Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi

We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. Here we adapt the method to a more general external formalism of labelled sequents and provide sufficient criteria on the Kripke-frame characterization of a logic that guarantee the IPs. In particular, we show that classes of frames definable by quantifier-free Horn formulas correspond to logics with the IPs. These criteria capture the modal cube and the infinite family of transitive Geach logics

AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs

Greater incidence of depression with hypnotic use than with placebo

Abstract Background Although it has been claimed that insomnia causes an increased risk for depression, adequate controlled trials testing this hypothesis have not been available. This study contrasted the incidence of depression among subjects receiving hypnotics in randomized controlled trials versus those receiving placebo. Methods The incidence of depression among patients randomized to hypnotic drugs or placebo was compiled from prescribing information approved by the United States Food and Drug Administration (FDA) and from FDA New Drug Application documents. Available data for zolpidem, zaleplon, eszopiclone, and ramelteon were accessed. Results Data for 5535 patients randomized to a hypnotic and for 2318 randomized to placebo were compiled. The incidence of depression was 2.0% among participants randomized to hypnotics as compared to 0.9% among those randomized in parallel to placebo (p Conclusion Modern hypnotics were associated with an increased incidence of depression in data released by the FDA. This suggests that when there is a risk of depression, hypnotics may be contra-indicated. Preventive treatments such as antidepressant drugs, cognitive-behavioral therapy, or bright light might be preferred. Limitations in the FDA data prevented a formal meta-analysis, and there was a lack of information about drop-out rates and definitions of depression. Trials specifically designed to detect incident depression when treating insomnia with hypnotic drugs and better summarization of adverse events in trials submitted to the FDA are both necessary.</p

Time to Scale Up Preexposure Prophylaxis Beyond the Highest-Risk Populations? Modeling Insights From High-Risk Women in Sub-Saharan Africa

OBJECTIVES: New HIV infections remain higher in women than men in sub-Saharan Africa. Preexposure prophylaxis (PrEP) is an effective HIV prevention measure, currently prioritized for those at highest risk, such as female sex workers (FSWs), for whom it is most cost-effective. However, the greatest number of HIV infections in sub-Saharan Africa occurs in women in the general population. As countries consider wider PrEP scale-up, there is a need to weigh the population-level impact, cost, and relative cost-effectiveness to inform priority setting. METHODS: We developed mathematical models of HIV risk to women and derived tools to highlight key considerations for PrEP programming. The models were fitted to South Africa, Zimbabwe, and Kenya, spanning a range of HIV burden in sub-Saharan Africa. The impact, cost, and cost-effectiveness of PrEP scale-up for adolescent girls and young women (AGYW), women 25 to 34 years old, and women 35 to 49 years old were assessed, accounting for differences in population sizes and the low program retention levels reported in demonstration projects. RESULTS: Preexposure prophylaxis could avert substantially more infections a year among women in general population than among FSW. The greatest number of infections could be averted annually among AGYW in South Africa (24-fold that for FSW). In Zimbabwe, the greatest number of infections could be averted among women 25 to 34 years old (8-fold that for FSW); and in Kenya, similarly between AGYW and women 25 to 34 years old (3-fold that for FSW). However, the unit costs of PrEP delivery for AGYW, women 25 to 34 years old, and women 35 to 49 years old would have to reduce considerably (by 70.8%-91.0% across scenarios) for scale-up to these populations to be as cost-effective as for FSW. CONCLUSIONS: Preexposure prophylaxis has the potential to substantially reduce new HIV infections in HIV-endemic countries in sub-Saharan Africa. This will necessitate PrEP being made widely available beyond those at highest individual risk and continued integration into a range of national services and at community level to significantly bring down the costs and improve cost-effectiveness

Bright green light treatment of depression for older adults [ISRCTN69400161]

