In the modal literature various notions of completeness have been studied for normal modal logics. Four of these are defined here, viz. (plain) completeness, first-order completeness, canonicity and possession of the finite model property — and their connections are studied. Up to one important exception, all possible inclusion relations are either proved or disproved. Hopefully, this helps to establish some order in the jungle of concepts concerning modal logics. In the course of the exposition, the interesting properties of first-order definability (...) and preservation under ultrafilter extensions are introduced and studied as well. (shrink)

In the Laura Ashworth case in 2008, the Human Tissue Authority considered itself bound to overturn a deceased daughter's alleged wish that one of her kidneys should go to her mother, who at the time had end stage kidney failure and was on dialysis. 12 This was so even though Laura's earlier wish to be a living donor would most likely have been authorised, had the formal assessment process begun. The decision provoked much criticism. The recent Department of Health document (...) Requested Allocation of a Deceased Donor Organ, published 29 March 2010, developed by the UK health administrations together with the HTA and NHS Blood and Transplant , which is the main organ allocation body in the UK, seeks to resolve this ethical dilemma by setting out the circumstances in which requests for such deceased donations may be acceptable. 3 The most important conditions appear to be:a. the donation must be unconditional in nature;b. there must be …. (shrink)

Transplantation research on samples and organs from deceased donors in England, Wales and Northern Ireland is under threat. The key problems relate to difficulties encountered in gaining consent for research projects, as distinct from consent to donation for clinical transplantation. They are due partly to the terms of the Human Tissue Act 2004 (the 2004 Act), and partly to its interpretation by the Human Tissue Authority (HTA). They include excessive interaction with donor representatives regarding ‘informed consent’ to research projects, uncertainty (...) as to the scope and duration of a donor's ‘authority’ over an organ, and restrictions caused by the apparent need for licensing of transplantation research under the 2004 Act, combined with lack of certainty, or guidance, as to the distinction between ‘research’, which requires a licence, and ‘service development’, which does not. In our view this confusion hinders and deters Specialist Nurses for Organ Donation in approaching donor representatives and discussing possible research projects with them. It has also, as we have reported elsewhere, led to abandonment of research projects for fear of liability, despite both Research Ethics Committee (REC) approval and donor consent. Such problems do not seem to occur under the transplant laws of most other comparable jurisdictions. The Transplantation Ethics Symposium, ‘The ethics of organ retrieval: goals, rights and responsibilities’, hosted by the MRC Centre for Transplantation at King's College London in December 2010, revealed that many senior clinicians and researchers, administrators, and lawyers are both unclear and in disagreement concerning the effects of the 2004 Act and the extent to which it is adhered to or ignored in practice. In this paper we examine the difficulties encountered and suggest solutions based on a less restrictive interpretation of the 2004 Act, or, more probably, a regulatory change under its authority. We propose that, in the long term, a law which includes consent for REC-approved research within the general consent for organ donation and transplantation seems preferable to the present system, both ethically and in practical terms. (shrink)

Gabbay has gathered an enormous amount of results; some of them important and novel, others important but already known, many rather routine, however. The organization of this material shows grave defects, both in the exposition and in its logical structure. Intensional logic appears as a vast collection of (often duplicated) loosely connected results. This may be a true reflection of the present state of the subject, but it does not contribute to a better understanding of it, let alone advance it.

We give in this paper a sufficient condition, cast in semantic terms, for Hallden-completeness in normal modal logics, a modal logic being said to be Hallden-complete (or Ήallden-reasonable') just in case for any disjunctive formula provable in the logic, where the disjuncts have no propositional variables in common, one or other of those disjuncts is provable in the logic.

In this study, complex dynamics of Briggs–Rauscher reaction system is investigated analytically and numerically. First, the Briggs–Rauscher reaction system is reduced into a new nonlinear parametric oscillator. The Melnikov method is used to derive the condition of the appearance of horseshoe chaos in the cases ω = Ω and ω ≠ Ω. The performed numerical simulations confirm the obtained analytical predictions. Second, the prediction of coexisting attractors is investigated by solving numerically the new nonlinear parametric ordinary differential equation via the (...) fourth-order Runge–Kutta algorithm. As results, it is found that the new nonlinear chemical system displays various coexisting behaviors of symmetric and asymmetric attractors. In addition, the system presents a rich variety of bifurcations phenomena such as symmetry breaking, symmetry restoring, period doubling, reverse period doubling, period-m bubbles, reverse period-m bubbles, intermittency, and antimonotonicity. On the contrary, emerging chaotic band attractors and period-1, period-3, period-9, and period-m bubbles routes to chaos occur in this system. (shrink)

This collection of essays, addresses, and one interview come from the years 1966-73 and cover a wide spectrum of interest, dealing with such general topics as 'The Absence of God in Modern Culture' and 'The Future of Christianity.'.