Two notions of compactness in Gödel logics

Compactness is an important property of classical propositional logic. It can be defined in two equivalent ways. The first one states that simultaneous satisfiability of an infinite set of formulae is equivalent to the satisfiability of all its finite subsets. The second one states that if a set of formulae entails a formula, then there is a finite subset entailing this formula as well.In propositional many-valued logic, we have different degrees of satisfiability and different possible definitions of entailment, hence the questions of compactness is more complex. In this paper we will deal with compactness of Gödel, Gödel_Δ, and Gödel_～ logics.There are several results (all for the countable set of propositional variables) concerning the compactness (based on satisfiability) of these logic by Cintula and Navara, and the question of compactness (based on entailment) for Gödel logic was fully answered by Baaz and Zach (see papers [3] and [2]).In this paper we give a nearly complete answer to the problem of compactness based on both concepts for all three logics and for an arbitrary cardinality of the set of propositional variables. Finally, we show a tight correspondence between these two concepts     

The use of artificial neural networks and multiple linear regression in modelling work–health relationships: Translating theory into analytical practice

Although psychological theory acknowledges the existence of complex systems and the importance of nonlinear effects, linear statistical models have been traditionally used to examine relationships between environmental stimuli and outcomes. The way we analyse these relationships does not seem to reflect the way we conceptualize them. The present study investigated the application of connectionism (artificial neural networks) to modelling the relationships between work characteristics and employee health by comparing it with a more conventional statistical linear approach (multiple linear regression) on a sample of 1003 individuals in employment. Comparisons of performance metrics indicated differences in model fit, with neural networks to some extent outperforming the linear regression models, such that R ² for worn-out and job satisfaction were significantly higher in the neural networks. Most importantly, comparisons revealed that the predictors in the two approaches differed in their relative importance for predicting outcomes. The improvement is attributed to the ability of the neural networks to model complex nonlinear relationships. Being unconstrained by assumptions of linearity, they can provide a better approximation of such psychosocial phenomena. Nonlinear approaches are often better fitted for purpose, as they conform to the need for correspondence between theory, method, and data.     

Should we rely on the Kenward–Roger approximation when using linear mixed models if the groups have different distributions?

The study explores the robustness to violations of normality and sphericity of linear mixed models when they are used with the Kenward–Roger procedure (KR) in split‐plot designs in which the groups have different distributions and sample sizes are small. The focus is on examining the effect of skewness and kurtosis. To this end, a Monte Carlo simulation study was carried out, involving a split‐plot design with three levels of the between‐subjects grouping factor and four levels of the within‐subjects factor. The results show that: (1) the violation of the sphericity assumption did not affect KR robustness when the assumption of normality was not fulfilled; (2) the robustness of the KR procedure decreased as skewness in the distributions increased, there being no strong effect of kurtosis; and (3) the type of pairing between kurtosis and group size was shown to be a relevant variable to consider when using this procedure, especially when pairing is positive (i.e., when the largest group is associated with the largest value of the kurtosis coefficient and the smallest group with its smallest value). The KR procedure can be a good option for analysing repeated‐measures data when the groups have different distributions, provided the total sample sizes are 45 or larger and the data are not highly or extremely skewed.     

The give-or-take-some dilemma: An empirical investigation of a hybrid social dilemma

We describe and empirically investigate a hybrid social dilemma that merges give-some and take-some dilemmas by allowing individuals to choose to either give or to take resources from a shared resource pool. Study 1 finds that (a) group size increases the inequality among group members and the likelihood of creating the public good, while reducing the amount of wasted resources; (b) larger bonuses increase provision rates; and (c) asymmetry in the wealth distribution of the group members induces higher levels of inequality of the final outcomes. Following the logic of appropriateness, players with high (low) endowments were more likely to give toward (take from) the shared resource. Study 2 finds that the tendency of the players with high (low) endowments to give (take) is amplified as the difference between endowment levels increased, and the players’ behavior is correlated with, and predictable from, independent judgments of what is perceived as appropriate.     

