On the Algebraizability of the Implicational Fragment of Abelian Logic

In this paper we consider the implicational fragment of Abelian logic \({{{\sf A}_{\rightarrow}}}\) . We show that although the Abelian groups provide an semantics for the set of theorems of \({{{\sf A}_{\rightarrow}}}\) they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi (Mem Am Math Soc 77, 1989). In the second part of the paper, we investigate an extension of \({{{\sf A}_{\rightarrow}}}\) in the same language and having the same set of theorems and show that this new consequence relation is algebraizable with the Abelian groups as its equivalent algebraic semantics. Finally, we show that although \({{{\sf A}_{\rightarrow}}}\) is not algebraizable, it is order-algebraizable in the sense of Raftery (Ann Pure Appl Log 164:251–283, 2013).     

Family therapy in primary health care: Skills training and outcome evaluation

Some of the theoretical tenets of family therapy such as emphasis on the activation and utilization of existing family resources and the importance it accords to context appear to have a good fit with primary health care's commitment to empowering individuals in their struggle against ill health and the circumstances in which it occurs. This paper explores the possibility of teaching a problem-solving approach to family therapy to nurses in a South African primary health care system. Training consisted of conceptual, pragmatic, and self-growth exercises, and trainees' conceptual and performance skills were compared to the skills of a group of untrained nurses.We thank Bukelwa Selema, co-trainer on the program, for her contributions to joining effectively with the nurses and enriching the experiential process. We also thank Dr. P.J. Beukes, Dr. J.H. Olivier, Dr. G.M. Louw, Matron L.C. Langley and other staff in the Soweto primary health care system for their support. In particular, we are grateful to nursing sisters Martha Nkoane and Millicent Matomela, who roleplayed clients on the videotaped training modules. We are also grateful to Edcent Williams, who was one of the videotape raters, and Mike Spruce, Ricky Snyders, Nico Cloete, Ricky Mauer, and Brenda Radebe for their inputs at various stages of designing and implementing the programme.     

Naïve Comprehension and Contracting Implications

In his paper [6], Greg Restall conjectured that a logic supports a naïve comprehension scheme if and only if it is robustly contraction free, that is, if and only if no contracting connective is definable in terms of the primitive connectives of the logic. In this paper, we present infinitely many counterexamples to Restall's conjecture, in the form of purely implicational logics which are robustly contraction free, but which trivialize naïve comprehension.