Conditional Probability and Defeasible Inference

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey–Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of non-monotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).Expectation is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. The research of both authors was supported in part by a grant from NSF, and, for Parikh, also by support from the research foundation of CUNY.     

条件推理与概率判断

选取6个具体内容的条件命题和1个纯形式的条件命题作为实验材料,以大学生为被试,深入探讨了条件推理的认知加工机制。结果发现,大学生被试对四种推理形式的认可程度主要与范畴前提的概率值成正比,条件推理似乎是一种基于概率判断的直觉而高效的认知加工过程,进一步证实了Oaksford（2000）以及Evans（2003）等人的观点。     

Cut-Elimination for Quantified Conditional Logic

A semantic embedding of quantified conditional logic in classical higher-order logic is utilized for reducing cut-elimination in the former logic to existing results for the latter logic. The presented embedding approach is adaptable to a wide range of other logics, for many of which cut-elimination is still open. However, special attention has to be payed to cut-simulation, which may render cut-elimination as a pointless criterion.     

Some Embedding Theorems for Conditional Logic

We prove some embedding theorems for classical conditional logic, covering ‘finitely cumulative’ logics, ‘preferential’ logics and what we call ‘semi-monotonic’ logics. Technical tools called ‘partial frames’ and ‘frame morphisms’ in the context of neighborhood semantics are used in the proof.     

The Role of Negation in Conditional Inference

This paper addresses the issue of how negative components affect people's ability to draw conditional inferences. The study was motivated by an attempt to resolve a difficulty for the mental models theory of Johnson-Laird and Byrne, whose account of matching bias in the selection task is apparently inconsistent with Johnson-Laird's explanation of the double negation effects in conditional inference reported by Evans, Clibbens, and Rood (1995). Two experiments are reported, which investigate frequencies of conditional inferences with task presentation similar to that of the selection task in two respects: the presence of a picture of four cards and the use of implicit negations in the premises. The latter variable was shown to be critical and demonstrated a new phenomenon: Conditional inferences of all kinds are substantially suppressed when based on implicitly negative premises. This phenomenon was shown to operate independently of and in addition to the double negation effect. A third experiment showed that the implicit negation effect could be extended to the paradigm in which people are asked to produce their own conclusions. It is argued that these two effects can be explained within either the mental models theory or the inference rule theory, of propositional reasoning, but that each will require some revision in order to offer a convincing account.     

On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.     

Iterated Belief Revision and Conditional Logic

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl's ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors' Triviality Result.     

The Sabbath: Implications for Mental Health

Jewish tradition established the Sabbath as a special day. Its observance was both part of a religious tradition and an example of psychological health. The author explores the values and attitudes that underlie Sabbath observance, identifies some of the themes and behaviors most characteristic of these observances, and relates these to current mental health practices.     

Models of burnout: Implications for interventions

Three process models of burnout are discussed, Cherniss' process model, Golembiewski's phase model and Leiter's process model. Empirical support for each model is reported. The models make different contributions to the problem of burnout and its development, and the kind of interventions that follow from each model seem to represent different targets. The strengths and weaknesses of the three models are assessed, and the relative merits of individual versus organizational level interventions are addressed. More model-driven research is necessary to reduce the problem of burnout for individuals and organizations.     

Social Neuroscience: Progress and Implications for Mental Health

ABSTRACT— Social neuroscience is a new, interdisciplinary field devoted to understanding how biological systems implement social processes and behavior. Social neuroscience capitalizes on biological concepts and methods to inform and refine theories of social behavior, and it uses social and behavioral constructs and data to inform and refine theories of neural organization and function. We focus here on the progress and potential of social neuroscience in the area of mental health. Research in social neuroscience has grown dramatically in recent years. Among the most active areas of research we found are brain-imaging studies in normal children and adults; animal models of social behavior; studies of stroke patients; imaging studies of psychiatric patients; and research on social determinants of peripheral neural, neuroendocrine, and immunological processes. We also found that these areas of research are proceeding along largely independent trajectories. Our goals in this article are to review the development of this field, examine some currently promising approaches, identify obstacles and opportunities for future advances and integration, and consider how this research can inform work on the diagnosis and treatment of mental disorders.     

