With these formal tools it can be established that natural language has examples of nary quantificational expressions that cannot be reduced to any composition of quantifiers of lesser degree. Accepted for publication in the Journal of Logic and Computation. 1
Multiple Negation Processing
"... This paper considers negative triggers (negative and negative quantifiers) and the interpretation of simple sentences containing more than one occurrence of those items (multiple negation sentences). In the most typical interpretations those sentences have more negative expressions than negations in ..."
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This paper considers negative triggers (negative and negative quantifiers) and the interpretation of simple sentences containing more than one occurrence of those items (multiple negation sentences). In the most typical interpretations those sentences have more negative expressions than negations in their semantic representation. It is first shown that this compositionality problem remains in current approaches. A principled algorithm for deriving the representation of sentences with multiple negative quantifiers in a DRT framework (Kamp & Reyle, 1993) is then introduced. The algorithm is under the control of an online checkin, keeping the complexity of negation autoembedding below a threshold of complexity. This mechanism is seen as a competence limitation imposing (and licensing) the "abrogation of composifionality" (May 1989) observed in the socalled negative concord readings (Labov 1972, Zanuttini 1991, Ladusaw 1992). A solution to the composifionality problem is thus proposed, which is based on a control on the processing input motivated by a limitation of the processing mechanism itself.
The Categorial FineStructure of Natural Language
, 2003
"... Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, i ..."
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Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves  amongst others  mixtures of interpretation and inference.
Irreducible Higher Order Functions in Natural Language
, 2004
"... Functions of type 〈n 〉 are characteristic functions on nary relations. In Beyond the Frege Boundary [6], Keenan established their importance for natural language semantics, by showing that natural language has many examples of irreducible type 〈n 〉 functions, where he called a function of type 〈n 〉 ..."
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Functions of type 〈n 〉 are characteristic functions on nary relations. In Beyond the Frege Boundary [6], Keenan established their importance for natural language semantics, by showing that natural language has many examples of irreducible type 〈n 〉 functions, where he called a function of type 〈n 〉 reducible if it can be represented as a composition of functions of type 〈1〉. We will give a normal form theorem for functions of type 〈n〉, and use this to show that natural language has many examples of irreducible type 〈n 〉 functions in a much stronger sense, where we take a function to be reducible if it can be represented as a composition of functions of lower types. Two ways to analyze NP V NP • Standard analysis of Every lawyer cheated a firm: this states a relation between the CN property of being a lawyer and the VP property of cheating firms, namely the relation of inclusion. Two ways to analyze NP V NP • Standard analysis of Every lawyer cheated a firm: this states a relation between the CN property of being a lawyer and the VP property of cheating firms, namely the relation of inclusion. This is called the Fregean analysis. Two ways to analyze NP V NP • Standard analysis of Every lawyer cheated a firm: this states a relation between the CN property of being a lawyer and the VP property of cheating firms, namely the relation of inclusion. This is called the Fregean analysis. • Alternative analysis: look at the complex expression Every lawyer a firm and interpret this as a function that takes a relation as its argument (a denotation of a transitive verb, such as cheated, accused, defended) and produces a truth value.
Computational Complexity of Multiquantifier Sentences
, 2009
"... We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multiquantifier sentences. First, we show that the standard semantic constructions that turn simple quantifiers into complex ones ..."
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We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multiquantifier sentences. First, we show that the standard semantic constructions that turn simple quantifiers into complex ones, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into the operations yielding intractable natural language multiquantifier expressions: branching and Ramseyfication. Next, we focus on a linguistic case study. We use computational complexity results to investigate semantic distinctions between quantified reciprocal sentences. We show a computational dichotomy between different readings of reciprocity. Finally, we go more into philosophical speculation on meaning, ambiguity and computational complexity. In particular, we investigate a possibility to revise the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multiquantifier sentences. The paper not only contributes to the field of the formal semantics but also illustrates how the tools of computational complexity theory might be succesfully used in linguistics and philosophy with an eye towards cognitive science.
Almost All Complex Quantifiers are Simple
"... Abstract. We prove that PTIME generalized quantifiers are closed under Boolean operations, iteration, cumulation and resumption. Key words: generalized quantifiers; computational complexity; polyadic quantifiers; Boolean combinations; iteration; cumulation; resumption 1 ..."
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Abstract. We prove that PTIME generalized quantifiers are closed under Boolean operations, iteration, cumulation and resumption. Key words: generalized quantifiers; computational complexity; polyadic quantifiers; Boolean combinations; iteration; cumulation; resumption 1