Martin D. S. Braine

Some Empirical Justification for a Theory of Natural Propositional Logic

Publisher Summary Within psychology, there are three approaches to the issue of the relation of logic to reasoning. One approach emphasizes nonlogical processes and biases. The second approach posits that subjects proceed by constructing a mental model of the information given and reason from the model. The third approach assumes that reasoning includes logical principles and that it has been the starting point for a substantial body of work in recent years. This chapter presents evidence supporting a particular repertory as the repertory of the kinds of inferences basic to the propositional reasoning of adults untutored in logic. The measures of the difficulty of direct reasoning problems can be predicted from the number of inferences of this repertory needed to solve a problem and can very well be predicted if the problem length and the kind of inference are also taken into account. The repertory was incorporated into a reasoning program that consists of a direct reasoning routine, coupled with some strategies to be used when the routine fails to solve a problem.

Development of comprehension of “or”: Evidence for a sequence of competencies ☆

Abstract Comprehension of various usages of “or” was investigated in children 5–6, 7–8, and 9–10 years old, and in college students. One task used imperatives containing “or.” and investigated the set union interpretation. In a second task, one puppet asserted a statement and another puppet contradicted it: subjects were asked whether both could be right, and whether one had to be right. A third task investigated the truth conditions for disjunctions. The fourth task presented reasoning problems that tested principles of inference involving “or.” It was found that all age groups, even the youngest, could make the logical inferences involving “or.” All age groups could also perceive contradictions, but subjects were less than unanimous that one of the puppets contradicting each other had to be right. Sensible truth judgments for disjunctions began to develop around 7–8 years. Set union was elicited in only a few adults. In general, except when it indicates set union, “or” is understood substantially earlier than the current literature suggests. Logical inference is one of the first uses in which children become competent, suggesting that the basic meaning of “or” is given by inference forms for reasoning with alternatives, not by truth conditions.

Responses to inconsistent premisses cannot count as suppression of valid inferences

Byrne (1989) claims to have demonstrated that context can suppress valid inferences like modus ponens. If substantiated, the claim would refute the idea that valid inferences cannot be countermanded without contradiction, although implicatures and invited inferences can be (e.g., Braine & Rumain, 1981; Geis & Zwicky, 1971; Grice, 1975). That, in turn, would invalidate one of the few available methods for distinguishing between inferences that are intuitively necessary and those that are merely implicated or invited. Thus, on conditional reasoning problems, Rumain, Connell, and Braine (1983) found that the common fallacies known as “denying the antecedent” and “asserting the consequent” can be suppressed by a kind of modification of the problem that leaves modus ponens untouched. Markovits (1984, 1985) has reported similar results. Byrne claims that by an essentially similar maneuver one can cause subjects to reject instances of modus ponens. She concludes that this sort of experimental maneuver provides no more reason for thinking that subjects have an inference rule for modusponens than that they have inference rules that generate the fallacies. We think that there are important differences between the problem modifications of Rumain et al. and of Byrne, and these lead us to dispute Byrne’s claims. In the experiment of Rumain et al. subjects reasoned about the content of a closed box. Some of the problems were ordinary conditional reasoning problems in that they presented a single conditional like:

Exploring language acquisition in children with a miniature artificial language: Effects of item and pattern frequency, arbitrary subclasses, and correction ☆

Abstract Very little of the artificial language experimentation in the literature has been done with children, although children are the primary target population to which experimenters wish to generalize. For this reason, we used children (7–10 years old) to explore the acquisition of a miniature artificial language with rules, patterns, subpatterns, and exceptions that are quite like those found in inflectional systems of natural languages. The first goal of the study was to explore two aspects of linguistic input—how frequency of presentation affects the relative roles of rote and rule or pattern learning, and the learnability of arbitrary subclasses. A second goal was to determine the effects of immediate corrective feedback on acquisition; and a third goal was to examine adult-child differences in learning. Overwhelmingly, the children learned via rules rather than by rote, but failed to distinguish the arbitrary subclasses. Frequency of presentation had specific effects on the acquisition of items and patterns. The immediacy of feedback had no significant effect on learning. Although there was a small (though significant) difference between the performance of the children and that of some adult subjects, overall, the results support the existence of a class of pattern learning skills that is common to children and adults and includes some aspects of syntax acquisition.

What sort of innate structure is needed to "bootstrap" into syntax?*

The paper starts from Pinkers theory of the acquisition of phrase structure; it shows that it is possible to drop all the assumptions about innate syntactic structure from this theory. These assumptions can be replaced by assumptions about the basic structure of semantic representation available at the outset of language acquisition, without penalizing the acquisition of basic phrase structure rules. Essentially, the role played by X-bar theory in Pinkers model would be played by the (presumably innate) structure of the language of thought in the revised parallel model. Bootstrapping and semantic assimilation theories are shown to be formally very similar, though making different primitive assumptions. In their primitives, semantic assimilation theories have the advantage that they can offer an account of the origin of syntactic categories instead of postulating them as primitive. Ways of improving on the semantic assimilation version of Pinkers theory are considered, including a way of deriving the NP-VP constituent division that appears to have a better fit than Pinkers to evidence on language variation.

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.

How does comprehension of passives develop? A comparison of actional and experiential verbs

Experiment I required first, third, and sixth graders to identify the actor or experiencer from active and passive sentences with actional and three subclasses of experiential verbs. Actional passives were understood better than experientials, with no difference among the subcategories of experiential verbs, and no effect of verb frequency or regularity. Response distributions for each verb type did not show two populations of subjects – one knowing and the other not knowing the passive – but approximately unimodal distributions whose mean increased with age. Experiment II studied preschoolers. Again, the actional passives were systematically easier than the experientials, and again, for neither verb type did the response distributions show two distinct subject populations, one competent and the other incompetent. The forms of the distributions cannot be wholly accounted for by fluctuating attention to cues to passivization, but indicate that many children have partial knowledge of the passive (increasing with age). A hypothesis about the nature of this partial knowledge accounts for the gradual acquisition and the difference between the verb types.

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 Phonological and Metaphonological Representation of Speech: Evidence from Fluent Backward Talkers

Abstract The psychological representation of phonemes and syllables was examined with a special group of subjects who voluntarily and rapidly rearrange speech units (i.e., “talk backward”). Each subject clearly used a primarily sound- or spelling-based representation to talk backward, and the present work focused on the sound-based skill. Backward speech differed from a total acoustic reversal: 12 subjects reordered phonemic units, and one reordered syllables. These speech units proved to be abstract to some degree, and hierarchically organized. However, the representation used in backward speech differed from the primary phonological system. It appeared to be a metaphonological system based on phonology but occasionally influenced also by orthography. Phonological principles seem to set lower limits for the size of units, and orthographic principles seem to set upper limits. A model of speech processing that includes both a primary, phonological, and a secondary, metaphonological level of representation is proposed.

Length constraints, reduction rules, and holophrastic processes in children's word combinations

Examination indicates that there is no real evidence that the apparently elliptical character of many early word combinations is due to deletion of content, or that there is a performance constraint that prevents children producing the longer utterances that their grammars could generate. Evidence is presented that questions the presumption, implicit in the length-constraint claim, that a constituent is less likely to be expanded (without deletion) when there are co-occurring constituents. The special character of both early word combinations and holophrases is explained by a lexical-insertion process in which a word representing a salient feature of the communication is inserted into an inappropriately high node, because the child lacks complete control of rules to realize the communication more fully.