n-ary group - Wikipedia
Your approach is adopted in Bruno Poizat, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic ( - ed or ), page The basic relationship we can describe with RDF is binary, namely a relathionship and basic vocabulary is proposed here(@@they appear in examples, but yet to be Actually the analysis is the same as that of "John teaches Mary math.". In mathematics, and in particular universal algebra, the concept of n-ary group is a generalization of the concept of group to a set G with an n-ary operation.
Unary relationship type A Unary relationship between entities in a single entity type is presented on the picture below. As we see, a person can be in the relationship with another person, such as: This is definetly the most used relationship type. Journalist writes an article.
Finitary relation - Wikipedia
This example can be implemented very easily. In the diagram below, we represent our ternary relationship with an extra table, which can be modelled in Vertabelo very quickly. In other words, a group can have specific classess only at one classrom.
Sometimes it is possible to replace a ternary or n-ary relationship by a collection of binary relationship connecting pairs of the original entities. However, in many cases it is hard to replace ternary relationship with two or more binary relationships because some information could be lost. Another ternary relationship presents a different situation — Teacher recommends a book for a class: In the example with groups and classes, the primary key consisted only of two foreign keys.
This meant that there could be only one classroom for a specific group and class. In this situation the primary key consists of all three foreign keys.
Hence it is commonly stipulated that all of the domains be nonempty. As a rule, whatever definition best fits the application at hand will be chosen for that purpose, and anything that falls under it will be called a relation for the duration of that discussion.
N-ary relationship types
If it becomes necessary to distinguish the two definitions, an entity satisfying the second definition may be called an embedded or included relation. If L is a relation over the domains X1, …, Xk, it is conventional to consider a sequence of terms called variables, x1, …, xk, that are said to range over the respective domains.
Such a function can also be called an indicator function, particularly in probability and statistics, to avoid confusion with the notion of a characteristic function in probability theory.
From the more abstract viewpoint of formal logic and model theorythe relation L constitutes a logical model or a relational structure that serves as one of many possible interpretations of some k-place predicate symbol. Because relations arise in many scientific disciplines as well as in many branches of mathematics and logicthere is considerable variation in terminology.
This article treats a relation as the set-theoretic extension of a relational concept or term.
A variant usage reserves the term "relation" to the corresponding logical entity, either the logical comprehensionwhich is the totality of intensions or abstract properties that all of the elements of the relation in extension have in common, or else the symbols that are taken to denote these elements and intensions.
Further, some writers of the latter persuasion introduce terms with more concrete connotations, like "relational structure", for the set-theoretic extension of a given relational concept.