To do or not to do? A cognitive consistency model for drawing conclusions from conditional instructions and advice

This paper investigates a cognitive consistency model of the directionality of conditional instructions and advice that use probability expressions to express uncertainty about the antecedent p. The proposed model combines world knowledge (conveyed by causal direction) with linguistic information (conveyed by polarity and negation), and predicts whether the complex sentence antecedent has a positive or negative directionality, which in turn predicts whether a positive or negative conclusion q will be drawn. The first experiment uses Do q if p conditionals to show that given a consequent q participants complete antecedents p with a probability expression in line with expected sentence directionality. The second experiment uses If p then do q conditionals to show similar effects in a reverse direction. A third experiment uses If p then do q conditionals to show that participants draw conclusions predicted by the cognitive consistency model but not by a decision-theoretic approach to reasoning.     

Developmental changes in conditional reasoning: Linguistic or logical?

This study investigated reasoning with abstract conditional sentences as a function of age. Subjects from third-grade to eleventh-grade were required to evaluate the conclusion of several conditional arguments. The results confirmed the previously established finding that performance improves with age, particularly between 11 and 15 years. This finding could be interpreted to indicate that individuals become more logical as they get older. However, another possible interpretation is that the meaning of a conditional sentence like pthenq for naive Ss may not always be given by the truth function pq true, $\text{p}\text{q}$ false, $\text{p}\text{q}$ true, and $\text{p}\text{q}$ true. Further analysis suggested that at 9 years individuals treat the connective in the sentence, ifpthenq, as if it were either a conjunctive or a biconditional, that the conjunctive meaning disappears with increasing age and after 13 years is gradually superceded by the conditional.     

Piaget's logical formalism for formal operations: An interpretation in context

Two interpretations of the equations used by B. Inhelder and J. Piaget in The growth of logical thinking from childhood to adolescence (London: Routledge & Kegan Paul, 1958) are discussed, with implication as the central example. The expression (p ? q) (p implies q) is said to be equal to $\text{(p · q)}\text{V}\text{(}\text{p}\text{· q)}\text{V}\text{(}\text{p}\text{·}\text{q}\text{)}$ (i.e.,p and q, or not p and q, or neither p nor q). According to one, (p ? q) asserts the existence of each case mentioned. According to the other, (p ? q) only asserts that current knowledge allows the possibility of each of the cases. Neither interpretation makes sense of all the relevant passages. Both can be combined in a consistent interpretation when attention is paid to the functional context of the subject's use of logical operations in this book: the “operations” describe the knowledge states which the subject can differentiate and relate, on his way to solving Inhelder's tasks. The logical notation used to represent these states is not a representational format attributed to the subject and manipulated by his cognitive processes, but part of a structuralist account of the subject's reasoning capacities.     

Nontransitive measurable utility

A new theory of preferences under risk is presented that does not use the transitivity and independence axioms of the von Neumann-Morgenstern linear utility theory. Utilities in the new theory are unique up to a similarity transformation (ratio scale measurement). They key to this generalization of the traditional linear theory lies in its representation of binary preferences by a bivariate rather than univariate real valued function. Linear theory obtains a linear function u on a set P of probability measures for which u(p) > u(q) if and only if p is preferred to q. The new theory obtains a skew-symmetric bilinear function φ on P × P for which φ(p, q) > 0 if and only if p is preferred to q. Continuity, dominance, and symmetry axioms are shown to be necessary and sufficient for the new representation.     

Bootstrap Contraction

We can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious candidate that can be the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction.     

Comparing the meanings of “if” and “all”

In this study, we compared the everyday meanings of conditionals (“if p then q”) and universally quantified statements (“all p are q”) when applied to sets of elements. The interpretation of conditionals was predicted to be directly related to the conditional probability, such that P(“if p then q”) = P(q|p). Quantified statements were assumed to have two interpretations. According to an instance-focused interpretation, quantified statements are equivalent to conditionals, such that P(“all p are q”) = P(q|p). According to a set-focused interpretation, “all p are q” is true if and only if every instance in set p is an instance of q, so that the statement would be accepted when P(q|p) = 1 and rejected when this probability was below 1. We predicted an instance-focused interpretation of “all” when the relation between p and q expressed a general law for an infinite set of elements. A set-focused interpretation of “all” was predicted when the relation between p and q expressed a coincidence among the elements of a finite set. Participants were given short context stories providing information about the frequency of co-occurrence of cases of p, q, not-p, and not-q in a population. They were then asked to estimate the probability that a statement (conditional or quantified) would be true for a random sample taken from that population. The probability estimates for conditionals were in accordance with an instance-focused interpretation, whereas the estimates for quantified statements showed features of a set-focused interpretation. The type of the relation between p and q had no effect on this outcome.     

