Predicting intermediate and multiple conclusions in propositional logic inference problems: Further evidence for a mental logic. (original) (raw)
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Psychological Review, 1994
argue that the mental model theory of prepositional reasoning is easy to refute, and they report 3 experiments that they believe falsify the theory. In contrast, Bonatti argues that the model theory is too flexible to be falsified. We show that O'Brien et al.'s experiments do not refute the model theory and that Bonatti's claims are ill founded. Formal rule theories of prepositional reasoning have 3 major weaknesses in comparison with the model theory: (a) They have no decision procedure; (b) they lack predictive power, providing no account of several robust phenomena (e.g., erroneous conclusions tend to be consistent with the premises); and (c) as a class of theories, they are difficult to refute experimentally.
Psychol Rev, 1994
argue that the mental model theory of prepositional reasoning is easy to refute, and they report 3 experiments that they believe falsify the theory. In contrast, Bonatti argues that the model theory is too flexible to be falsified. We show that O'Brien et al.'s experiments do not refute the model theory and that Bonatti's claims are ill founded. Formal rule theories of prepositional reasoning have 3 major weaknesses in comparison with the model theory: (a) They have no decision procedure; (b) they lack predictive power, providing no account of several robust phenomena (e.g., erroneous conclusions tend to be consistent with the premises); and (c) as a class of theories, they are difficult to refute experimentally.
Human Reasoning is Both Logical and Pragmatic
Intellectica. Revue de l'Association pour la Recherche Cognitive, 1991
Although several prominent critics have argued against any significant role for a logical or mathematical competence in human reasoning, we argue that such a competence is basic. Our approach to logical reasoning consists of (a) a basic set of inference schémas for logical particles such as if, and, not, and or that accounts for competence, (b) a reasoning program that implements them, and (c) a set of independently motivated pragmatic principles. We describe evidence that supports our approach, and then discuss several prominent arguments that have been made against competence models. We conclude that the critics have not established their case ; rather, reasoning errors seem to result from strategic and pragmatic demands that are beyond the scope of a basic competence. Finally, we discuss text comprehension as a case study of how logical and pragmatic processes work together in a single line of reasoning to provide a coherent and integrated representation. pragmatic processes work...
Reasoning Processes in Propositional Logic
Journal of Logic, …, 2010
We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who classified the formula correctly before timeout (accuracy) and the mean response time among those participants (latency). We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies (p < .0001). For tautologies the correlation between latency and minimum proof length in T was .89 and for non-tautologies the correlation between latency and minimum proof length in NT was .87.
An experimental study on pragmatic inferences: Processing implicatures and presuppositions
1 There is a restricted sense of the term 'linguistic' which would not include GCI inferences, because in a sense pragmatic inference arises from non-linguistic convention (presuppositions, however, would still be included). Nevertheless, GCIs are accounted for by a theory of human communication and can be considered to be triggered by the rational design of human reasoning. Thus they are in the broad use of the term of 'linguistic' origin.
Cognitive Psychology, 1985
We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals (must, can) totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain.
A Mixed Rasch Model of Dual-Process Conditional Reasoning Draft June 1, 2006 - Please do not quote
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, denying the antecedent, and modus tollens syllogisms featuring the same conditional; and (b) the average rate of determinate answers to , , and . 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.