Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out.The rough approximation of any fixed subset of the universe is the pair consisting of the best "open" approximation from the bottom and the best "closed" approximation from the top. The properties of this generalized rough approximation mapping are studied in the context of quasi-BZ lattice structures of "closed-open" ordered pairs (the "algebraic logic" of generalized rough set theory), comparing the results with the standard Pawlak approach. A particular weak form of rough representation is also studied.     

Reviews

Russell,Robert John, Murphy, Nancey and Peacocke, Arthur R. (eds) Chaos and Complexity: Scientific Perspectives on Divine Action
Tigue, John W. The Transformation of Consciousness in Myth: Integrating the Thought of Jung and Campbell     

Two Books for Teachers

Murphy, Nancey and Ellis, George F. R. On the Moral Nature of the Universe: Theology, Cosmology, and Ethics
Haught, John F. Science and Religion: From Conflict to Conversation     

ACADEMIC EFFECTS OF PROVIDING PEER SUPPORT IN GENERAL EDUCATION CLASSROOMS ON STUDENTS WITHOUT DISABILITIES

We studied the academic effects on peers without disabilities of serving as peer supports for students with disabilities in general education classrooms. Three peers were studied using a range of indicators, including academic engagement, coursework performance, and social validity assessments. Peers assisting a student with disabilities via curricular adaptation, assignment completion, and social facilitation constituted the multicomponent independent variable. We used withdrawal or multiple baseline designs to demonstrate positive benefits for peers for all measures used. In addition, follow-up data for 2 peers indicated that the positive changes associated with serving as a peer support were maintained for up to 2 months. Our results are discussed in relation to the possible academic and social effects of providing peer supports in general education classrooms for students with and without disabilities.     

Nodality effects during equivalence class formation: An extension to sight-word reading and concept development

Three students with moderate disabilities were taught to read and match-to-sample sight words comprising stimulus sets based upon the four food groups. We taught students conditional discriminations within four four-member sets using a single-sample/four-comparison procedure. Students were taught A-B, B-C, and C-D conditional discriminations for each of the four potential stimulus classes. Subsequent probes tested for relations based upon symmetry and one-node and two-node transitivity. The performances for all students indicated that symmetric relations emerged before one-node transitive relations, and that one-node transitive relations emerged before two-node transitive relations. These results are consistent with a pattern of responding, referred to as a "nodality effect," in which relations with fewer nodes are demonstrated prior to the demonstration of relations with a greater number of nodes. These results extend this area of research to sight-word reading for students with moderate disabilities.     

THE THEOLOGICAL ANTHROPOLOGY OF RALPH WENDELL BURHOE

Abstract. A central aim of Ralph Wendell Burhoe's scientific theology is to define and interpret the meaning of human existence in relation to “ultimate reality.” As such, it can be understood as an exercise in theological anthropology. For Burhoe, this ultimate reality is “nature,” understood as the total reality system which is studied by the sciences and which the sciences are showing to be the sole determiner of the way things are. This article discusses various aspects of Burhoe's theological anthropology, as well as its value and credibility, and raises questions concerning his understanding of the value of the individual and the problems of evil and human sinfulness.     

Comparing interspersed requests and social comments as antecedents for increasing student compliance

Two students were alternately presented with interspersed high-compliance requests and social comments as antecedents to low-compliance requests. An initial comparison demonstrated similar positive effects on compliance for interspersed requests and social comments. A second analysis indicated that the effectiveness of social comments for increasing compliance was related to the time interval between social comments and low-compliance requests.     

An advocacy intervention program for women with abusive partners: Six-month follow-up

Presented the 6-month follow-up findings of an experimental intervention designed to provide postshelter advocacy services to women with abusive partners. The intervention involved randomly assigning half the research participants to receive the free services of an advocate, 4 to 6 hours per week, for the first 10 weeks postshelter. One hundred forty-one battered women were interviewed about their experiences immediately upon their exit from a domestic violence shelter: 95% of the sample were interviewed 10 weeks thereafter (postintervention), and 93% were successfully tracked and interviewed 6 months later. At the 6-month follow-up, participants in both groups reported increased social support, increased quality of life, less depression, less emotional attachment to their assailants, and an increased sense of personal power. Although women in both groups reported some decrease in physical abuse over time, there were no statistically significant differences between those with and those without advocates, and abuse continued to be a problem for many women. Those who were still involved with their assailants continued to experience higher levels of abuse and had been more economically dependent upon the men prior to entering the shelter. Women who had worked with advocates continued to report being more satisfied with their overall quality of life than did the women in the control group. The authors thank the Editor and anonymous reviewers for their helpful comments. Thanks also to all present and past staff of the Community Advocacy Project, who helped in data collection and analyses. This work was supported by National Institute of Mental Health Grant 1R01 MH 44849.     

Teaching spontaneous requests to children with autism using a time delay procedure with multi-component toys

Children with autism were taught spontaneous requests through a time delay procedure. Unlike previous research, which usually employed food as the target stimuli to be requested, the present study used toy pieces from multi-component toys. The procedure involved presenting a child with the target stimulus, with the trainer prompting the child by immediately modeling the request response. When the response was imitated without error, prompting was delayed with the time interval gradually being increased over trials. A spontaneous or imitated response was reinforced by giving the child the requested object. As the stimulus/model interval increased, children with autism were expected to initiate the request by themselves prior to the prompt. The efficacy of the time delay procedure was assessed using a multiple baseline across subject design with three Chinese boys with autism. Results showed that the three children acquired a 100% performance within five to nine sessions of training and the skill was maintained at the one-month and three-month followups. Furthermore, the learned response transferred to various conditions when tested across setting, person, toy, and food items. These results suggest that toys, the multi-component ones in particular, served well as reinforcers for language training. Furthermore these findings confirmed the practical utility of the time delay procedure for promoting spontaneous communication skills in children with autism.