Jakub Szymanik

Comprehension of simple quantifiers: empirical evaluation of a computational model.

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.

Intentional Communication: Computationally Easy or Difficult?

Human intentional communication is marked by its flexibility and context sensitivity. Hypothesized brain mechanisms can provide convincing and complete explanations of the human capacity for intentional communication only insofar as they can match the computational power required for displaying that capacity. It is thus of importance for cognitive neuroscience to know how computationally complex intentional communication actually is. Though the subject of considerable debate, the computational complexity of communication remains so far unknown. In this paper we defend the position that the computational complexity of communication is not a constant, as some views of communication seem to hold, but rather a function of situational factors. We present a methodology for studying and characterizing the computational complexity of communication under different situational constraints. We illustrate our methodology for a model of the problems solved by receivers and senders during a communicative exchange. This approach opens the way to a principled identification of putative model parameters that control cognitive processes supporting intentional communication.

Logic and Complexity in Cognitive Science

This chapter surveys the use of logic and computational complexity theory in cognitive science. We emphasize in particular the role played by logic in bridging the gaps between Marr’s three levels: representation theorems for non-monotonic logics resolve algorithmic/implementation debates, while complexity theory probes the relationship between computational task analysis and algorithms. We argue that the computational perspective allows feedback from empirical results to guide the development of increasingly subtle computational models. We defend this perspective via a survey of the role of logic in several classic problems in cognitive science (the Wason selection task, the frame problem, the connectionism/symbolic systems debate) before looking in more detail at case studies involving quantifier processing and social cognition. In these examples, models developed by Johan van Benthem have been supplemented with complexity analysis to drive successful programs of empirical research.

A computational approach to quantifiers as an explanation for some language impairments in schizophrenia

UNLABELLED We compared the processing of natural language quantifiers in a group of patients with schizophrenia and a healthy control group. In both groups, the difficulty of the quantifiers was consistent with computational predictions, and patients with schizophrenia took more time to solve the problems. However, they were significantly less accurate only with proportional quantifiers, like more than half. This can be explained by noting that, according to the complexity perspective, only proportional quantifiers require working memory engagement. LEARNING OUTCOMES (1) Working memory deficits can be a source of language disorders in schizophrenia. (2) Processing of proportional quantifiers, like more than half or less than half involves working memory. (3) Patients with schizophrenia are less accurate only with proportional quantifiers, like more than half. (4) This result support the computational model of quantifiers processing.

A Remark on Collective Quantification

We consider collective quantification in natural language. For many years the common strategy in formalizing collective quantification has been to define the meanings of collective determiners, quantifying over collections, using certain type-shifting operations. These type-shifting operations, i.e., lifts, define the collective interpretations of determiners systematically from the standard meanings of quantifiers. All the lifts considered in the literature turn out to be definable in second-order logic. We argue that second-order definable quantifiers are probably not expressive enough to formalize all collective quantification in natural language.

Improving methodology of quantifier comprehension experiments

Recently, research devoted to computational modeling of uantifier comprehension has been extensively published in this ournal.McMillan, Clark,Moore,Devita, andGrossman (2005)using euroimaging methods examined the pattern of neuroanatomical ecruitment while subjects were judging the truth-value of stateents containing natural language quantifiers. The authors were onsidering two standard types of quantifiers: first-order (e.g., all”, “some”, “at least 3”) and higher-order quantifiers (e.g., “more han half”, “an even number of”). They presented the data showing hat all quantifiers recruit the right inferior parietal cortex, which s associated with numerosity, but only higher-order quantifiers ecruit the prefrontal cortex, which is associated with executive esources, like working memory. In the latest paper Troiani, Peelle, lark, and Grossman (2009) assessed quantifier comprehension in atients with corticobasal degeneration (CBD) and healthy subects. They compared numerical quantifiers, like “at least 3”, which equire magnitude processing, and logical quantifiers, like “some”, hich can be understood using a simple form of perceptual logic. heir findings are consistent with the claim that numerical quantier comprehension depends on a lateral parietal–dorsolateral refrontal network, but logical quantifier comprehension epends instead on a rostromedial prefrontal–posterior cingulate etwork. According to the authors of the mentioned studies, their results erify a particular computational model of natural language quanifier comprehension posited by linguists and logicians (see e.g., an Benthem, 1986). One of the authors of the present coment has challenged this statement by invoking differences – issed in (McMillan et al., 2005) – between logical (expressibil-

Quantifiers and working memory

The paper presents a study examining the role of working memory in quantifier verification. We created situations similar to the span task to compare numerical quantifiers of low and high rank, parity quantifiers and proportional quantifiers. The results enrich and support the data obtained previously in [1,2,3] and predictions drawn from a computational model [4,5].

A note on a generalization of the Muddy Children puzzle

We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifiers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specific informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety).

Working Memory Mechanism in Proportional Quantifier Verification

The paper explores the cognitive mechanisms involved in the verification of sentences with proportional quantifiers (e.g. “More than half of the dots are blue”). The first study shows that the verification of proportional sentences is more demanding than the verification of sentences such as: “There are seven blue and eight yellow dots”. The second study reveals that both types of sentences are correlated with memory storage, however, only proportional sentences are associated with the cognitive control. This result suggests that the cognitive mechanism underlying the verification of proportional quantifiers is crucially related to the integration process, in which an individual has to compare in memory the cardinalities of two sets. In the third study we find that the numerical distance between two cardinalities that must be compared significantly influences the verification time and accuracy. The results of our studies are discussed in the broader context of processing complex sentences.

On the Identification of Quantifiers' Witness Sets: A Study of Multi-quantifier Sentences

Natural language sentences that talk about two or more sets of entities can be assigned various readings. The ones in which the sets are independent of one another are particularly challenging from the formal point of view. In this paper we will call them ‘Independent Set (IS) readings’. Cumulative and collective readings are paradigmatic examples of IS readings. Most approaches aiming at representing the meaning of IS readings implement some kind of maximality conditions on the witness sets involved. Two kinds of maximization have been proposed in the literature: ‘Local’ and ‘Global’ maximization. In this paper, we present an online questionnaire whose results appear to support Local maximization. The latter seems to capture the proper interplay between the semantics and the pragmatics of multi-quantifier sentences, provided that witness sets are selected on pragmatic grounds.