MOST intelligent people are accurate and SOME fast people are intelligent.: Intelligence,working memory,and semantic processing of quantifiers from a computational perspective

The paper explores the relationship between intelligence and the semantic processing of natural language quantifiers. The first study revealed that intelligence is positively associated with the subjects' performance when solving a picture verification task with one of the four types of sentences: Aristotelian (e.g. ‘All cars are red’), parity (e.g. ‘An even number of cars are red’), numerical (e.g. ‘More than five cars are red’), and proportional (‘More than half of the cars are red’). The strongest relationship was observed between the cognitive ability and the accuracy of proportional sentences, in accordance with the computational theory which predicts the highest engagement of working memory (WM) within the group of proportional quantifiers. Moreover, individuals with higher intelligence reacted faster, but this was observed only in case of quantifiers with low complexity. Exploring further, in the second study we found that WM and intelligence were both significant predictors of subjects' score on proportional sentences. In the third study, we examined the relationships between quantifiers, intelligence, short-term memory (STM), and executive control function. STM was correlated with all types of quantifiers that need counting and keeping track of elements (parity, numerical, and proportional). Only proportional quantifiers were associated with cognitive control. The obtained results are discussed within the computational paradigm of language processing.     

Quantifier comprehension in corticobasal degeneration

In this study, we investigated patients with focal neurodegenerative diseases to examine a formal linguistic distinction between classes of generalized quantifiers, like "some X" and "less than half of X." Our model of quantifier comprehension proposes that number knowledge is required to understand both first-order and higher-order quantifiers. The present results demonstrate that corticobasal degeneration (CBD) patients, who have number knowledge impairments but little evidence for a deficit understanding other aspects of language, are impaired in their comprehension of quantifiers relative to healthy seniors, Alzheimer's disease (AD) and frontotemporal dementia (FTD) patients [F(3,77)=4.98; p<.005]. Moreover, our model attempts to honor a distinction in complexity between classes of quantifiers such that working memory is required to comprehend higher-order quantifiers. Our results support this distinction by demonstrating that FTD and AD patients, who have working memory limitations, have greater difficulty understanding higher-order quantifiers relative to first-order quantifiers [F(1,77)=124.29; p<.001]. An important implication of these findings is that the meaning of generalized quantifiers appears to involve two dissociable components, number knowledge and working memory, which are supported by distinct brain regions.     

Theory discovery from data with mixed quantifiers

Convergent realists desire scientific methods that converge reliably to informative, true theories over a wide range of theoretical possibilities. Much attention has been paid to the problem of induction from quantifier-free data. In this paper, we employ the techniques of formal learning theory and model theory to explore the reliable inference of theories from data containing alternating quantifiers. We obtain a hierarchy of inductive problems depending on the quantifier prefix complexity of the formulas that constitute the data, and we provide bounds relating the quantifier prefix complexity of the data to the quantifier prefix complexity of the theories that can be reliably inferred from such data without background knowledge. We also examine the question whether there are theories with mixed quantifiers that can be reliably inferred with closed, universal formulas in the data, but not without.     

Plans and Semantics in Human Processing of Language

The analogy between humans and computers as language processors has previously been exploited primarily with respect to the parsing or analysis phase of processing, as opposed to a synthesis phrase. Here we pursue the analogy on the synthesis side by positing cognitive algorithms that correspond to target language code generated by a compiler. We consider the computational resource demands of these cognitive algorithms and compare them to what is required to carry out syntactic and semantic processing. It is argued that cognitive demands are responsible for certain empirical results in developmental psycholinguistics that have previously been attributed to syntactic complexity. The analysis suggests new empirical studies whose results, in turn, provide support for the analysis.     

Number sense and quantifier interpretation

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

On the Expressive Power of Monotone Natural Language Quantifiers over Finite Models

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties – here called CE quantifiers – one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle.     

Mereological Composition and Plural Quantifier Semantics

Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings clarity to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial.     

Commodious Axiomatization of Quantifiers in Multiple-Valued Logic

We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers.     

Quantifiers and Congruence Closure

We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1).     