Bias in the Reporting of Family History: Implications for Clinical Care

Family history of cancer is critical for identifying and managing patients at risk for cancer. However, the quality of family history data is dependent on the accuracy of patient self reporting. Therefore, the validity of family history reporting is crucial to the quality of clinical care. A retrospective review of family history data collected at a community hospital between 2005 and 2009 was performed in 43,257 women presenting for screening mammography. Reported numbers of breast, colon, prostate, lung, and ovarian cancer were compared in maternal relatives vs. paternal relatives and in first vs. second degree relatives. Significant reporting differences were found between maternal and paternal family history of cancer, in addition to degree of relative. The number of paternal family histories of cancer was significantly lower than that of maternal family histories of cancer. Similarly, the percentage of grandparents' family histories of cancer was significantly lower than the percentage of parents' family histories of cancer. This trend was found in all cancers except prostate cancer. Self-reported family history in the community setting is often influenced by both bloodline of the cancer history and the degree of relative affected. This is evident by the underreporting of paternal family histories of cancer, and also, though to a lesser extent, by degree. These discrepancies in reporting family history of cancer imply we need to take more care in collecting accurate family histories and also in the clinical management of individuals in relation to hereditary risk.     

论条件推理中的两种"高概率结论效应"

用随机抽取的139名大学生和研究生被试,对Oaksford设计的4条条件推理规则的认可度,以及对组成这4条条件推理规则的前后件认可度进行了评定,并根据被试对"条件规则"、组成条件规则的"前件"和"后件"等三个因素上的评定结果各区分为"高"和"低"两个水平.而后对被试在不同评定条件下对每条规则的四种推理结果进行了统计分析.实验结果既支持Oaksford等提出的"推理者对组成条件推理规则的不同的前后件概率组合对推理结论的认可度会有影响"这一观点,也支持邱江等得出的"不同的条件概率对推理者进行推理时对结论认可度的高低会有影响"的论断.前者可称之为"前后件概率的高概率结论效应",后者可称之为"条件概率的高概率结论效应".     

Identity in Mares-Goldblatt Models for Quantified Relevant Logic

Journal of Philosophical Logic - Mares and Goldblatt (The Journal of Symbolic Logic, 71(01), 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the...     

Abstract: Inference and Interval Estimation for Indirect Effects With Latent Variable Models

Models specifying indirect effects (or mediation) and structural equation modeling are both popular in the social sciences. Yet relatively little research has compared methods that test for indirect effects among latent variables and provided precise estimates of the effectiveness of different methods.

This simulation study provides an extensive comparison of methods for constructing confidence intervals and for making inferences about indirect effects with latent variables. We compared the percentile (PC) bootstrap, bias-corrected (BC) bootstrap, bias-corrected accelerated (BC _a ) bootstrap, likelihood-based confidence intervals (Neale & Miller, 1997), partial posterior predictive (Biesanz, Falk, and Savalei, 2010), and joint significance tests based on Wald tests or likelihood ratio tests. All models included three reflective latent variables representing the independent, dependent, and mediating variables. The design included the following fully crossed conditions: (a) sample size: 100, 200, and 500; (b) number of indicators per latent variable: 3 versus 5; (c) reliability per set of indicators: .7 versus .9; (d) and 16 different path combinations for the indirect effect (α = 0, .14, .39, or .59; and β = 0, .14, .39, or .59). Simulations were performed using a WestGrid cluster of 1680 3.06GHz Intel Xeon processors running R and OpenMx.

Results based on 1,000 replications per cell and 2,000 resamples per bootstrap method indicated that the BC and BC _a bootstrap methods have inflated Type I error rates. Likelihood-based confidence intervals and the PC bootstrap emerged as methods that adequately control Type I error and have good coverage rates.     

A Deep Inference System for the Modal Logic S5

We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms. Presented by Heinrich Wansing     

Generalized Fiducial Inference for Binary Logistic Item Response Models

Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a Bayesian posterior distribution. However, no prior distribution needs to be specified, which renders GFI more suitable when no a priori information about model parameters is available. In the current paper, we apply GFI to a family of binary logistic item response theory models, which includes the two-parameter logistic (2PL), bifactor and exploratory item factor models as special cases. Asymptotic properties of the resulting fiducial distribution are discussed. Random draws from the fiducial distribution can be obtained by the proposed Markov chain Monte Carlo sampling algorithm. We investigate the finite-sample performance of our fiducial percentile CI and two commonly used Wald-type CIs associated with maximum likelihood (ML) estimation via Monte Carlo simulation. The use of GFI in high-dimensional exploratory item factor analysis was illustrated by the analysis of a set of the Eysenck Personality Questionnaire data.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.