Discrete tense logic with infinitary inference rules and systematic frame constants: A Hilbert-style axiomatization

The paper deals with the problem of axiomatizing a system 1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 (immediate successor) and -1 (immediate predecessor). 1 is like the Segerberg-Sundholm system W1 in working with so-called infinitary inference rules; on the other hand, it differs from W1 with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a now operator, and, most importantly, with respect to (iii) the presence in of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of 1.The present contribution reports research done under the auspices of the Swedish Council for Research in the Humanities and the Social Sciences (HSFR), project On the Legal Concepts of Rights and Duties: an Analysis Based on Deontic and Causal Conditional Logic. I wish to thank the anonymous referee for his/her extremely patient and accurate revision work, and Krister Segerberg for his helpful suggestions.     

Formal operations and postformal reasoning: A replication

The relationship between formal operations and postformal reasoning was examined by using the Shayer (1978) chemicals problem to assess formal operations and the Commons, et al. (1982) four-story problem to measure postformal reasoning. The subjects were 35 undergraduate social science and humanities students. None of the subjects who were classified as concrete operational or transitional on the chemicals task showed postformal reasoning. The hypothesis that full format operations are a necessary condition of post-formal reasoning and the expectation that subjects showing full formal operations are more likely than others to exhibit postformal reasoning was not supported.     

Abductive inference in defeasible reasoning: a model for research programmes

Abduction is regarded as the inference process that goes from observations to explanations within a more general context or theoretical framework. There are good characterizations of abduction of surprising observations in monotonic theories. Also, in normal logic programs there are a tight relation among SLDNF and the abduction of negative literals. However, a problem that faces abduction is the explanation of anomalous observations, i.e., observations that are contradictory with respect to the current theory. For this reason, in this work we will consider the problem of embedding abduction of surprising and anomalous observations in defeasible (nonmonotonic) theories. We discuss some issues arising the pragmatic acceptance of abductive inferences in defeasible theories, and how to accommodate anomalous observations and characterize all the possible outcomes that a defeasible theory may face when confronted with new evidence. We explore the use of partial structures approach as a semantic foundation for our system. Finally, we discuss an application of our system as a formal device for representing the methodology of scientific research programmes. In this representation, a programme is regarded as a defeasible theory that draws predictions. When confronted with surprising or anomalous observations, the programme protects itself by means of heuristic procedures, which are represented in our system as abductive inference procedures.     

Students' complex problem-solving abilities: Their structure and relations to reasoning ability and educational success

Complex Problem Solving (CPS) is considered to be a promising candidate for capturing higher order thinking skills that are emphasized in new educational curricula but are not adequately measured by traditional intelligence tests. However, little is known about its psychometric structure and its exact relation to intelligence and educational success—especially in student populations. This study is among the first to use a large and representative sample of secondary school students (N = 563) to examine different measurement models of CPS—that conceptualize the construct as either faceted or hierarchical—and their implications for the construct's validity. Results showed that no matter which way it was conceptualized, CPS was substantially related to reasoning and to different indicators of educational success. Controlling for reasoning within a joint hierarchical measurement model, however, revealed that the impressive external validity was largely attributable to the variance that CPS shares with reasoning, suggesting that CPS has only negligible incremental validity over and above traditional intelligence scales. On the basis of these results, the value of assessing CPS within the educational context is discussed.     

Higher-order structure and relational reasoning: contrasting analogical and thematic relations

A popular explanation of younger children's success in analogy tasks is that lower-level associative reasoning strategies are used. Younger children are said to have a primarily associative understanding of analogy, with the ability to coordinate sets of relations largely emerging later in development (Goldman, Pellegrino, Parseghian, & Sallis, 1982; Sternberg & Nigro, 1980). One way of testing the associative claim is to pit young children's emergent analogical abilities against thematic (associative) relations, which are known to play an important role in the knowledge structures of young children. The present experiments presented 4-, 5- and 9-year-old children with a:b::c:d analogies in a picture choice format, offering a choice between Analogy and Thematic responses. Only the Analogy responses were correct in terms of the higher-order structure of the analogies. The results showed that the Analogy responses were consistently preferred to the Thematic responses by children of all ages. It is concluded that analogy is an important building block for learning from an early age.     

Melting chocolate and melting snowmen: analogical reasoning and causal relations

Children's performance in the classical a:b::c:d analogy task is traditionally very poor prior to the Piagetian stage of formal operations. The interpretation has been that the ability to reason about higher-order relations (the relations between the a:b and c:d parts of the analogy) is late-developing. However, an alternative possibility is that the relations used to date in the analogies are too difficult for younger children. Two experiments presented children aged 3, 4 and 6 years with a:b::c:d analogies which were based on relations of physical causality such as melting and cutting, for example chocolate bar:melted chocolate::snowman:melted snowman. Understanding of these particular causal relations is known to develop between the ages of 3 and 4 years. It was found that even 3-year-olds could solve the classical analogies if they understood the causal relations on which they were based.     