The logic in language: How all quantifiers are alike,but each quantifier is different

Quantifier words like each, every, all and three are among the most abstract words in language. Unlike nouns, verbs and adjectives, the meanings of quantifiers are not related to a referent out in the world. Rather, quantifiers specify what relationships hold between the sets of entities, events and properties denoted by other words. When two quantifiers are in the same clause, they create a systematic ambiguity. “Every kid climbed a tree” could mean that there was only one tree, climbed by all, or many different trees, one per climbing kid. In the present study, participants chose a picture to indicate their preferred reading of different ambiguous sentences – those containing every, as well as the other three quantifiers. In Experiment 1, we found large systematic differences in preference, depending on the quantifier word. In Experiment 2, we then manipulated the choice of a particular reading of one sentence, and tested how this affected participants’ reading preference on a subsequent target sentence. We found a priming effect for all quantifiers, but only when the prime and target sentences contained the same quantifier. For example, all-a sentences prime other all-a sentences, while each-a primes each-a, but sentences with each do not prime sentences with all or vice versa. In Experiment 3, we ask whether the lack of priming across quantifiers could be due to the two sentences sharing one fewer word. We find that changing the verb between the prime and target sentence does not reduce the priming effect. In Experiment 4, we discover one case where there is priming across quantifiers – when one number (e.g. three) is in the prime, and a different one (e.g. four) is in the target. We discuss how these findings relate to linguistic theories of quantifier meaning and what they tell us about the division of labor between conceptual content and combinatorial semantics, as well as the mental representations of quantification and of the abstract logical structure of language.     

“At least one” problem with “some” formal reasoning paradigms

In formal reasoning, the quantifier "some" means "at least one and possibly all." In contrast, reasoners often pragmatically interpret "some" to mean "some, but not all" on both immediate-inference and Euler circle tasks. It is still unclear whether pragmatic interpretations can explain the high rates of errors normally observed on syllogistic reasoning tasks. To address this issue, we presented participants (reasoners) in the present experiments either standard quantifiers or clarified quantifiers designed to precisely articulate the quantifiers' logical interpretations. In Experiment 1, reasoners made significantly more logical responses and significantly fewer pragmatic responses on an immediate-inference task when presented with logically clarified as opposed to standard quantifiers. In Experiment 2, this finding was extended to a variant of the immediate-inference task in which reasoners were asked to deduce what followed from premises they were to assume to be false. In Experiment 3, we used a syllogistic reasoning task and observed that logically clarified premises reduced pragmatic and increased logical responses relative to standard ones, providing strong evidence that pragmatic responses can explain some aspects of the errors made in the syllogistic reasoning task. These findings suggest that standard quantifiers should be replaced with logically clarified quantifiers in teaching and in future research.     

Curiosity‐based learning in infants: a neurocomputational approach

Infants are curious learners who drive their own cognitive development by imposing structure on their learning environment as they explore. Understanding the mechanisms by which infants structure their own learning is therefore critical to our understanding of development. Here we propose an explicit mechanism for intrinsically motivated information selection that maximizes learning. We first present a neurocomputational model of infant visual category learning, capturing existing empirical data on the role of environmental complexity on learning. Next we “set the model free”, allowing it to select its own stimuli based on a formalization of curiosity and three alternative selection mechanisms. We demonstrate that maximal learning emerges when the model is able to maximize stimulus novelty relative to its internal states, depending on the interaction across learning between the structure of the environment and the plasticity in the learner itself. We discuss the implications of this new curiosity mechanism for both existing computational models of reinforcement learning and for our understanding of this fundamental mechanism in early development.     

A Two Dimensional Tense-modal Sortal Logic

We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.     

Evaluating evidence of psychological adaptation: how do we know one when we see one?