Grammatical Aspect in Early Child Mandarin: Evidence from a Preferential Looking Experiment

The study assessed 30-month-old Mandarin-speaking children’s awareness of aspectual distinctions involving the perfective marker le and the imperfective marker zhe in a preferential looking experiment. In the experiment, we presented our child subjects with a choice between two video clips (one depicting a closed event and the other depicting an on-going event), in the presence of an auditory stimulus (either the le sentence, the zhe sentence or the control sentence without any aspect marker). Children’s looking behavior in the task was recorded and analyzed. The results revealed 30-month-old children’s emerging sensitivity to the aspectual contrast between le and zhe. This was manifest by an increase in looking to the closed event when hearing the le sentence and an increase in looking to the on-going event when hearing the zhe sentence. The absence of le or zhe in the control sentence did not result in any increase or decrease in looking to either event. We also found that the effect of le on children’s looking behavior was immediate whereas the effect of zhe was late. We attributed this difference to the facilitative role of le in children’s sentence processing as well as their preference for the event boundary. The results lend support to the continuity view that functional morphemes like aspect markers are available to children early in language development.     

Reasoning as we read: Establishing the probability of causal conditionals

Indicative conditionals of the form if p then q (e.g., if student tuition fees rise, then applications for university places will fall) invite consideration of a hypothetical event (e.g., tuition fees rising) and of one of its possible consequences (e.g., applications falling). Since a rise in tuition fees is an uncertain event with equally uncertain consequences, a reader may believe the statement to a greater or lesser extent. As a conditional is read, the earliest point at which this probabilistic evaluation can take place is as the consequent clause is wrapped up (e.g., as the critical word fall is read in the example above). Wrap-up processing occurs at the end of the clause, as it is evaluated and integrated into the evolving discourse representation. Five sources of probability may plausibly influence the evaluation of a conditional as it is wrapped up; these are P(p), P(q), P(pq), P(q|p), and P(not-p or q). A total of 128 conditionals were constructed, with these probabilities calculated for each item in a pretest. The conditionals were then embedded in vignettes and read by 36 participants on a word-by-word basis. Using linear mixed-effects modeling, we found that wrap-up reading times were predicted by pretest ratings of P(p) and P(q|p). There was no influence of P(q), P(pq), or P(not-p or q) on wrap-up reading times. Our findings are consistent with the suppositional theory of conditionals proposed by Evans and Over (2004) but do not support the mental-models theory advanced by Johnson-Laird and Byrne (2002).     

The role of overt activity in children's sentence production

Nursery schooler's abilityto associate pairs of toys was assessed under four experimental conditions: (1) control, (2) S manipulating the toys, (3) S generating a sentence, and (4) S generating a sentence while manipulating the toys. All three S-involvement conditions produced significantly better recognition performance than the control but contrary to initial predictions, the difference between the sentence-only and sentence-plus-manipulation conditions was not significant. In contrast to previous research, Ss in the sentence-only conditions had little difficulty producing sentences when asked. Of interest was the finding that the quality of sentence production was poorer in the sentence-plus-manipulation condition than in the sentence-only condition. Results are discussed in terms of the possible “conflict” produced when the child is required to engage in more than one overt activity simultaneously.     

Connectives and narrative text: The role of continuity

Connectives are text devices that signal the relation between adjacent sentences. Recently there has been a surge of research interest in the role played by connectives in on-line processing. The present research tested the hypothesis that connectives will impact on-line processing to the extent that they signal a text event that represents a departure from the continuity of the events stated in the text. In Experiment 1, participants generated sentences to follow a stimulus sentence. An additive, causal, or adversative connective (or no connective) was provided to serve as the first word of the participants’ sentence. Results showed that sentences generated in response to additive or causal connectives depicted text events that were continuous with the stimulus text. In contrast, sentences generated in response to adversative connectives depicted discontinuous text events. In Experiments 2 and 3, participants read coherent sentence pairs containing inappropriately placed additive, causal, or adversative connectives. Support for the continuity hypothesis was found when it was shown that adversative connectives led to the greatest amount of processing disruption, as measured by longer reading time on the postconnective sentence (Experiment 2) and lower ratings of coherence (Experiment 3). Future research in this area is discussed.     

