Multiple -conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks (...) the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions. (shrink)

Does South Africa need a common moral language? Many people are of the opinion that South Africa finds itself 'after Babel’ and needs a common moral language (1). The author considers some of the arguments of people who disagree with this analysis, because they do not define the problem in this way (2); because they find the language- or Babel-methaphor confusing (3); because they agree with the description of the problem, but not with the suggested solution, namely a common moral (...) language (4); or because they accept the solution, but do not regard it as the proper task of the Christian church to be involved in this search for a common moral language (5). (shrink)

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field.

The physician-patient relationship has changed over the last several decades, requiring a systematic reevaluation of the competing demands of patients, physicians, and families. In the era of genetic testing, using a model of patient care known as the family covenant may prove effective in accounting for these demands. The family covenant articulates the roles of the physician, patient, and the family prior to genetic testing, as the participants consensually define them. The initial agreement defines the boundaries of autonomy and benefit (...) for all participating family members. The physician may then serve as a facilitator in the relationship, working with all parties in resolving potential conflicts regarding genetic information. The family covenant promotes a fuller discussion of the competing ethical claims that may come to bear after genetic test results are received. (shrink)