Bin Zhao

In this paper, we introduce the variety of equality algebras endowed with universal quantifiers (called uE-algebras), and establish an equivalent category for the corresponding category. Most significantly, we present an expansion of uE-algebras by enriching them with an internal state operator (which are referred to as state uE-algebras), and investigate some of their fundamental algebraic properties. In particular, we discuss the correspondence between state m-deductive systems and m-congruences of state uE-algebras. We also provide a set of characterizations for subdirectly irreducible state uE-algebras, together with characterizations for local and simple state-morphism uE-algebras, which play a crucial role in studying the variety of state uE-algebras. Finally, using the notion of adjoint m-pairs, we obtain a representation for state-morphism operators on uE-algebras.

Since the outbreak of the COVID-19 pandemic, the physical and mental health of older adults has been threatened. Promoting physical and mental health through physical activity has therefore become a strategy for healthy aging. In order to better understand the impact of the participation of older adults in physical activity, this paper selects different types of physical activity, and examines the relationship between them and subjective well-being through the analysis of the mediation effect of outdoor exercise environment and the regulating effect of exercise form. In this cross-sectional study, a questionnaire survey was conducted in mainland China. The main data come from 903 older adults in five urban areas in Chengdu, Sichuan Province. The surveys were carried out using the Physical Activity Rating Scale, Newfoundland Subjective Well-Being Scale, Exercise Environment Scale, and Exercise Form Scale. SPSS was used for statistical analysis, linear regression analysis was adopted for processing data, and AMOS was used to establish a mediation model. The mediating variable is the outdoor exercise environment, and the moderating variable is exercise form; gender, age, education level, and monthly income were used as control variables. The study results showed that different physical activities were significantly, positively correlated with the subjective well-being of older adults ; among the activities, tai chi had the strongest effect on the subjective well-being of older adults. Outdoor exercise environment played a mediating role between different physical activity types and subjective well-being of older adults [tai chi: β = 0.030, 95% CI ; health qigong: β = 0.018, 95% CI ; walking and jogging: β = 0.034, 95% CI ]. Exercise form moderated the subjective well-being of older adults in different physical activities. The results of this study demonstrate that the outdoor exercise environment plays a mediating role between different physical activities and the subjective well-being of older adults, and the form of exercise can also moderate the impact of different physical activities on the subjective well-being of older adults. This study has enlightening significance for psychological intervention with older adults facing stress, anxiety and depression.

The literature on error sharing has focused on employees’ cost–benefit assessment to predict whether employees will disclose self-made errors. Our study advances this line of research by adopting a different theoretical lens and examining leaders’ role in promoting employee error sharing. Drawing primarily upon social learning theory, we expected that when team leaders openly talk about their own errors within teams, through their behavior, they would set an example for team members and encourage members’ error sharing with team leaders. Based on a sample of 353 employees within 95 teams, we found a positive link between leader error sharing and team member error sharing; in addition, we found that ethical leadership evaluation partially mediates this positive link. Moreover, we found that leader error sharing was positively related to the team error management climate, which moderated the relationship between ethical leadership evaluation and team member error sharing in such a way that the positive relationship becomes stronger under a higher error management climate. Our findings highlight the critical roles played by leaders in promoting employees’ error sharing.

Tracking representationalism is the theory that phenomenal consciousness is a matter of tracking physical properties in an appropriate way. This theory holds that phenomenal character can be explained in terms of representational content, and it also entails that there is unlikely to be a strong correlation between phenomenal character and neural states. However, the empirical evidence shows that both claims cannot be true. So, tracking representationalism is wrong. Its fault is due to ignoring the internal correlation of experience, the existence of which shows that phenomenal character is shaped by neural states to a large extent, so it cannot be wholly explained by representational content.

Bosbach and Riečan states on residuated lattices both are generalizations of probability measures on Boolean algebras. Just from the observation that both of them can be defined by using the canonical structure of the standard MV-algebra on the unit interval [0, 1], generalized Riečan states and two types of generalized Bosbach states on residuated lattices were recently introduced by Georgescu and Mureşan through replacing the standard MV-algebra with arbitrary residuated lattices as codomains. In the present paper, the Glivenko theorem is first extended to residuated lattices with a nucleus, which gives several necessary and sufficient conditions for the underlying nucleus to be a residuated lattice homomorphism. Then it is proved that every generalized Bosbach state (of type I, or of type II) compatible with the nucleus on a nucleus-based-Glivenko residuated lattice is uniquely determined by its restriction on the nucleus image of the underlying residuated lattice, and every relatively generalized Riečan state compatible with the double relative negation on an arbitrary residuated lattice is uniquely determined by its restriction on the double relative negation image of the residuated lattice. Our results indicate that many-valued probability theory compatible with nuclei on residuated lattices reduces in essence to probability theory on algebras of fixpoints of the underlying nuclei.