Aphasic adults' understanding of complex adverbial sentences

Twelve aphasics with relatively preserved auditory comprehension were tested for their understanding of four adverbial sentence types expressing the temporal order of events. The relative effects of order of mention, adverbial choice, and adverbial clause placement on subjects' comprehension were investigated. Only adverbial choice was significant with aphasics producing more errors of temporal order on after than before sentences. Subjects' error patterns were not similar to those of children acquiring language. The results are discussed with respect to the theory of lexical marking and the regression hypothesis.     

Musical metaphors: Evidence for a spatial grounding of non-literal sentences describing auditory events

This study investigated whether the spatial terms high and low, when used in sentence contexts implying a non-literal interpretation, trigger similar spatial associations as would have been expected from the literal meaning of the words. In three experiments, participants read sentences describing either a high or a low auditory event (e.g., The soprano sings a high aria vs. The pianist plays a low note). In all Experiments, participants were asked to judge (yes/no) whether the sentences were meaningful by means of up/down (Experiments 1 and 2) or left/right (Experiment 3) key press responses. Contrary to previous studies reporting that metaphorical language understanding differs from literal language understanding with regard to simulation effects, the results show compatibility effects between sentence implied pitch height and response location. The results are in line with grounded models of language comprehension proposing that sensory motor experiences are being elicited when processing literal as well as non-literal sentences.     

Grammatical aspect and event recognition in children’s online sentence comprehension

This study investigated whether or not the temporal information encoded in aspectual morphemes can be used immediately by young children to facilitate event recognition during online sentence comprehension. We focused on the contrast between two grammatical aspectual morphemes in Mandarin Chinese, the perfective morpheme –le and the (imperfective) durative morpheme –zhe. The perfective morpheme –le is often used to indicate that an event has been completed, whereas the durative morpheme –zhe indicates that an event is still in progress or continuing. We were interested to see whether young children are able to use the temporal reference encoded in the two aspectual morphemes (i.e., completed versus ongoing) as rapidly as adults to facilitate event recognition during online sentence comprehension. Using the visual world eye-tracking paradigm, we tested 34 Mandarin-speaking adults and 99 Mandarin-speaking children (35 three-year-olds, 32 four-year-olds and 32 five-year-olds). On each trial, participants were presented with spoken sentences containing either of the two aspectual morphemes while viewing a visual image containing two pictures, one representing a completed event and one representing an ongoing event. Participants’ eye movements were recorded from the onset of the spoken sentences. The results show that both the adults and the three age groups of children exhibited a facilitatory effect trigged by the aspectual morpheme: hearing the perfective morpheme –le triggered more eye movements to the completed event area, whereas hearing the durative morpheme –zhe triggered more eye movements to the ongoing event area. This effect occurred immediately after the onset of the aspectual morpheme, both for the adults and the three groups of children. This is evidence that young children are able to use the temporal information encoded in aspectual morphemes as rapidly as adults to facilitate event recognition. Children’s eye movement patterns reflect a rapid mapping of grammatical aspect onto the temporal structures of events depicted in the visual scene.     

A successive-conditionalization approach to disjunctive and syllogistic reasoning

With p and q each standing for a familiar event, a disjunctive statement, “either p or q”, seems quite different from its material conditional, “if not p then q”. The notions of sufficiency and necessity seem specific to conditional statements. It is surprising, however, to find that perceived sufficiency and necessity affect disjunctive reasoning in the way they affect conditional reasoning. With B and C each standing for a category name, a universal statement, “all B are C”, seems stronger than its logically equivalent conditional statement, “if B then C”. However, the effects of perceived sufficiency or necessity were found to be as pronounced in conditional reasoning as in syllogistic reasoning. Furthermore, two experiments also showed that (a) MP (modus ponens)-comparable disjunctive reasoning was as difficult as MT (modus tollens)-comparable disjunctive reasoning, and that (b) MT-comparable syllogisms were easier to solve than MT problems in conditional reasoning.     