BACKGROUND: Bright white light has been successfully used for the treatment of depression. There is interest in identifying which spectral colors of light are the most efficient in the treatment of depression. It is theorized that green light could decrease the intensity duration of exposure needed. Late Wake Treatment (LWT), sleep deprivation for the last half of one night, is associated with rapid mood improvement which has been sustained by light treatment. Because spectral responsiveness may differ by age, we examined whether green light would provide efficient antidepressant treatment in an elder age group. METHODS: We contrasted one hour of bright green light (1,200 Lux) and one hour of dim red light placebo (<10 Lux) in a randomized treatment trial with depressed elders. Participants were observed in their homes with mood scales, wrist actigraphy and light monitoring. On the day prior to beginning treatment, the participants self-administered LWT. RESULTS: The protocol was completed by 33 subjects who were 59 to 80 years old. Mood improved on average 23% for all subjects, but there were no significant statistical differences between treatment and placebo groups. There were negligible adverse reactions to the bright green light, which was well tolerated. CONCLUSION: Bright green light was not shown to have an antidepressant effect in the age group of this study, but a larger trial with brighter green light might be of value

Mortality Risk of Hypnotics: Strengths and Limits of Evidence

Sleeping pills, more formally defined as hypnotics, are sedatives used to induce and maintain sleep. In a review of publications for the past 30 years, descriptive epidemiologic studies were identified that examined the mortality risk of hypnotics and related sedative-anxiolytics. Of the 34 studies estimating risk ratios, odds ratios, or hazard ratios, excess mortality associated with hypnotics was significant (p &lt; 0.05) in 24 studies including all 14 of the largest, contrasted with no studies at all suggesting that hypnotics ever prolong life. The studies had many limitations: possibly tending to overestimate risk, such as possible confounding by indication with other risk factors; confusing hypnotics with drugs having other indications; possible genetic confounders; and too much heterogeneity of studies for meta-analyses. There were balancing limitations possibly tending towards underestimates of risk such as limited power, excessive follow-up intervals with possible follow-up mixing of participants taking hypnotics with controls, missing dosage data for most studies, and over-adjustment of confounders. Epidemiologic association in itself is not adequate proof of causality, but there is proof that hypnotics cause death in overdoses; there is thorough understanding of how hypnotics euthanize animals and execute humans; and there is proof that hypnotics cause potentially lethal morbidities such as depression, infection, poor driving, suppressed respiration, and possibly cancer. Combining these proofs with consistent evidence of association, the great weight of evidence is that hypnotics cause huge risks of decreasing a patient's duration of survival

Intuitionistc probability and the Bayesian objection to dogmatism

Given a few assumptions, the probability of a conjunction is raised, and the probability of its negation is lowered, by conditionalising upon one of the conjuncts. This simple result appears to bring Bayesian confirmation theory into tension with the prominent dogmatist view of perceptual justification – a tension often portrayed as a kind of ‘Bayesian objection’ to dogmatism. In a recent paper, David Jehle and Brian Weatherson observe that, while this crucial result holds within classical probability theory, it fails within intuitionistic probability theory. They conclude that the dogmatist who is willing to take intuitionistic logic seriously can make a convincing reply to the Bayesian objection. In this paper, I argue that this conclusion is premature – the Bayesian objection can survive the transition from classical to intuitionistic probability, albeit in a slightly altered form. I shall conclude with some general thoughts about what the Bayesian objection to dogmatism does and doesn’t show

Can Modal Skepticism Defeat Humean Skepticism?

My topic is moderate modal skepticism in the spirit of Peter van Inwagen. Here understood, this is a conservative version of modal empiricism that severely limits the extent to which an ordinary agent can reasonably believe “exotic” possibility claims. I offer a novel argument in support of this brand of skepticism: modal skepticism grounds an attractive (and novel) reply to Humean skepticism. Thus, I propose that modal skepticism be accepted on the basis of its theoretical utility as a tool for dissolving philosophical paradox

Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme in which a unique set is selected in some way. However, in this paper we consider the alternative approach in which all consistent sets are kept, leading to a type of `many world-views' picture of the quantum theory. It is shown that a natural way of handling this situation is to employ the theory of varying sets (presheafs) on the space \B of all Boolean subalgebras of the orthoalgebra \UP of history propositions. This approach automatically includes the feature whereby probabilistic predictions are meaningful only in the context of a consistent set of history propositions. More strikingly, it leads to a picture in which the `truth values', or `semantic values' of such contextual predictions are not just two-valued (\ie true and false) but instead lie in a larger logical algebra---a Heyting algebra---whose structure is determined by the space \B of Boolean subalgebras of \UP.Comment: 28 pages, LaTe