A study of disjunctive reasoning

Summary Whilst it is currently fashionable to construct sequential models of reasoning, the results of recent experiments on conditional reasoning tasks are apparently incompatible with this notion. There is evidence of two orthogonal statistical components, one logical and the other non-logical. It has been suggested that non-logical tendencies are response biases independent of the linguistic structure of the rule. However, certain results suggest that the matching bias observed in conditional tasks may not occur with disjunctives.Two experiments are reported in which subjects generated subjective truth tables for disjunctive rules, in which the presence and absence of negative components was varied. Experiment I provided a powerful test of the matching bias hypothesis and found no evidence of its presence. The presence of negative components did, however, systematically affect performance. Experiment II, with the aid of latency measurements, provided support for the hypothesis that negatives were affecting the ease of interpretation of the disjunctive sentences, with one negative component causing at least as much difficulty as two.In discussion, it is pointed out that the present results can be reconciled with those on conditional tasks, on the assumption that matching bias is a special case of associational biases which are dependent on the linguistic form of the rule. It still appears necessary to retain the distinction between logical and non-logical components of the performance. However, this does not necessarily imply parallel processes underlying the data. A single muddled thought process, in which a rational sequential strategy fails to be consistently applied, could give rise to the type of data obtained.     

A logical expression of reasoning

A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive logic specially designed to serve as the monotonic support for LPR. Axiomatics and semantics for LPD, together with a completeness proof, are provided. Once LPD has been given, LPR may be defined via a concept of extension over LPD. Although the construction of LPR extensions is first presented in standard style, for the sake of comparison with existing non-monotonic formalisms, alternative more elegant and intuitive ways for constructing non-monotonic LPR extensions are also given and proofs of their equivalence are presented.     

A neurocomputational system for relational reasoning

The representation and manipulation of structured relations is central to human reasoning. Recent work in computational modeling and neuroscience has set the stage for developing more detailed neurocomputational models of these abilities. Several key neural findings appear to dovetail with computational constraints derived from a model of analogical processing, 'Learning and Inference with Schemas and Analogies' (LISA). These include evidence that (i) coherent oscillatory activity in the gamma and theta bands enables long-distance communication between the prefrontal cortex and posterior brain regions where information is stored; (ii) neurons in prefrontal cortex can rapidly learn to represent abstract concepts; (iii) a rostral-caudal abstraction gradient exists in the PFC; and (iv) the inferior frontal gyrus exerts inhibitory control over task-irrelevant information.     

A factor-analytic study of reasoning abilities

A battery of 32 tests was administered to a sample including 144 Air Force Officer Candidates and 139 Air Cadets. The factor analysis, using Thurstone's complete centroid method and Zimmerman's graphic method of orthogonal rotations, revealed 12 interpretable factors. The non-reasoning factors were interpreted asverbal comprehension, numerical facility, perceptual speed, visualization, andspatial orientation. The factors derived from reasoning tests were identified asgeneral reasoning, logical reasoning, education of perceptual relations, education of conceptual relations, education of conceptual patterns, education of correlates, andsymbol substitution. The logical-reasoning factor corresponds to what has been called deduction, but eduction of correlates is perhaps closer to an ability actually to make deductions. The area called induction appears to resolve into three eduction-of-relations factors. Reasoning factors do not appear always to transcend the type of test material used.Under Contract N6onr-23810 with the Office of Naval Research. The views expressed here are not nesessarily shared by the Office of Naval Research. These studies are under the general direction of J. P. Guilford. P. R. Christensen is assistant director. A. L. Comrey was in direct charge of this study during its early stages and R. F. Green during most of its progress.     

A base logic for default reasoning

Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between “local inferences” (to infer a conclusion from a subset of given premises) and “global inferences” (to infer a conclusion from the entire set of given premises). These conceptual analyses are captured by a formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Studies), 2003 (special issue) by Ye Feng     

A transitive-chain theory of syllogistic reasoning

A new theory of syllogistic reasoning, called the transitive-chain theory, is presented. The transitive-chain theory proposes that information about set relations is represented in memory by pairs of informational components. The theory further proposes that information about set relations is integrated by applying a small set of rules to transitive chains of these set relations. The rules that are applied to these chains are specified in detail. The theory is cast in terms of information-processing models for variants of the syllogistic reasoning task, and then mathematical models that quantify each of these information-processing models are presented. In a series of five experiments, the transitive-chain theory provides a good account of the response-choice data for syllogisms with various types of content, quantifiers, and logical relations (categorical and conditional). The results of these experiments offer tentative answers to four issues in the theory of syllogistic reasoning: (a) representation of premise information; (b) combination of premise information; (c) sources of difficulty in syllogistic reasoning; and (d) generality of the processes used in syllogistic reasoning.     