Drawing conclusions from choice response time models: A tutorial using the linear ballistic accumulator

Cognitive models of choice and response times can lead to deeper insights into the processes underlying decisions than standard analyses of accuracy and response time data. The application of these models, however, has historically been reserved for the authors of the models, and their associates. Recently, choice response time models have become more accessible through the release of user-friendly software for estimating their parameters. The aim of this tutorial is to provide guidance about the process of using these parameter estimates and associated model fits to make conclusions about experimental data. We use an application of one response time model, the linear ballistic accumulator, as an example to demonstrate the steps required to select an appropriate parametric characterization of a data set. We also discuss how to evaluate the quality of the agreement between model and data, including guidelines for presenting model predictions for group-level data.     

Learning from experience in nonlinear environments: Evidence from a competition scenario

We test people’s ability to learn to estimate a criterion (probability of success in a competition scenario) that requires aggregating information in a nonlinear manner. The learning environments faced by experimental participants are kind in that they are characterized by immediate, accurate feedback involving either naturalistic outcomes (information on winning and/or ranking) or the normatively correct probabilities. We find no evidence of learning from the former and modest learning from the latter, except that a group of participants endowed with a memory aid performed substantially better. However, when the task is restructured such that information should be aggregated in a linear fashion, participants learn to make more accurate assessments. Our experiments highlight the important role played by prior beliefs in learning tasks, the default status of linear aggregation in many inferential judgments, and the difficulty of learning in nonlinear environments even in the presence of veridical feedback.     

An ERP investigation of conditional reasoning with emotional and neutral contents

In two experiments we investigate conditional reasoning using event-related potentials (ERPs). Our goal was to examine the time course of inference making in two conditional forms, one logically valid (Modus Ponens, MP) and one logically invalid (Affirming the Consequent, AC). We focus particularly on the involvement of semantically-based inferential processes potentially marked by modulations of the N400. We also compared reasoning about emotional and neutral contents with separate sets of stimuli of differing linguistic complexity across the two experiments. Both MP and AC modulated the N400 component, suggesting the involvement of a semantically-based inferential mechanism common across different logical forms, content types, and linguistic features of the problems. Emotion did not have an effect on early components, and did not interact with components related to inference making. There was a main effect of emotion in the 800–1050 ms time window, consistent with an effect on sustained attention. The results suggest that conditional reasoning is not a purely formal process but that it importantly implicates semantic processing, and that the effect of emotion on reasoning does not primarily operate through a modulation of early automatic stages of information processing.     

Speech stress recognition using semi-eager learning

Homo-sapiens suffer from psychogenic pain due to current day lifestyle. According to psychologists, stress is the most destructive form of psychalgia and it is a vicious companion for this species. Immoderate levels of stress may lead to the death of many individuals. Normally, the presence of stress gives rise to certain emotions which can be detected to predict stress levels of a person. This paper proposes the development of mechanized and efficient Speech Emotion Recognition (SER) for stress level analysis. The paper investigates the performance of perceptual based speech features like Revised Perceptual Linear Prediction Coefficients, Bark Frequency Cepstral Coefficients, Perceptual Linear Predictive Cepstrum, Gammatone Frequency Cepstral coefficient, Mel Frequency Cepstral Coefficient, Gammatone Wavelet Cepstral Coefficient and Inverted Mel Frequency Cepstral Coefficients on SER. The novelty of this work involves application of a SemiEager (SemiE) learning algorithm for evaluating auditory cues. SemiE offers advantages over eager and lazy based learning by reducing the computational cost. Stress level recognition being the main objective, the Speech Under Simulated and Actual Stress (SUSAS) benchmark database is used for performance analysis. A comparative analysis is presented to demonstrate the improvement in the SED performance. An overall accuracy of 90.66% recognition of stress related emotions is achieved.     

An overview of algorithmic approaches to compute optimum entropy distributions in the expert system shell MECore (extended version)

The expert system shell MECore provides a series of knowledge management operations to define probabilistic knowledge bases and to reason under uncertainty. To provide a reference work for MECore algorithmics, we bring together results from different sources that have been applied in MECore and explain their intuitive ideas. Additionally, we report on our ongoing work regarding further development of MECore's algorithms to compute optimum entropy distributions and provide some empirical results. Altogether this paper explains the intuition of important theoretical results and their practical implications, compares old and new algorithmic approaches and points out their benefits as well as possible limitations and pitfalls.