David P. O'Brien

A theory of if: A lexical entry, reasoning program, and pragmatic principles.

The theory has 3 parts: (a) A lexical entry defines the information about if in semantic memory; its core comprises 2 inferences schemas, Modus Ponens and a schema for Conditional Proof; the latter operates under a constraint that explains differences between if and the material conditional of standard logic. (b) A propositional-logic reasoning program specifies a routine for reasoning from information as interpreted to a conclusion. (c) A set of pragmatic principles governs how an if sentence is likely to be interpreted in context

Propositional reasoning by mental models? Simple to refute in principle and in practice.

Two experiments compared the predictions of mental-models theory with a mental-logic theory. Results show that people do not make fallacious inferences predicted by mental-models theory but not predicted by mental-logic theory and that people routinely make many valid inferences predicted by mental-logic theory that should be too difficult on mental-models theory. Thus, the mental-logic theory accounts better for the data. A difference between the two theories concerning predictions about the order in which inferences are made was also investigated. The data clearly favor the mental-logic theory. It is argued that the mental-logic theory provides the more plausible description of the actual psychological processes in propositional reasoning.

Predicting propositional logic inferences in text comprehension

Abstract Three experiments investigated whether the propositional logic reasoning model of Braine, Reiser, and Rumain (1984) can account for propositional logic inferences made in text comprehension. The operative part of the model consists of a set of inference schemas together with a routine for using them to draw inferences. In Experiment 1 subjects read stories and performed two tasks: the first asked them to indicate whether a final sentence made sense in the context of the story; the second asked them whether a piece of information was presented in the story or needed to be inferred. In Experiment 2 we omitted the first task and replicated the second task. Results showed that (a) subjects had no difficulty making the inferences necessary to judge the sensibleness of the final sentence and (b) subjects often believed that information derived from model-predicted inferences had been presented to them in the story, although subjects rarely believed that information derived from other logically valid inferences had been presented in the text. In Experiment 3 subjects were presented with abstract versions of the logical form of the stories and were asked to write whatever follows from the premises. It turned out that the inferences that subjects think follow from only the meaning of the logical particles correspond closely to the ones that they draw reading the stories, and both are well predicted by the model investigated. We argue that any complete account of the inferences people make in discourse comprehension must include some propositional logic inferences, and, more particularly, that the inference-schema model we examined provides a precise starting hypothesis about the propositional logic inference generator used in text comprehension.

The Development of Conditional Reasoning: An Iffy Proposition

Publisher Summary This chapter attempts to make some sense of the competing claims concerning conditional-reasoning competence. The competence model is based on the natural deduction approach to standard logic; modus ponens and the schema for conditional proof provide inference rules for simple conditionals and, together with the recognition of the constraints imposed by universal quantification, they provide a model for reasoning with universally quantified conditionals. Piagets account of conditional reasoning is inadequate on logical grounds, that is, it confuses simple and quantified conditionals, but it is possible to make fairly clear empirical predictions when quantifiers are assumed. Ennis and Brainerd have argued that Piagets account of formal operational thought is wrong because children have some ability to evaluate conditional syllogisms correctly. However, Piaget argued that successful performances on many conditional reasoning tasks can be obtained without a formal operational appreciation of the conditional. Given that the class-inclusion logic structure of concrete operational thought should be sufficient for reasoning with simple conditionals; this does not appear to be a warranted dismissal of the theoretical expectations. Rather, the appropriate assessment of formal operational competency with conditionals appears to concern performances in judging universally quantified conditionals.

Human reasoning includes a mental logic

Oaksford & Chater (O&C) have rejected logic in favor of probability theory for reasons that are irrelevant to mental-logic theory, because mental-logic theory differs from standard logic in significant ways. Similar to O&C, mental-logic theory rejects the use of the material conditional and deals with the completeness problem by limiting the scope of its procedures to local sets of propositions.

