Y She

In this paper, we investigate universal and existential quantifiers on NM-algebras. The resulting class of algebras will be called monadic NM-algebras. First, we show that the variety of monadic NM-algebras is algebraic semantics of the monadic NM-predicate logic. Moreover, we discuss the relationship among monadic NM-algebras, modal NM-algebras and rough approximation spaces. Second, we introduce and investigate monadic filters in monadic NM-algebras. Using them, we prove the subdirect representation theorem of monadic NM-algebras, and characterize simple and subdirectly irreducible monadic NM-algebras. Finally, we present the monadic NM-logic and prove its completeness with respect to monadic NM-algebras. These results constitute a crucial first step for providing an algebraic foundation for the monadic NM-predicate logic.

The socialist core value system as the system to the public of the commitment and efforts to practice the most basic, the most important values ​​and ideals and the dominant ideological norms, aimed at seeking revolutionary ideals and the modern two-way combination of political ethics, national identity and modern civilization mutual indulgence, and moral and national traditions of civic body with each other, accurate and profound expression of the reform and opening up the practice of contemporary Chinese people of all social and public value of rational belief and on the basis of ethnic and cultural heart good order deep clamor. Whether it is from the immediate or long term, as a systematic project, the real core value system and the key, through effective institutional arrangement in order to achieve fairness and justice as the core of the socialist harmonious society, the goal of a good system of civilization and modern civil society to develop citizenship as the core, and constantly enhance the value of people on the reasonable belief of the general social acceptance and actual Fulfillment conscious awareness, and promote the core values ​​of the effective internalization. The basic and the most important value of the socialism core value system is not only to aim at seeking a two-way combination of the revolutionary ideals and the modem political ethics, an accommodation of national identity and modem civilization but also to express modem Chinese people's deep requests for reasonable social and public value of faith and the soul of Chinese national culture during the reform and opening-up period. The key for construction of the core value system no matter at present or in the future is to achieve the goal of construction a harmonious society with socialism justice as the core by effective system

A 2 × 2 experiment was conducted to compare the effectiveness of using diagrams to writing summaries for students given biological information to learn and who possessed different levels of expertise in that topic area. A main effect of learning strategy used on number of idea units encoded was found: drawing diagrams was superior to writing summaries. However, no interaction effect between learning strategies and expertise was found. An examination of students’ subjective ratings of cognitive load revealed that those with low expertise reported higher levels of cognitive load when constructing diagrams. These findings suggest that using diagrams is effective for identifying and encoding important information when learning, but that it would be helpful to provide guidance about diagram use particularly to students who are novices in the topic area to reduce cognitive load.

The main purpose of this note is to characterize consistency of logic theories in propositional logic by means of topological concept. Based on the concepts of truth degree of formulas and similarity degree between formulas the concept of logic metric space has been proposed by the first author. It is proved in this note that a closed logic theory Γ is consistent if and only if it contains no interior point in the logic metric space. Moreover the relationship between logic closedness and topological closedness of a logic theory Γ is discussed. Finally, the concept of full divergency is also characterized by means of the topological concept of density

The category \(\mathbb {DRDL}{'}\), whose objects are c-differential residuated distributive lattices satisfying the condition \(\textbf{CK}\), is the image of the category \(\mathbb {RDL}\), whose objects are residuated distributive lattices, under the categorical equivalence \(\textbf{K}\) that is constructed in Castiglioni et al. (Stud Log 90:93–124, 2008). In this paper, we introduce weak monadic residuated lattices and study some of their subvarieties. In particular, we use the functor \(\textbf{K}\) to relate the category \(\mathbb {WMRDL}\), whose objects are weak monadic residuated distributive lattices, and the category \(\mathbb {WMDRDL}{'}\), whose objects are pairs formed by an object of \(\mathbb {DRDL}{'}\) and a center weak universal quantifier.