Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

Impact of Team Familiarity in the Operating Room on Surgical Complications

BACKGROUND: The quality of surgical performance depends on the technical skills of the surgical team as well as on non-technical skills, including teamwork. The present study evaluated the impact of familiarity among members of the surgical team on morbidity in patients undergoing elective open abdominal surgery. METHODS: A retrospective analysis was performed to compare the surgical outcomes of patients who underwent major abdominal operations between the first month (period I) and the last month (period II) of a 6-month period of continuous teamwork (stable dyads of one senior and one junior surgeon formed every 6 months). Of 117 patients, 59 and 58 patients underwent operations during period I and period II, respectively, between January 2010 and June 2012. Team performance was assessed via questionnaire by specialized work psychologists; in addition, intraoperative sound levels were measured. RESULTS: The incidence of overall complications was significantly higher in period I than in period II (54.2 vs. 34.5 %; P = 0.041). Postoperative complications grade <3 were significantly more frequently diagnosed in patients who had operations during period I (39.0 vs. 15.5 %; P = 0.007), whereas no between-group differences in grade ≥3 complications were found (15.3 vs. 19.0 %; P = 0.807). Concentration scores from senior surgeons were significantly higher in period II than in period I (P = 0.033). Sound levels during the middle third part of the operations were significantly higher in period I (median above the baseline 8.85 dB [range 4.5-11.3 dB] vs. 7.17 dB [5.24-9.43 dB]; P < 0.001). CONCLUSIONS: Team familiarity improves team performance and reduces morbidity in patients undergoing abdominal surgery.