Rules in relevant logic — II: Formula representation

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A ₁ .A ₂ . ... .A _n B, the conjunctive form,A ₁&A ₂ & ...A _n B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A ₁&A ₂& ...A _n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C.I acknowledge help from anonymous referees for guidance in preparing Part II, and especially for the suggestion that Theorem 9 could be expanded to fully contraction-less logics.     

Mathematica: A flexible design environment for neural networks

Several neural networks were developed inMathematica in order to explore the role of “spiky” neurons in neural network memory simulations. UsingMathematica for this task confirmed its value as a powerful tool for neural network development: It exhibited distinct advantages over other environments in programming ease, flexibility of data structures, and the graphical assessment of network performance.     

Need probability affects retention: A direct demonstration

Recent memory theory has emphasized the concept ofneed probability—that is, the probability that a given piece of learned information will be tested at some point in the future. It has been proposed that, in real-world situations, need probability declines over time and that the memory-loss rate is calibrated to match the progressive reduction in need probability (J. R. Anderson & Schooler, 1991). The present experiments were designed to examine the influence of the slope of the need-probability curve on the slope of the retention curve. On each of several trials, subjects memorized a list of digits, then retained the digits in memory for 1, 2, 4, 8, or 16 sec. Some trials ended with a recall test; other trials ended with the message, “no test.” In Experiment 1, the likelihood of encountering a memory test (i.e., the need probability) was made to either increase or decrease as the retention interval increased; in Experiment 2, need probability either was flat (invariant across retention intervals) or decreased as the retention interval increased. The results indicated that the shape of the need-probability curve influenced the slope of the retention curve (Experiment 1) and that the effect became larger as the experimental session progressed (Experiment 2). The findings support the notion that memory adapts to need probabilities and that the rate of forgetting is influenced by the slope of the need-probability curve. In addition, all of the forgetting curves approximated a power function, suggesting that need probability influences the slope but not the form of forgetting.     

EFFECTS OF HIGH-PROBABILITY REQUESTS ON THE SOCIAL INTERACTIONS OF YOUNG CHILDREN WITH SEVERE DISABILITIES

High-probability requests were used to increase social interactions in 3 young boys with severe disabilities who had been identified as severely socially withdrawn. A multiple baseline design across participants was used to evaluate the effects of high-probability request intervention on (a) social initiations, (b) social responses, (c) continued interactions, and (d) performance of high- and low-probability requests. The students were observed in a second setting to examine generalization effects across peers who did not participate in the training sequence and settings. The results demonstrated that the high-probability requests increased the students' responsiveness to low-probability requests to initiate social behavior. Increases were also found in (a) unprompted initiations and extended interactions to the training peers, (b) unprompted initiations and extended interactions to peers who were not involved in the training procedure, and (c) generalized unprompted initiations and interactions in a second nontraining setting. The students maintained increased levels of initiations and interactions after all prompts were removed from both the training and nontraining settings.     

Piaget and Vygotsky Revisited: Dialogue or Assimilation?

In response to suggestions for merging Piagetian and Vygotskian psychology on the basis of their apparent similarity (e.g., Glassman, 1994), it is argued that numerous differences between the two paradigms constitute fundamental principled disagreements, and that these ought not to be minimized or simplified. Some fundamental differences involve underlying philosophy, social influences on development, the nature of the developmental process itself, developmental stages, and universality of cognitive structures. It is argued that a project of combining Piagetian and Vygotskian psychology would be premature at best, and that continued dialogue between these two distinct perspectives would be of greater value.     

Target and nontarget grouping in visual search

Results recently reported by Driver, McLeod, and Dienes (1992) are used to contrast three accounts of visual search—in particular, their mechanism for easy conjunction search. In the Driver et al. study, the target was defined by a conjunction of form and movement; the key manipulation was phase in both target and nontarget motion sets. Mechanisms working separately on each display element (inhibition from nontarget features, facilitation from target features) are unable to explain large effects of phase, since this is defined only by relationships between one element and another. As implemented in the guided search model of Cave and Wolfe (1990), local suppression between similar elements is also unable to account for the results. More promising is an approach based on perceptual grouping: Elements moving in phase can be selected (target motion) or rejected (nontarget motion) as a group. Rather than a bias against elements that are similar to or grouped with their neighbors, there is a bias to treat grouped elements together.     

On the application of J.M. Keynes's approach to decision making

It is shown that J. M. Keynes was the originator of what is called a weighted monetary value (WMV) approach to decision making under uncertainty and risk as opposed to either the expected monetary value (EMV) or subjective expected utility (SEU) approaches.     

Self-esteem and Rogers' core conditions in close friends: A latent variable pathanalysis of panel data

A LISREL or path analysis with latent variables was used to test the Rogerian-derived hypothesis that self-esteem is determined by the degree to which a person has a current close friend who is seen to be unconditionally accepting, empathic, and congruent. The revised Barrett-Lennard (1964) Relationship Inventory and Rosenberg (1965) Self-Esteem Scale were completed by 38 female and 28 male students on two occasions 15 weeks apart. The hypothesis was conjimzed for unconditionality of acceptance (which was positive) and the core conditions combined. In addition, the temporal relationships between the core conditions were analysed. Level of acceptance was reciprocally related to both empathy and congruence, while prior congruence had a negative but nonsignajicant association with unconditionality of acceptance.