Is there a memory for sentences?

A critical discussion of the model of sentence memory which enjoyed greatest popularity in the psycholinguistic research of the sixties, namely the model based on the deep-structure-plus-tag hypothesis of sentence memory, is presented together with the results of an experiment on prompted recall for sentences with various intervals after presentation and with two types of instructions. This experiment contributed to show that immediate memory for sentences can be affected by appropriate instructions, and that after a short time after presentation only the main semantic information of the sentences is recalled. An alternative model is presented, based on the notion of storage of the meaningful elements of the sentences in a rather abstract form, and of recall as a reconstructive process to produce new sentences. The results of two new experiments on sentence memory, the first a free and prompted recall experiment with children, the second a recognition memory study with adolescents, are then presented and discussed in relation to the model.     

Matrix differential calculus with applications to simple,hadamard, and kronecker products

Several definitions are in use for the derivative of an m × p matrix function F(X) with respect to its n × q matrix argument X. We argue that only one of these definitions is a viable one, and that to study smooth maps from the space of n × q matrices to the space of m × p matrices it is often more convenient to study the map from nq-space to mp-space. Also, several procedures exist for a calculus of functions of matrices. It is argued that the procedure based on differentials is superior to other methods of differentiation, and leads inter alia to a satisfactory chain rule for matrix functions.     

汉语句子可继续性对句子理解加工的即时影响

通过操纵动词与后接词的关系,来产生搭配异常并控制句子的可继续性,研究汉语词汇信息在句子加工中的即时作用。实验一利用跨通道技术,发现动一名词搭配异常对目标名词的加工有即时影响,形容词条件下可继续性对目标形容词的加工有即时影响;实验二采用眼动技术,发现名词条件和形容词条件下可继续性均有显著的即时影响。结果显示,语义等多种词汇信息被通达后立即共同参与了汉语句子加工。     

The Syllogistic with Unity

We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.     

Do we map remembrances to the left/back and expectations to the right/front of a mental timeline? Space–time congruency effects with retrospective and prospective verbs

Recent experimental studies have shown that people code time in terms of a mental timeline which typically runs from left to right or from back to front. Determining the cognitive function of this mental timeline for language processing, however, is still an unsettled issue. Whereas the studies of Ulrich and Maienborn (2010) and Ulrich et al. (2012) argue against an automatic activation of the mental timeline for the interpretation of tense and temporal adverbials at sentence level, Sell and Kaschak (2011) observe an automatic activation for the processing of past- and future-related sentences in small stories. The present paper reports the results of three experiments which examine the processing of sentences with retrospective and prospective verbs (e.g., to remember, to regret vs. to expect, to announce) in present tense, which locate a second, embedded event in the past or the future. When temporal information was task-relevant, a space–time congruency effect emerged (Experiment 1). This suggests that the mental timeline is not only linked to overtly deictic linguistic material but may also be construed in a more intricate way through the compositional construction of sentence meaning. The congruency effect disappeared, however, when temporal information was task-irrelevant (Experiments 2 and 3), suggesting that the mental timeline is not functionally involved in the cognitive processing of these especially demanding two-event sentences. The results of the present study support the conclusion that the relevant factor driving an automatic activation of the mental timeline is not the number of linguistically expressed events, but might rather be the number of sentential units.     

Syntactic structure building in the anterior temporal lobe during natural story listening

The neural basis of syntax is a matter of substantial debate. In particular, the inferior frontal gyrus (IFG), or Broca’s area, has been prominently linked to syntactic processing, but the anterior temporal lobe has been reported to be activated instead of IFG when manipulating the presence of syntactic structure. These findings are difficult to reconcile because they rely on different laboratory tasks which tap into distinct computations, and may only indirectly relate to natural sentence processing. Here we assessed neural correlates of syntactic structure building in natural language comprehension, free from artificial task demands. Subjects passively listened to Alice in Wonderland during functional magnetic resonance imaging and we correlated brain activity with a word-by-word measure of the amount syntactic structure analyzed. Syntactic structure building correlated with activity in the left anterior temporal lobe, but there was no evidence for a correlation between syntactic structure building and activity in inferior frontal areas. Our results suggest that the anterior temporal lobe computes syntactic structure under natural conditions.