On the Consistency of the Δ1 1-CA Fragment of Frege's Grundgesetze

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing ¹ ₁-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.     

Evaluating the Impact of Genetic Counseling and Testing with Signal Detection Methods

One measure of the impact of genetic counseling and testing (GCT) is the extent to which it fosters behavioral change that is consistent with mutation status. We describe and illustrate how two different signal detection methods, receiver operating characteristic (ROC) analysis and recursive partitioning, can be used in this context to evaluate the impact of GCT. We analyzed real screening behavior data obtained in the 12 months following GCT for Hereditary Nonpolyposis Colon Cancer (HNPCC) using these two different signal detection approaches. Each approach demonstrated that GCT had an impact on behavioral outcomes, and was effective in fostering behavioral outcomes appropriate to mutation status. The ROC approach demonstrated that GCT was effective because mutation positive and mutation negative individuals could be distinguished on the basis of the number of recommended screening behaviors. The recursive partitioning approach demonstrated that GCT was effective because there were generally high rates of adherence to screening guidelines among subjects. The recursive partitioning technique also identified four subgroups of subjects, each with distinct characteristics, for which tailored interventions could be developed to increase rates of adherence to screening guidelines. Signal detection methods are easily implemented and are useful techniques for evaluating the impact of GCT.     

The Value of Sacrifices

ABSTRACT

Most authors who discuss the normative impact of sacrifices do so with regards to the impact that a sacrifice can have on the practical reasons of the agent who makes it. A different and underappreciated phenomenon of sacrifices is their other-regarding normative impact: the sacrifice of person A can have an impact on the practical reasons of person B, either by generating practical reasons for B to act in certain ways or by intensifying existing reasons of B for specific courses of action. This paper asks when and why sacrifices have such other-regarding normative impact and argues that sacrifices can have other-regarding normative impact because sacrifices can be intrinsically good. The intrinsic value of sacrifices is explained by the recursive account of value: sacrifices are intrinsically good if and because they are appropriate responses to intrinsic values, and appropriate responses to intrinsic values are themselves intrinsically good. Furthermore, sacrifices are difficult to make, and successful pursuit in difficult activities can also be intrinsically good.     

Model-based recursive partitioning of extended redundancy analysis with an application to nicotine dependence among US adults

Extended redundancy analysis (ERA) is used to reduce multiple sets of predictors to a smaller number of components and examine the effects of these components on a response variable. In various social and behavioural studies, auxiliary covariates (e.g., gender, ethnicity) can often lead to heterogeneous subgroups of observations, each of which involves distinctive relationships between predictor and response variables. ERA is currently unable to consider such covariate-dependent heterogeneity to examine whether the model parameters vary across subgroups differentiated by covariates. To address this issue, we combine ERA with model-based recursive partitioning in a single framework. This combined method, MOB-ERA, aims to partition observations into heterogeneous subgroups recursively based on a set of covariates while fitting a specified ERA model to data. Upon the completion of the partitioning procedure, one can easily examine the difference in the estimated ERA parameters across covariate-dependent subgroups. Moreover, it produces a tree diagram that aids in visualizing a hierarchy of partitioning covariates, as well as interpreting their interactions. In the analysis of public data concerning nicotine dependence among US adults, the method uncovered heterogeneous subgroups characterized by several sociodemographic covariates, each of which yielded different directional relationships between three predictor sets and nicotine dependence.     

The intrinsic difficulty of recursive functions

This paper deals with a philosophical question that arises within the theory of computational complexity: how to understand the notion of INTRINSIC complexity or difficulty, as opposed to notions of difficulty that depend on the particular computational model used. The paper uses ideas from Blum's abstract approach to complexity theory to develop an extensional approach to this question. Among other things, it shows how such an approach gives detailed confirmation of the view that subrecursive hierarchies tend to rank functions in terms of their intrinsic, and not just their model-dependent, difficulty, and it shows how the approach allows us to model the idea that intrinsic difficulty is a fuzzy concept. Jan Zygmunt     

On Intermediate Predicate Logics of some Finite Kripke Frames,I. Levelwise Uniform Trees

An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case.     

On Modal Logics of Partial Recursive Functions

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established. Presented by Melvin Fitting     

Patrol evaluation research: a multiple-baseline analysis of saturation police patrolling during day and night hours

The effects of a carefully monitored and increased police patrol on the report of crime were examined in four patrol zones. Overall patrol movement was increased to four times normal levels and slow patrol movement (under 20 mph) to around 30 times normal levels for 10 days. The patrol was active in two zones between 9:00 a.m. and 5:00 p.m. and in the other two zones between 7:00 p.m. and 3:00 a.m. A multiple-baseline design and time-series statistical analyses showed statistically reliable changes in reported levels of Part I crime (such as robbery, burglary, and aggravated assault) during both night patrols, but not in the day patrols. In both night-patrol zones, there were also reliable increases from saturation patrol to postsaturation patrol in report of Part I crime after the night patrol was terminated. Neither of the day patrols showed significant crime report changes on termination. Despite statistically reliable decreases in report of crime during nighttime hours, the value of saturation patrolling as a crime-prevention technique was questioned on cost/benefit grounds.     

芬太尼用于无痛胃镜检查优于等效剂量瑞芬太尼的临床研究

在无痛胃镜检查中观察并比较等效剂量瑞芬太尼和芬太尼血流动力学指标、氧饱和度的影响以及不良反应的发生率。择期无痛胃镜检查ASAⅠ级～Ⅱ级的患者90例,随机分为丙泊酚＋芬太尼组（PF组,n=40）和丙泊酚＋瑞芬太尼组（PR组,n=50）,记录患者睫毛反射消失时间、胃镜操作时间、苏醒时间以及用药前（T1）、睫毛反射消失时（T2）、胃镜过咽喉部时（T3）、胃镜退出时（T4）、苏醒时（T5）等时点血流动力学指标和氧饱和度。结果两组患者较术前都有明显的血压下降,PR组窦性心动过缓20例（40．8%）、PF组8例（20．0％）,PR组窦性心动过缓发生率明显增加（P〈0．05）。用于无痛胃镜检查麻醉时,瑞芬太尼不良反应较多,芬太尼相对更为安全。     

Levels of theory‐of‐mind reasoning in competitive games

The literature on recursive theory of mind (TOM) reasoning in interactive decision making (reasoning of the type “I think that you think that I think…”) has been pessimistic, suggesting that adults attribute to others levels of reasoning that are low and slow to increase with learning. In four experiments with college‐age adults playing sequential games, we examined whether choices and predictions were consistent with believing that others pursue their immediate self‐interest, or with believing that others reason through their own decision making, with fixed‐sum games that were simpler and more competitive. This manipulation led to higher‐level default TOM reasoning; indeed, reasoning against a lower‐level opponent was frequently consistent with assuming the opponent's reasoning to be higher‐level, leading to sub‐optimal choices. We conclude that TOM reasoning is not of a low level in all game settings; rather, individuals may display effective TOM reasoning, reflecting realistic assumptions about their opponents, in competitive and relatively simple games. Copyright © 2010 John Wiley & Sons, Ltd.