Sources of difficulty in deductive reasoning: The THOG task

The THOG task presents four designs constructed from two shapes and two colours. Subjects are told that the experimenter has written down one of the shapes and one of the colours and are provided the rule that if, and only if, any design has either the shape or the colour, but not both, written down, then it is a THOG. Finally, they are given an exemplar and are asked to classify the remaining designs. Successful solution requires construction of hypotheses, reasoning under each hypothesis, and comparison of the results under each to reach a final conclusion. Few subjects are able to provide adequate responses on the standard version of the task. We present the results of four experiments, with 160 undergraduates each presented with one of eight versions of the task. Experiments 1 and 2 indicate that (1) some subjects think that the properties that are written down are identical to those of the exemplar, although these are not the same subjects who exhibit the modal error pattern, (2) many subjects correctly understand the disjunction of the rule but fail to consider the hypotheses, and (3) poor initial encoding of the problem is not easily corrected. Experiment 3 investigates the sufficiency of the claim of Griggs and Newstead (1982) that appropriate problem solution follows from explicit presentation of all problem information (including use of positive labels for properties that are not written down), and Experiment 4 investigates the necessity of the claim. The results of Experiments 3 and 4 show that presenting positive category labels does increase the frequency of correct solution; however, positive category labels are not necessary for such improvement. Separation of the labels of the THOG rule from those of the exemplar, or informing subjects that only one other design is a THOG, also increases the frequency of successful solution. The results suggest that many people have some fairly sophisticated reasoning skills. but application of these skills is easily discouraged when the features of the task lead to poor initial encoding.

Conditionals and disjunctions in mental-logic theory:: A response to Liu and Chou (2012) and to López Astorga (2013)

Liu and Chou (2012) presented a two-step theory to describe reasoning both on the four traditional conditional syllogisms and on four parallel syllogisms that replace the conditional with a disjunction. �怀is article proposes that although Liu and Chou show that the words if and or play an important role in generating the data they report, their theory provides no explanation of how these words play any role. �怀e article also corrects an assertion by Lopez Astorga (2013) that mental-logic theory accounts for the �耀ndings of Liu and Chou by interpreting if as the material conditional. Instead I show why mental-logic theory rejects the material conditional and accounts for the data using a proceduralsemantics approach to the meaning of logic particles. �怀e article concludes that a theory like that of Liu and Chou requires something like mental-logic theory to account for their data.

Raciocínio sobre probabilidades condicionais: as evidências a favor da hipótese freqüentista se fundamentam em comparações errôneas

Reasoning about conditional probabilities: the evidence for the frequentist hypothesis has relied on flawed comparisons. Gigerenzer and Hoffrage (1995) and Cosmides and Tooby (1996) proposed a frequentist hypothesis that claims that although people rarely make judgements about conditional probabilities that concord with the normative standards of Bayes’s theorem, such judgements can be elicited when a problem is presented in terms of frequencies rather than probabilities. These two articles together reported 10 experiments with 89 problem versions in support of their prediction, with people consistently solving frequentist-formatted problems more frequently than probabilist-formatted problems. The results of two experiments reported here, however, show that their results can be explained as resulting from two experimental confounds that have to do with the presence vs. absence of a response format and with the use of whole numbers vs. decimal fractions. In Experiment 1 we found that the frequentist problems were solved only when presented with a response format that can encourage accurate guesses, and in Experiment 2 we found that frequentist- and probabilist- formatted problems were solved equally often when presented with the response format and with whole numbers rather than with decimal fractions. The results are discussed in terms of their negative implications for the frequentist hypothesis.

Se e Quando: Sinônimos?!!!

Conditional and temporary sentences are identicals, except for the conjunctions: antecedent events whose ocurrence is certain are introduced by when and those incertain by if. In some contexts, this subtle difference disappears, and it is possible to exchange one conjunction for another without altering the meaning of the sentence (Dias & Vanderlei, 1999; Reilly, 1986). This research, realized with undergraduate students, intended to compare the idea of certainty transmitted by conditional and temporary sentences, as well as to verify if the idea of certainty transmitted by each type of sentence changes in function of the verbal tense in which it is expressed. The analyses identified that verbal tense is the variable that influences more strongly to bring near the meaning of those types of sentences. The semantic overlap in the present tense happens because the meaning of the connective if changes, transmitting more certainty than in the past or in the future.

Evaluation of evidence for sufficiency, for necessity, and for necessity-and-sufficiency

We report two experiments with 120 undergraduate subjects. The tasks presented clearly articulated hypotheses concerning necessity, sufficiency, and necessity-and-sufficiency, together with possible combinations of treatment conditions, and required subjects to judge whether, according to the hypotheses, the relevant outcomes will occur, will not occur, or might occur. The patterns of responses reveal how subjects understand the extensions of the concepts, i.e. what each hypothesis permits, requires, and excludes. Only necessity-and-sufficiency hypotheses generally led to logically adequate responses, and the most typical error for both necessity hypotheses and sufficiency hypotheses was to treat them as extensionally equivalent to necessity-and-sufficiency. This error tendency was more evident for necessity than for sufficiency hypotheses. Further, although responses to both necessity hypotheses and sufficiency hypotheses were affected by the complexity of the hypothesized conditions, responses to necessity-and-sufficiency hypotheses were not. We argue that the results are not a function of a response bias but reflect differences in the way the hypotheses are understood. Implications for the causal attribution literature are discussed.