Computational Semantics for Monadic Quantifiers

2007

Neuropsychologia

Research presented in this journal by McMillan et al. (2005) is the first attempt to investigate the neural basis of natural language quantifiers (see also McMillan et al. (2006) for evidence on quantifier comprehension in patients with focal neurodegenerative disease and Clark and Grossman (2006) for more general discussion). It was devoted to study brain activity during comprehension of sentences with generalized quantifiers. Using BOLD fMRI the authors examined the pattern of neuroanatomical recruitment while subjects were judging the truth-value of statements containing natural language quantifiers. According to the authors their results verify a particular com- * The author would like to express his appreciation to Theo Janssen for comments on the manuscript.

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confidence: 88%

Section: Quantifiers and Working Memorymentioning

confidence: 99%

A comment on a neuroimaging study of natural language quantifier comprehension

2007

Neuropsychologia

“…Both “an even number” and “an odd number” are quantifiers recognized by two‐state finite automata with a transition from the first state to the second and vice versa. In general, exactly the quantifiers definable in divisibility logic, FO ( D n ) (i.e., first‐order logic enriched by all quantifiers “divisible by n ,” for n ≥ 2), are recognized by finite automata (FA) (see Mostowski, 1998).…”

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confidence: 99%

Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model

Zajenkowski

2010

Cognitive Science

We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality. In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon, the hypotheses and explanatory power of recent neuroimaging studies as well as provides evidence for the claim that human linguistic abilities are constrained by computational complexity.

“…It is then clear that definability and complexity of monadic quantifiers has been extensively studied. For example, it is known that on finite models monadic quantifiers definable in first-order logic are recognizable by acyclic finite-automata (van Benthem 1986); first-order logic enriched by all quantifiers of the form ''divisible by n'' corresponds to the class of regular languages (Mostowski 1998); and that proportional quantifiers, like ''most'', can be recognized by push-down automata (van Benthem 1986). Those results suggest that the verification of monadic quantifiers in natural language should be relatively easy.…”

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confidence: 99%

Computational complexity of polyadic lifts of generalized quantifiers in natural language

2010

Linguist and Philos

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 multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide an insight into branching operation yielding intractable natural language multi-quantifier expressions. 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 of revising the Strong Meaning Hypothesis with complexity aspects to better account for meaning shifts in the domain of multi-quantifier sentences. The paper not only contributes to the field of formal semantics but also illustrates how the tools of computational complexity theory might be successfully used in linguistics and philosophy with an eye towards cognitive science.