A modal logic amalgam of classical and intuitionistic propositional logic

A famous result, conjectured by G\"odel in 1932 and proved by McKinsey and Tarski in 1948, says that $\varphi$ is a theorem of intuitionistic propositional logic IPC iff its G\"odel-translation $\varphi'$ is a theorem of modal logic S4. In this paper, we extend an intuitionistic version of modal logic S1+SP, introduced in our previous paper (S. Lewitzka, Algebraic semantics for a modal logic close to S1, J. Logic and Comp., doi:10.1093/logcom/exu067) to a classical modal logic L and prove the following: a propositional formula $\varphi$ is a theorem of IPC iff $\square\varphi$ is a theorem of L (actually, we show: $\Phi\vdash_{IPC}\varphi$ iff $\square\Phi\vdash_L\square\varphi$, for propositional $\Phi,\varphi$). Thus, the map $\varphi\mapsto\square\varphi$ is an embedding of IPC into L, i.e. L contains a copy of IPC. Moreover, L is a conservative extension of classical propositional logic CPC. In this sense, L is an amalgam of CPC and IPC. We show that L is sound and complete w.r.t. a class of special Heyting algebras with a (non-normal) modal operator.Comment: 18 page

Some remarks on semantics and expressiveness of the Sentential Calculus with Identity

Suszko's Sentential Calculus with Identity SCI results from classical propositional calculus CPC by adding a new connective $\equiv$ and axioms for identity $\varphi\equiv\psi$ (which we interpret here as `propositional identity'). We reformulate the original semantics of SCI in terms of Boolean prealgebras establishing a connection to `hyperintensional semantics'. Furthermore, we define a general framework of dualities between certain SCI-theories and Lewis-style modal systems in the vicinity of S3. Suszko's original approach to two SCI-theories corresponding to S4 and S5 can be formulated as a special case. All these dualities rely particularly on the fact that Lewis' `strict equivalence' is axiomatized by the SCI-principles of `propositional identity'.Comment: 31 page

Laser performance of perylenebis (dicarboximide) dyes with long secondary alkyl chains

The laser performance and related photophysical properties of two very soluble perylene dyes with long chain secondary alkyl groups were investigated in cyclohexane solution. With a dye laser as pump source a tuning range of 555–580 nm was obtained at an optimum concentration of 3×10–4 M. The quantum efficiencies (=0.29 and 0.21) were better than 1/2 that of rhodamine 6G. No photodegradation was observed over an excitation period of several hours

Tobacco use disorder and the risk of suicide mortality

Background and aims Tobacco use may be a risk factor for suicide mortality; however, prior research has produced equivocal findings and has been limited by relatively small sample sizes to study the rare event of suicide, as well as a lack of adjustment for other important factors, including psychiatric illness. We estimate the predictive association between tobacco use disorder and the risk of suicide mortality, adjusting for other important variables. Design A prospective cohort study. Setting The U nited S tates V eterans H ealth A dministration ( VHA ). Participants All individuals who received VHA services in fiscal year (FY) 2005 and were alive at the start of FY 2006 ( n  = 4 863 086). Measurements Tobacco use disorder was assessed via FYs 2004–05 VHA National P atient C are D atabase records. The outcome of suicide mortality was assessed during the follow‐up interval from the beginning of FY 2006 to the end of FY 2008 using N ational D eath I ndex records. Findings Of the 4 863 086 individuals in the study, 4823 died by suicide during the follow‐up interval. In the unadjusted model, tobacco use disorder was associated with an increased risk of suicide [hazard ratio (HR) = 1.88; 95% confidence interval (CI) = 1.76, 2.02]. After adjustment for model covariates, the association remained statistically significant, although attenuated (HR = 1.36, 95% CI = 1.27, 1.46). Conclusions Tobacco use disorder may confer a modest excess risk of death by suicide. Psychiatric disorders may partially explain the relationship between tobacco use disorder and suicide.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102156/1/add12381.pd

Internet use by older adults with bipolar disorder: international survey results

Background: The world population is aging and the number of older adults with bipolar disorder is increasing. Digital technologies are viewed as a framework to improve care of older adults with bipolar disorder. This analysis quantifies Internet use by older adults with bipolar disorder as part of a larger survey project about information seeking. Methods: A paper-based survey about information seeking by patients with bipolar disorder was developed and translated into 12 languages. The survey was anonymous and completed between March 2014 and January 2016 by 1222 patients in 17 countries. All patients were diagnosed by a psychiatrist. General estimating equations were used to account for correlated data. Results: Overall, 47% of older adults (age 60 years or older) used the Internet versus 87% of younger adults (less than 60 years). More education and having symptoms that interfered with regular activities increased the odds of using the Internet, while being age 60 years or older decreased the odds. Data from 187 older adults and 1021 younger adults were included in the analysis excluding missing values. Conclusions: Older adults with bipolar disorder use the Internet much less frequently than younger adults. Many older adults do not use the Internet, and technology tools are suitable for some but not all older adults. As more health services are only available online, and more digital tools are developed, there is concern about growing health disparities based on age. Mental health experts should participate in determining the appropriate role for digital tools for older adults with bipolar disorder.We acknowledge support by the Open Access Publication Funds of the SLUB/TU Dresden (Grant No. IN-1502335)