A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them

Three equivalent ordinal notation systems in cubical Agda

We present three ordinal notation systems representing ordinals below epsilon zero in type theory, using recent type-theoretical innovations such as mutual inductive-inductive definitions and higher inductive types. We show how ordinal arithmetic can be developed for these systems, and how they admit a transfinite induction principle. We prove that all three notation systems are equivalent, so that we can transport results between them using the univalence principle. All our constructions have been implemented in cubical Agda

Economic burden of chronic bronchitis in the United States: a retrospective case-control study

Christopher M Blanchette1, Melissa H Roberts1, Hans Petersen1, Anand A Dalal2, Douglas W Mapel31Division of Clinical and Outcomes Research, Lovelace Respiratory Research Institute, Kannapolis, NC, USA; 2US Health Outcomes, GlaxoSmithKline, Research Triangle Park, NC, USA; 3Lovelace Clinic Foundation, Albuquerque, NM, USABackground: Chronic bronchitis (CB) is often misdiagnosed or diagnosed at a later stage of chronic obstructive pulmonary disease (COPD). We examined how this later diagnosis may impact health care costs and utilization during the 12 months prior to and 24 months post initial CB diagnosis.Methods: This retrospective case-control analysis used claims data from a large US database from July 1, 2003 through June 30, 2007. Patients with CB aged 40 years and older were propensity matched (N = 11,674) to patients without evidence of COPD or asthma by demographics, CB diagnosis quarter/year, and comorbidities. Group differences were assessed using Student's t-test and Pearson chi-square test statistics.Results: Six months prediagnosis, CB patients had higher frequencies of any hospitalization (9.6%, 6.7%; P < 0.05), emergency department/urgent care visits (13.3%, 6.7%; P < 0.05), and prescriptions (97.3%, 94.1%; P < 0.05). Six months postdiagnosis, CB patients had 5.6 times more hospitalizations (P < 0.05) and 3.1 times more emergency department/urgent care visits (P < 0.05) compared with controls. Mean total costs (US) for CB patients 12 months prediagnosis were significantly higher than controls (months 12–7: 4212, 3826; P < 0.05; months 6–1: 5289, 4285; P < 0.05). CB patients had higher mean total costs (8919; P < 0.05) 6 months postdiagnosis. Costs remained $2429 higher for CB patients 19–24 months postdiagnosis (P < 0.05).Conclusion: Health care costs and utilization among CB patients are increased both prior to diagnosis and during the 2 years postdiagnosis. This study suggests that not accurately diagnosing CB early has a substantial impact on health care costs, and that the economic burden for CB patients remains elevated even after adjustment for comorbidities associated with COPD.Keywords: chronic bronchitis, burden, economic, chronic obstructive pulmonary diseas

Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution traces. We have implemented the approach in Isabelle/HOL as a lightweight concurrency verification tool that supports reasoning about the control and data flow of concurrent programs with shared variables at different levels of abstraction. This is illustrated on two simple verification examples

Alcohol Policies and Alcoholic Cirrhosis Mortality in the United States

Introduction Stronger alcohol policies predict decreased alcohol consumption and binge drinking in the United States. We examined the relation- ship between the strength of states’ alcohol policies and alcoholic cirrhosis mortality rates. Methods We used the Alcohol Policy Scale (APS), a validated assessment of policies of the 50 US states and Washington DC, to quantify the efficacy and implementation of 29 policies. State APS scores (the- oretical range, 0–100) for each year from 1999 through 2008 were compared with age-adjusted alcoholic cirrhosis death rates that oc- curred 3 years later. We used Poisson regression accounting for state-level clustering and adjusting for race/ethnicity, college edu- cation, insurance status, household income, religiosity, policing rates, and urbanization. Results Age-adjusted alcoholic cirrhosis mortality rates varied signific- antly across states; they were highest among males, among resid- ents in states in the West census region, and in states with a high proportion of American Indians/Alaska Natives (AI/ANs). Higher APS scores were associated with lower mortality rates among fe- males (adjusted incidence rate ratio [IRR], 0.91 per 10-point in- crease in APS score; 95% confidence interval [95% CI], 0.84–0.99) but not among males (adjusted IRR, 0.97; 95% CI, 0.90–1.04). Among non-AI/AN decedents, higher APS scores were also associated with lower alcoholic cirrhosis mortality rates among both sexes combined (adjusted IRR, 0.89; 95% CI, 0.82–0.97). Policies were more strongly associated with lower mortality rates among those living in the Northeast and West census regions than in other regions. Conclusions Stronger alcohol policy environments are associated with lower al- coholic cirrhosis mortality rates. Future studies should identify un- derlying reasons for racial/ethnic and regional differences in this relationship