Evolutionary psychologists argue that human nature contains many discrete psychological adaptations. Each adaptation is theorized to have been functional in humans' ancestral past, and empirical evidence that an attribute is an adaptation can come from showing it possesses complexity, efficiency, universality, and other features of special design. In this article, we present a tutorial review of the evidentiary forms that evolutionary psychologists commonly use to document the existence of human adaptations. We also present a heuristic framework for integrating and evaluating cross-disciplinary evidence of adaptation. Pregnancy sickness, incest avoidance, men's desires for multiple sex partners, and an easily learned fear of snakes are evaluated as possible human adaptations using this framework. We conclude that future research and teaching in evolutionary psychology would benefit from more fully utilizing cross-disciplinary frameworks to evaluate evidence of human adaptation.     

How much is ‘quite a bit’? Mapping between numerical values and vague quantifiers

Vague quantifiers, terms like “quite a bit” and “hardly ever”, are often used in the response scales of psychology and social science questionnaires to measure the frequency of certain behaviours. However, responses to such questions arc confounded because people differ in their interpretations of vague quantifiers. We propose that people interpret vague quantifiers by constructing a notion of how most people behave. Examining a critical topic for media researchers–estimating the amount of television walched–we conducted two split-ballot experiments in national surveys. Our first study (n = 1028) demonstrates that the amount people think other people watch varies according to how much television they watch themselves and the behaviour of their social group. Our second experiment (n = 1106) extends this result to the interpretation of vague quantifiers. These findings shed light on the psychological processes involved when interpreting vague quantifiers, and bring into question the validity of many survey results.     

When being included is being excluded: A note on complement set focus and the inclusion relation

Some negative quantifiers lead to pronominal reference patterns that are different from those obtained with positive quantifiers (Moxey & Sanford, 1993). This has been interpreted as meaning that the negatives give rise to a focus on the complement set (Moxey & Sanford, 1987); so, given few of the children enjoyed the trip, focus is on those who did not enjoy the trip. To date, this interpretation has depended on subjective judgments as to which set an anaphoric plural pronoun is referring to, allowing other interpretations of the data to be given by discourse semanticists. In two studies, we use the attachment patterns associated with the expression including, thereby circumventing the judgment problem. We show that a case like not many people enjoyed the race, including John leads to a representation in which John maps into the set of individuals who did not enjoy the race. We test and support the earlier claim that complement set focus is driven by denials associated with some negative quantifiers.     

Monotone Quantifiers Emerge via Iterated Learning

Natural languages exhibit many semantic universals, that is, properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal, the monotonicity universal. While the existing work has shown that quantifiers satisfying the monotonicity universal are easier to learn, we provide a more complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, we show that quantifiers satisfy the monotonicity universal evolve reliably in an iterated learning paradigm with neural networks as agents.     

The Skolem-Löwenheim theorem in toposes

The topos theory gives tools for unified proofs of theorems for model theory for various semantics and logics. We introduce the notion of power and the notion of generalized quantifier in topos and we formulate sufficient condition for such quantifiers in order that they fulfil downward Skolem-Löwenheim theorem when added to the language. In the next paper, in print, we will show that this sufficient condition is fulfilled in a vast class of Grothendieck toposes for the general and the existential quantifiers.     

Effects of syllable structure in aphasic errors: implications for a new model of speech production

Current models of word production assume that words are stored as linear sequences of phonemes which are structured into syllables only at the moment of production. This is because syllable structure is always recoverable from the sequence of phonemes. In contrast, we present theoretical and empirical evidence that syllable structure is lexically represented. Storing syllable structure would have the advantage of making representations more stable and resistant to damage. On the other hand, re-syllabifications affect only a minimal part of phonological representations and occur only in some languages and depending on speech register. Evidence for these claims comes from analyses of aphasic errors which not only respect phonotactic constraints, but also avoid transformations which move the syllabic structure of the word further away from the original structure, even when equating for segmental complexity. This is true across tasks, types of errors, and, crucially, types of patients. The same syllabic effects are shown by apraxic patients and by phonological patients who have more central difficulties in retrieving phonological representations. If syllable structure was only computed after phoneme retrieval, it would have no way to influence the errors of phonological patients. Our results have implications for psycholinguistic and computational models of language as well as for clinical and educational practices.     

Output‐sensitive complexity of multiobjective combinatorial optimization

We study output‐sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output‐sensitive, that is, its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of multiobjective combinatorial optimization problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions.