Are conjunctive inferences easier than disjunctive inferences? A comparison of rules and models

Seeing inferences: brain dynamics and oculomotor signatures of non-verbal deduction

We often express our thoughts through words, but thinking goes well beyond language. Here we focus on an elementary but basic thinking process, disjunction elimination, elicited by elementary visual scenes deprived of linguistic content, describing its neural and oculomotor correlates. We track two main components of a nonverbal deductive process: the construction of a logical representation (A or B), and its simplification by deduction (not A, therefore B). We identify the network active in the two phases and show that in the latter, but not in the former, it overlaps with areas known to respond to verbal logical reasoning. Oculomotor markers consistently differentiate logical processing induced by the construction of a representation, its simplification by deductive inference, and its maintenance when inferences cannot be drawn. Our results reveal how integrative logical processes incorporate novel experience in the flow of thoughts induced by visual scenes.

Modeling Item Difficulty in a Dynamic Test

The Concept Formation subtest of the Woodcock Johnson Tests of Cognitive Abilities represents a dynamic test due to continual provision of feedback from examiner to examinee. Yet, the original scoring protocol for the test largely ignores this dynamic structure. The current analysis applies a dynamic adaptation of an explanatory item response theory model to evaluate the impact of feedback on item difficulty. Additionally, several item features (rule type, number of target shapes) are considered in the item difficulty model. Results demonstrated that all forms of feedback significantly reduced item difficulty, with the exception of corrective feedback that could not be directly applied to the next item in the series. More complex and compound rule types also significantly predicted item difficulty, as did increasing the number of shapes, thereby supporting the response process aspect of validity. Implications for continued use of the Concept Formation subtest for educational programming decisions are discussed.

The Analytic Truth and Falsity of Disjunctions

Disjunctive inferences are difficult. According to the theory of mental models, it is because of the alternative possibilities to which disjunctions refer. Three experiments corroborated further predictions of the mental model theory. Participants judged that disjunctions, such as Either this year is a leap year or it is a common year are true. Given a disjunction such as Either A or B, they tended to evaluate the four cases in its 'partition': A and B, A and not-B, not-A and B, not-A and not-B, as 'possible' or 'impossible' in ways that bore out the difference between inclusive disjunctions ('or both') and exclusive disjunctions ('but not both'). Knowledge usually concerns what is true, and so when participants judge that a disjunction is false, or contingent, and evaluate the cases in its partition, they depend on inferences that yield predictable errors. They tended to judge that disjunctions, such as follows: Either the food is cold or else it is tepid, but not both, are true, though in fact they could be false. They tended to infer 'mirror-image' evaluations that yield the same possibilities for false disjunctions as those for true disjunctions. The article considers the implications of these results for alternative theories based on classical logic or on the probability calculus.

Differential roles of polar orbital prefrontal cortex and parietal lobes in logical reasoning with neutral and negative emotional content

To answer the question of how brain pathology affects reasoning about negative emotional content, we administered a disjunctive logical reasoning task involving arguments with neutral content (e.g. Either there are tigers or women in NYC, but not both; There are no tigers in NYC; There are women in NYC) and emotionally laden content (e.g. Either there are pedophiles or politicians in Texas, but not both; There are politicians in Texas; There are no pedophiles in Texas) to 92 neurological patients with focal lesions to various parts of the brain. A Voxel Lesion Symptom Mapping (VLSM) analysis identified 16 patients, all with lesions to the orbital polar prefrontal cortex (BA 10 & 11), as being selectively impaired in the emotional reasoning condition. Another 17 patients, all with lesions to the parietal cortex, were identified as being impaired in the neutral content condition. The reasoning scores of these two patient groups, along with 23 matched normal controls, underwent additional analysis to explore the effect of belief bias. This analysis revealed that the differences identified above were largely driven by trials where there was an incongruency between the believability of the conclusion and the validity of the argument (i.e. valid argument/false conclusion or invalid argument/true conclusion). Patients with lesions to polar orbital prefrontal cortex underperformed in incongruent emotional content trials and over performed in incongruent neutral content trials (compared to both normal controls and patients with parietal lobe lesions). Patients with lesions to parietal lobes underperformed normal controls (at a trend level) in neutral trials where there was a congruency between the believability of the conclusion and the validity of the argument (i.e. valid argument/true conclusion or invalid argument/false conclusion). We conclude that lesions to the polar orbital prefrontal cortex (i) prevent these patients from enjoying any emotionally induced cognitive boost, and (ii) block the belief bias processing route in the neutral condition. Lesions to parietal lobes result in a generalized impairment in logical reasoning with neutral content.