Teaching inference in personality test interpretation: verbal abstract reasoning and the TAT

Instructors of personality assessment are challenged with teaching students how to execute the tacit thinking skills necessary to make sound test interpretations. The author provides a concrete tool for teaching students how to make interpretive inferences from verbal personality test data utilizing the construct of verbal abstract reasoning. Applied specifically to Thematic Apperception Test interpretation, the author discusses how the construct of verbal abstract reasoning can be utilized: as a model for providing explicit instruction on the implicit process of drawing inferences in test interpretation; for grounding students in data when constructing interpretations and avoiding making overpersonalized interpretations; as a means of basing interpretations on a convergence of data; as a means of gauging the level of confidence one can place in interpretations; and for understanding inferences drawn from other tests, such as the Rorschach.     

Analogical reasoning in 2-year-olds: The development of access and relational inference

Eighty-four 24- and 30-month-old children were tested with two analogy tasks: formal and problem solving. Experiment 1 included three Groups: relations specified, relations unspecified, and associative control (no exposure to base relations). In Experiment 2 the relation that linked that a- and b-terms in formal problems was explicitly shown in order to reduce relational inference demands. In Experiment 1, children responded systematically to the formal problems when given two chances to answer each question. In Experiment 2, children were systematic on their first responses. In the problem-solving task the rates of spontaneous analogies produced were similar to those seen in older children. However, unlike older children, 2-year-olds benefited minimally from prompts. We believe this may indicate that 2-year-olds have difficulty explicitly controlling their analogical activity. We conclude early analogical abilities may be limited by weak relational inference abilities and difficulty intentionally initiating access.     

In search for schemata underlying the inference of traits from interpersonal sentiment relations

Three schemata relevant to the inference of traits attributed to a and b from respectively reciprocal liking and disliking relations between a and b are derived from the research literature: (a) Homogeneity according to which likable traits would be attributed to a and b if they like each other, while dislikable traits if they dislike each other; (b) balance according to which more similarity would be attributed to a and b if they like each other than if they dislike each other, the relative similarity effect being localized on a likableness dimension; (c) positivity bias according to which favorable traits would be attributed irrespective of the stimulus information given. An experiment is reported which provides support for the three schemata with the exception that no unequivocal evidence is obtained for the restriction of the balance effect to a likableness dimension. Further, individual Ss are found not to have stable preferences for particular schemata but to switch readily from one schema to the other.     

The relevance of selecting what's relevant: A dual process approach to transitive reasoning with spatial relations

The present paper focuses on the heuristic selection process preceding the actual transitive reasoning process. A part of the difficulty of transitive reasoning lies in the selection of the relevant problem aspects. Two experiments are presented using the paradigm introduced by Markovits, Dumas, and Malfait (1995 Markovits, H., Dumas, C. and Malfait, N. 1995. Understanding transitivity of a spatial relationship: A developmental analysis. Journal of Experimental Child Psychology, 59: 124–141.  [Google Scholar]), in which children were asked to make “higher than” inferences about arrays of coloured blocks. In order to discriminate between genuine transitive inference and a simple strategy of relative position, Markovits et al. interspersed white blocks with the coloured blocks, such that the relative position strategy leads to erroneous responses. However, we argue that the white blocks cause confusion due to their ambiguity, which interferes with the heuristic selection process. Two methodological adaptations were introduced, which are hypothesised to facilitate the selection process and improve transitive reasoning: (1) the white blocks were replaced by coloured blocks, and (2) a less abstract context was added to the experimental design. The colour manipulation leads to a clear increase in the use of a transitive strategy by 9-year-old children; 8-year-old children mainly used the relative position strategy. When adding a context story, 9-year-old children used the transitive strategy regardless of the colour of the interspersed blocks. The overall performance of 8-year-olds improved slightly. These results are interpreted as support for a dual-process model of transitive reasoning.     

