Some Empirical Justification for a Theory of Natural Propositional Logic

Braine, Martin D. S.; Reiser, Brian J.; Rumain, Barbara

doi:10.1016/s0079-7421(08)60365-5

Cited by 124 publications

(217 citation statements)

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“…Braine, Reiser, & Rumain, 1984;Rips, 1994) be somehow extended to deal with temporal reasoning of the present sort (the A-series of McTaggart, 1927, as we discussed in the Introduction)? In the case of B-series reasoning, which depends on "before", "after", and other such relations, it is a simple matter to introduce meaning postulates to capture their logical properties, e.g:…”

Section: Discussionmentioning

confidence: 99%

Tense, Aspect, and Temporal Reasoning

Schaeken¹

1996

Thinking & Reasoning

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We report two experiments on temporal reasoning with problems, such as:John has cleaned the house. John is taking a shower. John is going to read the paper. Mary always does the dishes when John cleans the house. Mary always drinks her coffee when John reads the paper. What for Mary is the relation between doing the dishes and drinking coffee?The experiments showed that problems such as this one, which require one mental model, elicited correct answers more often than did those requiring multiple models (e.g. with the second premise modified to "John has taken a shower", so that the order between the events in the first two premises is not fixed). These multiple-model problems, in turn, elicited more correct answers than did multiple-model problems with no valid answers (e.g. with the second premise modified to "John has taken a shower", and the fifth premise modified to "Mary always drinks her coffee when John takes a shower"). One-model problems were also solved more quickly than multiple-model problems, which were solved more quickly than problems with no valid answers. These results corroborated the predictions of the mental model theory of reasoning. INTRODUCTIONReasoning about temporal relations is an important aspect of everyday thinking. If you know the following facts:Requests for reprints should be sent to Walter Schaeken, Laboratory of Experimental Psychology, Department of Psychology, Tiensestraat 102, B-3000 Leuven, Belgium.We thank Andreas de Troy for implementing the program used to carry out the Experiment. The children became ill after going to the cinema. They ate seafood before they went to the cinema. then you can infer:The children became ill after they ate seafood.Although logicians have devised various "temporal logics", and linguists have investigated many aspects of temporal language, the topic of temporal reasoning has been strangely neglected by psychologists. They have studied the perception of time (e.g. Fraisse, 1963), how children conceive of time (e.g. Piaget, 1969), but they have carried out few studies, if any, of how individuals reason on the basis of temporal relations.Following McTaggart (1927; see Miller & Johnson-Laird, 1976, Sec.6.2), we distinguish two ways of thinking about (and describing) temporal order. First, an event can be past, present, or future (McTaggart's A-series). Second, one event can be earlier or later than another (McTaggart's B-series). Any relation described in terms of the A-series can be described in terms of the Bseries, but the converse is not true. We have previously made an experimental investigation of how subjects reason on the basis of B-series relations, i.e. temporal connectives, such as "before", "after", and "while". The experiments were carried out in Flemish, which has connectives that correspond to these English terms (see Schaeken, Johnson-Laird, & d'Ydewalle, in press). They were designed to test the predictions of the theory of reasoning based on mental models (see e.g. Johnson-Laird, 1983;Johnson-Laird & Byrne, 1991). The subjects i...

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Section: Discussionmentioning

confidence: 99%

Tense, Aspect, and Temporal Reasoning

Schaeken¹

1996

Thinking & Reasoning

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“…At this level, the program does not distinguish between exclusive and inclusive interpretations of a disjunction, which, as the example shows, it represents in two models. It is able, however, to make the correct responses to the 61 so-called direct reasoning problems of Braine, Reiser, and Rumain (1984), and the number of models it constructs predicts their difficulty just as well as Braine's theory even though, unlike that theory, it does not depend on parameters estimated from the data (Johnson-Laird, Byrne, & Schaeken, 1992). At Level 2, the program takes mental footnotes into account in combining models.…”

Section: The Theory Of Mental Modelsmentioning

confidence: 99%

Conditionals: A theory of meaning, pragmatics, and inference.

Johnson‐Laird

Byrne²

2002

Psychological Review

657

759

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The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals.

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“…In one of the most popular of these mental logic theories, Braine (1990;Braine & O'Brien, 1991) assumed that these schemas constitute a natural logic that makes use of what he defined as primary skills. The inferences pertaining to these primary skills were assumed to be universal, often made more or less automatically and as a consequence essentially without errors by adults (Braine, Reiser, & Rumain, 1984). Concerning If, it was assumed that the primary skill corresponds to Modus Ponens: when two propositions of the form if p then q and p are available, the rule derives a conclusion of the form q.…”

Section: A Late Developmental Achievementmentioning

confidence: 99%

Probability in reasoning: A developmental test on conditionals

Barrouillet

Gauffroy

2015

Cognition

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a b s t r a c tProbabilistic theories have been claimed to constitute a new paradigm for the psychology of reasoning. A key assumption of these theories is captured by what they call the Equation, the hypothesis that the meaning of the conditional is probabilistic in nature and that the probability of If p then q is the conditional probability, in such a way that P(if p then q) = P(q|p). Using the probabilistic truth-table task in which participants are required to evaluate the probability of If p then q sentences, the present study explored the pervasiveness of the Equation through ages (from early adolescence to adulthood), types of conditionals (basic, causal, and inducements) and contents. The results reveal that the Equation is a late developmental achievement only endorsed by a narrow majority of educated adults for certain types of conditionals depending on the content they involve. Agerelated changes in evaluating the probability of all the conditionals studied closely mirror the development of truth-value judgements observed in previous studies with traditional truth-table tasks. We argue that our modified mental model theory can account for this development, and hence for the findings related with the probability task, which do not consequently support the probabilistic approach of human reasoning over alternative theories.

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Some Empirical Justification for a Theory of Natural Propositional Logic

Cited by 124 publications

References 20 publications

Tense, Aspect, and Temporal Reasoning

Tense, Aspect, and Temporal Reasoning

Conditionals: A theory of meaning, pragmatics, and inference.

Probability in reasoning: A developmental test on conditionals

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