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Polar/orbital PFC lesions result in impaired reasoning in emotional content reasoning.

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Polar/orbital PFC lesion patients overperform in neutral content reasoning trials.

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These differences were driven by incongruent reasoning trials.

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Parietal lesions result in impaired reasoning with neutral but not emotional content.

A New Look to a Classic Issue: Reasoning and Academic Achievement at Secondary School

Higher-order thinking abilities such as abstract reasoning and meaningful school learning occur sequentially. The fulfillment of these tasks demands that people activate and use all of their working memory resources in a controlled and supervised way. The aims of this work were: (a) to study the interplay between two new reasoning measures, one mathematical (Cognitive Reflection Test) and the other verbal (Deductive Reasoning Test), and a third classical visuo-spatial reasoning measure (Raven Progressive Matrices Test); and (b) to investigate the relationship between these measures and academic achievement. Fifty-one 4th grade secondary school students participated in the experiment and completed the three reasoning tests. Academic achievement measures were the final numerical scores in seven basic subjects. The results demonstrated that cognitive reflection, visual, and verbal reasoning are intimately related and predicts academic achievement. This work confirms that abstract reasoning constitutes the most important higher-order cognitive ability that underlies academic achievement. It also reveals the importance of dual processes, verbal deduction and metacognition in ordinary teaching and learning at school.

Directional effect in double conditionals with a construction task: The semantic hypothesis

The goal of this paper is to test the main predictions of the semantic hypothesis about the directional effect in double conditionals (such as, 'A only if B/only if C, B') with a construction task. The semantic hypothesis claims that directional effect can be explained by the inherent directionality of the relation between the relatum and the target object of the premises. According to this hypothesis, a directional effect should occur if only one of the end-terms of the premises takes the role of relatum: a) if the end-term that plays the role of relatum is in the first premise, a forward directional effect is predicted (from A to C); and b) if the end-term that plays the role of relatum is in the second premise, a backward directional effect is predicted (from C to A). On the other hand, it claims that there should be no directional effect when both end-terms take the role of relatum or when neither of the end-terms plays the role of relatum. Three experiments confirmed the main predictions of the semantic hypothesis in a construction task.

The modulation of disjunctive assertions

The theory of mental models postulates that disjunctions of the sort, A or B, where A and B are sensible everyday clauses, have a core meaning that allows an inclusive interpretation, referring to three possibilities: A and not-B, not-A and B, and A and B. The meaning of the clauses and knowledge can modulate this meaning by blocking the construction of at least one model of a possibility-for example, "Rui is playing tennis or he is surfing" blocks the model of Rui doing both activities. This theory is implemented in a computer program. Three experiments investigated the core interpretation and interpretations in which the contents of the clauses should block the model of A and B (as in the preceding example), the model of A and not-B, or the model of not-A and B. In Experiment 1, the participants listed the possibilities for each of the four sorts of disjunction. The results corroborated the predicted modulations. In Experiment 2, these predicted interpretations governed the conclusions that participants accepted from disjunctions and categorical premises. In Experiment 3, the predicted interpretations yielded reliable effects on the conclusions that the participants drew for themselves. We relate these results to theories of reasoning.

The negations of conjunctions, conditionals, and disjunctions

How do reasoners understand and formulate denials of compound assertions, such as conjunctions and disjunctions? A theory based on mental models postulates that individuals enumerate models of the various possibilities consistent with the assertions. It therefore predicts a novel interaction: in affirmations, conjunctions, A and B, which refer to one possibility, should be easier to understand than disjunctions, A or B, which refer to more than one possibility; in denials, conjunctions, not(A and B), which refer to more than one possibility, should be harder to understand than disjunctions, not(A or B), which do not. Conditionals are ambiguous and they should be of intermediate difficulty. Experiment 1 corroborated this trend with a task in which the participants selected which possibilities were consistent with assertions, such as: Bob denied that he wore a yellow shirt and he wore blue pants on Tuesday. Experiment 2 likewise showed that participants' own formulations of verbal denials yielded the same trend in which denials of conjunctions were harder than denials of conditionals, which in turn were harder than denials of disjunctions.

Unless Reasoning

We report the results of two experiments investigating conditional inferences from conditionalunlessassertions, such asJuan is not in León unless Nuria is in Madrid. Experiments 1 and 2 check Fillenbaum's hypothesis about the semantic similarity ofunlesswithif notandonly ifassertions; both also examine inferential endorsements (Experiment 1) and endorsements and latencies (Experiment 2) of the four logically equivalent conditional formulations:if A then B, if not-B then not-A, A only if Bandnot-A unless B. The results of these experiments show the similarity ofunlessandonly if, confirming that the representation of both conditionals from the outset probably include two possibilities directionally oriented from B to A; results also confirm the especial difficulty ofunlessassertions. The implications of the results are discussed in the context of recent psychological and linguistic theories of the meaning ofunless.

