The terminology and notation used in this paper have been introduced in the following articles: [29], [16], [12], [13], [11], [1], [2], [32], [18], [30], [24], [25], [26], [27], [3], [9], [34], [35], [33], [28], [15], [21], [37], [10], [31], [20], [23], [5], [14], [6], [22], [8], [4], [19], [36], and [7]. Let I be a set and let J be a relational structure yielding many sorted set indexed by I. ...

The extraordinary actions of a particular father and son became a popular topic of literati writers during late-Qing times and furthermore fueled an ongoing intellectual dispute. The father, Gong Zizhen 龔自珍 (1792–1841), was a renowned scholar credited by Liang Qichao 梁啟超 (1873–1929) for having initiated the important late-Qing intellectual turn from excessive evidential research to discussions ...

The articles [8], [5], [9], [1], [10], [11], [3], [2], [7], [4], and [6] provide the notation and terminology for this paper. We consider tree construction structures as extensions of 1-sorted structure as systems 〈 a carrier, rules 〉, where the carrier is a set and the rules constitute a relation between the carrier and the carrier∗. Let us note that there exists a tree construction structure ...

In this article we present several logical schemes. The scheme SubrelstrEx deals with a non empty relational structure A , a set B, and a unary predicate P , and states that: There exists a non empty full strict relational substructure S of A such that for every element x of A holds x is an element of S if and only if P [x] provided the following conditions are met: • P [B], and • B ∈ the carri...

Let I be a non empty set, let F be a group-like multiplicative magma family of I, and let i be an element of I. Note that F (i) is group-like. Let I be a non empty set, let F be an associative multiplicative magma family of I, and let i be an element of I. Observe that F (i) is associative. Let I be a non empty set, let F be a commutative multiplicative magma family of I, and let i be an elemen...

Let S be a non empty 1-sorted structure, let E be a set, let A be an action of the carrier of S on E, and let s be an element of S. We introduce A a s as a synonym of A(s). Let S be a non empty 1-sorted structure, let E be a set, let A be an action of the carrier of S on E, and let s be an element of S. Then A a s is a function from E into E. Let S be a unital non empty groupoid, let E be a set...