Resampling approach to statistical inference: Bootstrapping from event-related potentials data

We propose the use of the bootstrap resampling technique as a tool to assess the within-subject reliability of experimental modulation effects on event-related potentials (ERPs). The assessment of the within-subject reliability is relevant in all those cases when the subject score is obtained by some estimation procedure, such as averaging. In these cases, possible deviations from the assumptions on which the estimation procedure relies may lead to severely biased results and, consequently, to incorrect functional inferences. In this study, we applied bootstrap analysis to data from an experiment aimed at investigating the relationship between ERPs and memory processes. ERPs were recorded from two groups of subjects engaged in a recognition memory task. During the study phase, subjects in Group A were required to make an orthographic judgment on 160 visually presented words, whereas subjects in Group B were only required to pay attention to the words. During the test phase all subjects were presented with the 160 previously studied words along with 160 new words and were required to decide whether the current word was “old” or “new.” To assess the effect of word imagery value, half of the words had a high imagery value and half a low imagery value. Analyses of variance performed on ERPs showed that an imagery-induced modulation of the old/new effect was evident only for subjects who were not engaged in the orthographic task during the study phase. This result supports the hypothesis that this modulation is due to some aspect of the recognition memory process and not to the stimulus encoding operations that occur during the recognition memory task. However, bootstrap analysis on the same data showed that the old/new effect on ERPs was not reliable for all the subjects. This result suggests that only a cautious inference can be made from these data.     

Motivational determinants of reasoning about social relations: The role of need for cognitive closure

The role of need for cognitive closure (NFCC) in reasoning about social relations was investigated. Participants learned pairwise liking/disliking relations between people who could also be categorised on the basis of nationality and then had to group them into social cliques. The social clique structures were either consistent or inconsistent with the nationality categorisation, and the diagnostic information that was necessary to determine the number of cliques appeared either early or late in the information sequence. We expected participants under conditions of high (vs low) NFCC to rely more on heuristic processing. As predicted, high (vs low) NFCC participants were less accurate in their representations of cliques when the clique structure was inconsistent with the nationality category (Study 1 and 2) and when the diagnostic information was presented late (Study 1). The implications regarding the influence of NFCC on reasoning and the role of specific NFCC manipulations are discussed.     

Relating derived relations as a model of analogical reasoning: reaction times and event-related potentials

The current study aimed to test a Relational Frame Theory (RFT) model of analogical reasoning based on the relating of derived same and derived difference relations. Experiment 1 recorded reaction time measures of similar-similar (e.g., "apple is to orange as dog is to cat") versus different-different (e.g., "he is to his brother as chalk is to cheese") derived relational responding, in both speed-contingent and speed-noncontingent conditions. Experiment 2 examined the event-related potentials (ERPs) associated with these two response patterns. Both experiments showed similar-similar responding to be significantly faster than different-different responding. Experiment 2 revealed significant differences between the waveforms of the two response patterns in the left-hemispheric prefrontal regions; different-different waveforms were significantly more negative than similar-similar waveforms. The behavioral and neurophysiological data support the RFT prediction that, all things being equal, similar-similar responding is relationally "simpler" than, and functionally distinct from, different-different analogical responding. The ERP data were fully consistent with findings in the neurocognitive literature on analogy. These findings strengthen the validity of the RFT model of analogical reasoning and supplement the behavior-analytic approach to analogy based on the relating of derived relations.     

Domain-general contributions to social reasoning: theory of mind and deontic reasoning re-explored

Using older adults and dual-task interference, we examined performance on two social reasoning tasks: theory of mind (ToM) tasks and versions of the deontic selection task involving social contracts and hazardous conditions. In line with performance accounts of social reasoning, evidence from both aging and the dual-task method suggested that domain-general resources contribute to performance of these tasks. Specifically, older adults were impaired relative to younger adults on all types of social reasoning tasks tested; performance varied as a function of the demands these tasks placed on domain-general resources. Moreover, in younger adults, simultaneous performance of a working memory task interfered with younger adults' performance on both types of social reasoning tasks; here too, the magnitude of the interference effect varied with the processing demands of each task. Limits placed on social reasoning by executive functions contribute a great deal to performance, even in old age and in healthy younger adults under conditions of divided attention. The role of potentially non-modular and modular contributions to social reasoning is discussed.     

Counterfactual reasoning: From childhood to adulthood

The objective of this study was to describe the developmental progression of counterfactual reasoning from childhood to adulthood. In contrast to the traditional view, it was recently reported by Rafetseder and colleagues that even a majority of 6-year-old children do not engage in counterfactual reasoning when asked counterfactual questions (Child Development, 2010, Vol. 81, pp. 376–389). By continuing to use the same method, the main result of the current Study 1 was that performance of the 9- to 11-year-olds was comparable to that of the 6-year-olds, whereas the 12- to 14-year-olds approximated adult performance. Study 2, using an intuitively simpler task based on Harris and colleagues (Cognition, 1996, Vol. 61, pp. 233–259), resulted in a similar conclusion, specifically that the ability to apply counterfactual reasoning is not fully developed in all children before 12 years of age. We conclude that children who failed our tasks seem to lack an understanding of what needs to be changed (events that are causally dependent on the counterfactual assumption) and what needs to be left unchanged and so needs to be kept as it actually happened. Alternative explanations, particularly executive functioning, are discussed in detail.