Working Memory, Text Comprehension, and Propositional Reasoning: A New Semantic Anaphora WM Test

The aim of this study was to present a new working memory test following the line of work started by García-Madruga et al. (2007) and to examine its relation to reading comprehension and propositional reasoning measures. In that study we designed a new working memory span test –based on Daneman & Carpenter's (1980) Reading Span Test (RST)– in which the processing task called for an inferential decision –to resolve a pronominal anaphora based on Morpho-Syntactic cues– and had people recall the result of this inference. In the current study, besides the RST and the Morpho-Syntactic Anaphora test, we presented a new Semantic Anaphora measure. In order to check the validity of this new Working Memory (WM) task, we used the same reasoning task used in the previous study as well as a new reading comprehension test. The results show the tight relationship amongst working memory, reading comprehension and reasoning, and confirm the validity of the new WM measure.

The semantics of 'unless' conditionals: evidence from 'unless' and disjunctive inferences

We report the results of an experiment investigating conditional inferences from conditional assertions such as 'Juan won't go to León unless Nuria goes to Madrid' and 'Either Nuria goes to Madrid or Juan won't go to León'. This experiment addresses Dancygier's claims about the semantics of 'unless' by examining inferential endorsements of 'not-A unless B' and 'Either B or not-A' in the canonical order, presenting the categorical premise after the conditional assertions, and in the inverse order, presenting the categorical premise before the conditional assertions. The results of the experiment confirm that the representation of 'unless' includes two possibilities, although as Dancygier holds one of the possibilities may not be complete. The implications of the results are discussed in the context of the strategic nature of conditional reasoning and recent convergent theories of linguistic processing.

Mental models and human reasoning

To be rational is to be able to reason. Thirty years ago psychologists believed that human reasoning depended on formal rules of inference akin to those of a logical calculus. This hypothesis ran into difficulties, which led to an alternative view: reasoning depends on envisaging the possibilities consistent with the starting point--a perception of the world, a set of assertions, a memory, or some mixture of them. We construct mental models of each distinct possibility and derive a conclusion from them. The theory predicts systematic errors in our reasoning, and the evidence corroborates this prediction. Yet, our ability to use counterexamples to refute invalid inferences provides a foundation for rationality. On this account, reasoning is a simulation of the world fleshed out with our knowledge, not a formal rearrangement of the logical skeletons of sentences.

Deductive reasoning

This article begins with an account of logic, and of how logicians formulate formal rules of inference for the sentential calculus, which hinges on analogs of negation and the connectives if, or, and and. It considers the various ways in which computer scientists have written programs to prove the validity of inferences in this and other domains. Finally, it outlines the principal psychological theories of how human reasoners carry out deductions. Copyright © 2009 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.

Figural Effects in a Syllogistic Evaluation Paradigm

Abstract. Robust biases have been found in syllogistic reasoning that relate to the figure of premises and to the directionality of terms in given conclusions. Mental models theorists (e.g., Johnson-Laird & Byrne, 1991 ) have explained figural bias by assuming that reasoners can more readily form integrated models of premises when their middle terms are contiguous than when they are not. Biases associated with the direction of conclusion terms have been interpreted as reflecting a natural mode of reading off conclusions from models according to a “first-in, first-out principle.” We report an experiment investigating the impact of systematic figural and conclusion-direction manipulations on the processing effort directed at syllogistic components, as indexed through a novel inspection-time method. The study yielded reliable support for mental-models predictions concerning the nature and locus of figural and directionality effects in syllogistic reasoning. We argue that other accounts of syllogistic reasoning seem less able to accommodate the full breadth of inspection-time findings observed.

Mental models in deductive reasoning

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.

Priming in deduction: a spatial arrangement task

The mental model theory assumes that people reason by manipulating mental representations of states of the word, called "mental models." In the present study we used a new deduction task based on diagrammatic premises. We show that a premise can prime other premises that induce similar mental models in a way analogous to the case of words with related meanings, which prime one another. We present three experiments. In Experiment 1 we used an evaluation task. In Experiment 2, a construction task was used. The priming effect was obtained in both cases. In a third experiment we show that the priming effect was still present when partcipants were instructed to ignore a prime displayed before the premises. In all three experiments we compared determinate and indeterminate problems and found faster responses in the former.