On Categorical Equivalences of Commutative BCK-algebras

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G ₀), where G is an Abelian ℓ-group, G ₀ is a subset of the positive cone generating G ⁺ such that if u, v ∈ G ₀, then 0 ∨ (u - v) ∈ G ₀, and morphisms are ℓ-group homomorphisms h: (G, G ₀) → (G′,G′₀) with f(G ₀) ⫅ G′₀. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). This revised version was published online in June 2006 with corrections to the Cover Date.     

Generalization in a child's oppositional behavior across home and school settings

A 9-year-old clinic-referred boy, his mother, and his teacher were observed in 38 home and 38 school sessions on the same days. Categories of the boy's oppositional behavior and the inappropriate social attention of his mother and teacher were graphed to visually inspect changes during baseline, a parent-training phase, a follow-up phase, and a final parent-training booster phase. Parent-training phases produced reductions in the mother's inappropriate attention and in the boy's oppositional behavior, whereas the follow-up and baseline phases were associated with higher rates of these categories. Generalization occurred in the school across these home phases, as seen in the increase in rates of the boy's problem behavior, despite the lack of change in his teacher's attention. Correlational analyses of proportion scores reflecting the boy's home-school oppositional behavior and mother-teacher social attention suggested his responsiveness to relative changes in adult social contingencies across settings.     

Promoting response variability and stimulus generalization in martial arts training

The effects of reinforcement and extinction on response variability and stimulus generalization in the punching and kicking techniques of 2 martial arts students were evaluated across drill and sparring conditions. During both conditions, the students were asked to demonstrate different techniques in response to an instructor's punching attack. During baseline, the students received no feedback on their responses in either condition. During the intervention phase, the students received differential reinforcement in the form of instructor feedback for each different punching or kicking technique they performed during a session of the drill condition, but no reinforcement was provided for techniques in the sparring condition. Results showed that both students increased the number of different techniques they performed when reinforcement and extinction procedures were conducted during the drill condition, and that this increase in response variability generalized to the sparring condition.     

Refining the experimental analysis of academic skills deficits: Part I. An investigation of variables that affect generalized oral reading performance

Experimental analyses for improving reading fluency deficits have rarely targeted generalized increases in academic responding. As a consequence, the variables that may help students to generalize newly learned forms of academic responding like reading are not well understood. Furthermore, experimental analyses of reading fluency interventions have not systematically examined difficulty level as a variable that may affect instructional outcomes. The experiment reported in this paper expands (a) the measurement of the dependent variables to include generalized increases across tasks (reading passages) and (b) the combination of independent variables used to produce measurable generalized increases. The results demonstrate the importance of combining reward and instructional variables (including difficulty level) to produce generalized increases and how those variables can be meaningfully investigated prior to making treatment recommendations.     

Behavioral treatment of children with phonological disorder: the efficacy of vocal imitation and sufficient-response-exemplar training

This study examined whether sufficient-response-exemplar training of vocal imitation would result in improved articulation in children with phonological disorder, and whether improved articulation established in the context of vocal imitation would transfer to other verbal classes such as object naming and conversational speech. Participant 1 was 6 years old and attended first grade in a regular public school. Participant 2 was 5 years 4 months old and attended a public kindergarten. Both participants had normal hearing and no additional handicaps. A multiple baseline design across behaviors (target sounds or blends) was employed to examine whether the vocal imitation training resulted in improved articulation. Results showed that both participants improved articulation once training was implemented, and that the improved articulation transferred from vocal imitation to more natural speech such as object naming and conversational speech. Improvement established during training was maintained posttraining and at a 6-month follow-up.     

Recombinative generalization of within-syllable units in nonreading adults with mental retardation

Two adults with mental retardation demonstrated the recombination of within-syllable units (onsets and rimes) using a spoken-to-printed-word matching-to-sample (MTS) procedure. Further testing with 1 participant showed comprehension of the printed words. Printed-word naming was minimal before, but greater after, comprehension tests. The findings suggest that these procedures hold promise for further basic and applied analyses of word-attack skills.     

Visual field differences in spatial frequency discrimination

Subjects discriminated between sine-wave gratings that differed by either +/-0.125 octaves (small difference) or +/-1.0 octaves (large difference). Baseline stimuli consisted of either 1.0 or 4.0 cycles per degree gratings. A left visual field advantage was obtained for the small difference in frequency, with no visual field advantages for the large difference in frequency. Similarly, moderate support for right versus left visual field advantages in processing high versus low spatial frequencies was found, although these interactions were not statistically significant. The results are discussed in light of Kosslyn's (1987) categorical and coordinate framework.     

TRAINING AND GENERALIZATION OF SEXUAL ABUSE PREVENTION SKILLS FOR WOMEN WITH MENTAL RETARDATION

Previous research has shown that behavioral skills training to teach sexual abuse prevention skills to women with mental retardation results in skill acquisition but poor generalization. In this investigation we evaluated procedures for enhancing generalization following training. Five women with mental retardation received 10 behavioral skills training sessions followed by in situ training when the skills did not fully generalize. Behavioral skills training resulted in skill acquisition and in situ training produced generalized responding during naturalistic assessments.     

Self-Constitution in the Ethics of Plato and Kant

Plato and Kant advance a constitutional model of the soul, in which reason and appetite or passion have different structural and functional roles in the generation of motivation, as opposed to the familiar Combat Model in which they are portrayed as independent sources of motivation struggling for control. In terms of the constitutional model we may explain what makes an action different from an event. What makes an action attributable to a person, and therefore what makes it an action, is that it issues from the person's constitution, and therefore from the person as a whole, rather than from some force working on or in the person. This in turn implies an account of what makes an action good: what makes an action good is that it is deliberated upon and chosen in a way that unifies the person into a constitutional system. Through deliberative action we constitute ourselves as unified agents. Platonic justice and Kant's categorical imperative are shown to be normative standards for action because they are principles of self-constitution.