A visualization technique for Bayesian reasoning

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed problems with no instruction or external support, participants watched a video describing a visualization technique that used the length of bars to represent the probabilities provided in the problem. Participants then completed more problems with a chance to implement the technique by clicking interactive bars on the computer screen. Performance improved dramatically from the pretraining phase to the interactive‐bar phase. Participants maintained improved performance in transfer phases in which they were required to implement the visualization technique with either pencil‐and‐paper or no external medium. Accuracy levels for participants using the visualization technique were very similar to participants trained to solve the Bayes theorem equation. The results showed no evidence of learning across problems in the pretraining phase or for control participants who did not receive training, so the improved performance of participants using the visualization method could be uniquely attributed to the method itself. A classroom sample demonstrated that these benefits extend to instructional settings. The results show that people can quickly learn to perform Bayesian reasoning without using mathematical equations. We discuss ways that a spatial solution method can enhance classroom instruction on Bayesian inference and help students apply Bayesian reasoning in everyday settings.     

A second-order factor analysis of reasoning abilities

This article reports a second-order factor analysis of the 13 interpretable first-order factors of Adkins and Lyerly based on 66 variables for 200 Army men. The approach to simple structure for 6 second-order factors was unusually good. Loadings of the original 66 variables on the second-order factors were also obtained. Five of the factors are tentatively interpreted as Precision in Formation and Use of Verbal Concepts, General Verbal Fluency, Visualizing Spatial Constancy During Movement, Speed in Analysis, and Flexibility in Analysis.     

A reasoning method for a paraconsistent logic

A proof method for automation of reasoning in a paraconsistent logic, the calculus C1* of da Costa, is presented. The method is analytical, using a specially designed tableau system. Actually two tableau systems were created. A first one, with a small number of rules in order to be mathematically convenient, is used to prove the soundness and the completeness of the method. The other one, which is equivalent to the former, is a system of derived rules designed to enhance computational efficiency. A prototype based on this second system was effectively implemented.     

A dual-process specification of causal conditional reasoning

There are two accounts describing causal conditional reasoning: the probabilistic and the mental models account. According to the probabilistic account, the tendency to accept a conclusion is related to the probability by which cause and effect covary. According to the mental models account, the tendency to accept a conclusion relates to the availability of counterexamples. These two accounts are brought together in a dual-process theory: It is argued that the probabilistic reasoning process can be considered as a heuristic process whereas the mental models account can be seen as its analytic counterpart. Experiment 1 showed that the two processes differ on a temporal dimension: The variation in fast responses was best predicted by the variation in likelihood information, while the variation in slow responses was best predicted by variation in counterexample information. Experiments 2 and 3 validate the override principle: The likelihood conclusion can be overwritten when specific counterexamples are retrieved in time. In Experiment 2 both accounts were compared based on their difference in input. In Experiment 3 we used a verbal protocol analysis to validate the dual-process idea at the output level. The data of the three experiments provide converging support for framing the two reasoning accounts in a dual-process theory.     

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.     

A mixed Rasch model of dual-process conditional reasoning

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent (AC), denying the antecedent (DA), and modus tollens (MT) syllogisms featuring the same conditional; and (b) the average rate of determinate answers to AC, DA, and MT. This account receives indirect support from the extant literature and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.     

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.     

Causal reasoning

The main focus of this paper is the question as to what it is for an individual to think of her environment in terms of a concept of causation, or causal concepts, in contrast to some more primitive ways in which an individual might pick out or register what are in fact causal phenomena. I show how versions of this question arise in the context of two strands of work on causation, represented by Elizabeth Anscombe and Christopher Hitchcock, respectively. I then describe a central type of reasoning that, I suggest, a subject has to be able to engage in, if we are to credit her with causal concepts. I also point out that this type of reasoning turns on the idea of a physical connection between cause and effect, as articulated in recent singularist approaches of causation.     

Unless reasoning

We report the results of two experiments investigating conditional inferences from conditional unless assertions, such as Juan is not in León unless Nuria is in Madrid. Experiments 1 and 2 check Fillenbaum's hypothesis about the semantic similarity of unless with if not and only if assertions; 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 B and notA unless B. The results of these experiments show the similarity of unless and only 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 of unless assertions. The implications of the results are discussed in the context of recent psychological and linguistic theories of the meaning of unless.