We introduce and study the D-model, which reflects the simplest situation in which one wants to calibrate an observable. We discuss the question of representing the statistics of the D-model in the context of an effect algebra.

A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.

The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.

We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.

We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two.

A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.

Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a (...) direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice. (shrink)

A Heyting effect algebra (HEA) is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its universal group has the central comparability and central Rickart properties.

A Heyting effect algebra is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its universal group has the central comparability and central Rickart properties.

" Waldie speculates on the meanings and implications of the snapshots in this book and of snapshots generally, which he sees as expressions of "the hunger of memory.".

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)

We propose an alternative resolution of Simpson's paradox in multiple classification experiments, using a different maximum likelihood estimator. In the center of our analysis is a formal representation of free choice and randomization that is based on the notion of incompatible measurements.We first introduce a representation of incompatible measurements as a collection of sets of outcomes. This leads to a natural generalization of Kolmogoroff's axioms of probability. We then discuss the existence and uniqueness of the maximum likelihood estimator for a (...) probability weight on such a generalized sample space, given absolute frequency data.As a first example, we discuss an estimation problem with censured data that classically admits only biased ad hoc estimators.Next, we derive an explicit solution of the maximum likelihood estimation problem for a large class of experiments that arise from various kids of compositions of sample spaces. We identify the (categorical) direct sum of sample spaces as a representation of “free choice,” and the (categorical) direct product as a representation of “randomization.”Finally, we apply the foregoing discussion to the case of multiple classification experiments in order to show that there is no Simpson's paradox if the difference between free choice and randomization is recognized in the structure of the experiment.A comparison between our new estimator and the “usual” calculation can be summarized as follows: Pooling the data over one classification factor in the “usual” way in fact destroys or ignores the information contained in it, whereas our proposed maximum likelihood estimator is a proper marginal over this factor that “averages out” the information contained in it. The estimators agree with each other in the case of proportional sample sizes. (shrink)

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)

Recent studies using functional magnetic resonance imaging of patients in a vegetative state have raised the possibility that such patients retain some degree of consciousness. In this paper, the ethical implications of such findings are outlined, in particular in relation to decisions about withdrawing life-sustaining treatment. It is sometimes assumed that if there is evidence of consciousness, treatment should not be withdrawn. But, paradoxically, the discovery of consciousness in very severely brain-damaged patients may provide more reason to let them die. (...) Although functional neuroimaging is likely to play an increasing role in the assessment of patients in a vegetative state, caution is needed in the interpretation of neuroimaging findings. (shrink)

Background: The traditional approach to resolving ethics concerns may not address underlying organisational issues involved in the evolution of these concerns. This represents a missed opportunity to improve quality of care “upstream”. The purpose of this study was to understand better which organisational issues may contribute to ethics concerns. Methods: Directed content analysis was used to review ethics consultation notes from an academic children’s hospital from 1996 to 2006 (N = 71). The analysis utilised 18 categories of organisational issues derived (...) and modified from published quality improvement protocols. Results: Organisational issues were identified in 68 of the 71 (96%) ethics consult notes across a range of patient settings and reasons for consultation. Thirteen of the 18 categories of organisational issues were identified and there was a median of two organisational issues per consult note. The most frequently identified organisational issues were informal organisational culture (eg, collective practices and approaches to situations with ethical dimensions that are not guided by policy), policies and procedures (eg, staff knows policy and/or procedural guidelines for an ethical concern but do not follow it) and communication (eg, communication about critical information, orders, or hand-offs repeatedly does not occur among services). Conclusions: Organisational issues contribute to ethical concerns that result in clinical ethics consults. Identifying and addressing organisational issues such as informal culture and communication may help decrease the recurrence of future similar ethics concerns. (shrink)

We bring out the fact that the essential new quality implied by the quantum theory is nonlocality; i.e., that a system cannot be analyzed into parts whose basic properties do not depend on the state of the whole system. This is done in terms of the causal interpretation of the quantum theory, proposed by one of us (D.B.) in 2952, involving the introduction of the “quantum potential.” We show that this approach implies a new universal type of description, in which (...) the standard or canonical form is always supersystem-system-subsystem; and this leads to the radically new notion of unbroken wholeness of the entire universe. Finally, we discuss some of the implications of extending these notions to the relativity domain, and in so doing, we indicate a novel concept of time, in terms of which relativity and quantum theory may eventually be brought together. (shrink)