Strong Boethius’ Thesis and Consequential Implication

The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying Aristotle's Thesis (p does not imply not p ) and Weak Boethius' Thesis (if p implies q, then p does not imply not q ). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of Strong Boethius' Thesis (that p implies q implies that p does not imply not q) is identified.     

Inverses for Normal Modal Operators

Given a 1-ary sentence operator , we describe L - another 1-ary operator - as as a left inverse of in a given logic if in that logic every formula is provably equivalent to L. Similarly R is a right inverse of if is always provably equivalent to R. We investigate the behaviour of left and right inverses for taken as the operator of various normal modal logics, paying particular attention to the conditions under which these logics are conservatively extended by the addition of such inverses, as well as to the question of when, in such extensions, the inverses behave as normal modal operators in their own right.     

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.     

A Comparison of Active Student Response and On-Task Instruction on the Acquisition and Maintenance of Health Facts by Fourth Grade Special Education Students

An alternating treatments design was used to compare the effects of active student response (ASR) and on-task (OT) instruction on the acquisition and maintenance of health facts during small-group lessons. Five students with learning difficulties (4 students identified as developmentally handicapped and 1 student identified as learning disabled) participated in daily instruction on weekly sets of 20 unknown health facts (10 facts assigned to the ASR condition and 10 to the OT condition). During ASR instruction, the teacher modeled the correct response to a health question that was presented visually on a health fact card, and the students immediately repeated the correct response in unison three times. During OT instruction, students attended visually to the health fact card as the teacher modeled the correct response. All 5 students made more correct responses on end-of-day tests on health facts taught with ASR instruction than they did on health facts taught with OT instruction. ASR instruction also produced consistently superior results on maintenance tests administered 2 weeks after instruction.     

Effects of Self-Correction on the Acquisition, Maintenance, and Generalization of the Written Spelling of Elementary School Children

We examined the effect of self-correction on the acquisition, maintenance, and generalization of written spelling of elementary school students attending an after-school clinic. Six students registered for remedial tutoring participated. During self-correction, students initially learned four proofreading marks and a procedure for using them that were subsequently applied as the students compared their spelling to a model. Results showed a functional effect between self-correction and improved student performance on target words. Using the self-correction procedure, the students spelled at least 98% of the target words accurately, maintained at least 85% of the correctly spelled words, and generalized at least 70% of the words at home, in context, and with word variations. Questionnaires administered to the students, their parents, and teachers indicated that students preferred self-correction. Parents noticed academic improvements in their child's spelling performance as well as positive changes in attitude toward school. Most teachers did not notice changes in spelling performance or attitude.     

REDUCING ESCAPE BEHAVIOR AND INCREASING TASK COMPLETION WITH FUNCTIONAL COMMUNICATION TRAINING,EXTINCTION AND RESPONSE CHAINING

The effects of functional communication training, extinction, and response chaining on 3 subjects' escape-maintained aberrant behavior were evaluated using a multielement design. Functional communication training consisted of teaching subjects a verbal response that was functionally equivalent to their aberrant behavior. Subjects initially were allowed to escape from a task contingent on the trained verbal response. In subsequent treatment phases, escape was contingent on the trained verbal response plus the completion of the specified number of steps in the task (response chaining). The number of steps was increased until a subject completed the task to obtain a break. Results showed that the treatment reduced rates of aberrant behavior and that the chaining procedure was effective in decreasing the availability of escape.     

The recollective experience of cross-modality confusion errors

There are at least two qualitatively different types of subjective experience that can accompany accurate recognition memory. Sometimes recognition is accompanied by conscious recollection of the learning episode (i.e., it isremembered), and in other cases it is not (i.e., it is simplyknown that the item is old). In the present study, we assessed the subjective experience that accompanies crossmodality confusion errors (misidentifying words as pictures) by measuring the extent to which subjects claimed toremember versusknow that the item was presented as a picture. The results of two experiments demonstrate that cross-modality confusion errors are often accompanied by conscious recollection, although not to the same extent as accurate memories. The findings also show that there is considerable overlap in the recollective experience that accompanies accurate and erroneous memories. Finally, the results support the contention that recollective experience cannot be directly inferred from test performance.     

The role of fairness orientation and supervisor attributions in absence disciplinary decisions

The present study investigated the role of the work value of fairness and attributions regarding the causes of absence in supervisor disciplinary decisions. It was hypothesized that supervisors who valued fairness, and those who made internal attributions regarding the cause of a particular absence incident, render more severe disciplinary decisions than supervisors who value fairness less, and who make external attributions. Furthermore, it was hypothesized that the degree to which supervisors valued fairness moderates the relationship between external attributions and the severity of disciplinary decisions. Using a policy capturing approach, results were consistent with predictions. Implications of the results for research and practice are discussed.