Definition is to describe or standardize the meaning of a word or concept by enumerating the basic attributes of a transaction or object. A defined transaction or object is called a defined project and its definition is called a defined project.

proposition

In modern philosophy, logic and linguistics, proposition refers to the semantics of a judgment, not the judgment sentence itself. When different sentences have the same semantics, they express the same proposition. For example, "Snow is white" (Chinese) and "Snow is white" (English) are different sentences, but they express the same proposition. Two different sentences in the same language may also express the same proposition. For example, the proposition just now can also be said that "the small crystal of ice is white", of course, this statement is not as good as the previous one.

Usually, a proposition refers to a closed judgment to distinguish it from an open judgment or predicate. In this case, the proposition is either true or false. The logical positivism of the philosophical school supports the concept of this proposition.

Some philosophers, such as John Searle, believe that other forms of language or behavior also determine propositions. The question of right and wrong is an inquiry about the truth of a proposition. Road traffic signs are also a proposition expressing no words and characters. You can also use declarative sentences to give a proposition without judging it. For example, the teacher asks students to express their opinions on a quotation, which is a proposition (that is, semantic) and the teacher does not judge it. In the last paragraph, only the proposition that "snow is white" is given, but there is no decision.

In propositional logic, all proved statements are called theorems.

A proposition or formula that is proved to be correct and can be used as a principle or law, such as a geometric theorem. Theorem is a true proposition (axiom or other theorems that have been proved), and it is proved to be a correct conclusion after logical restriction, that is, another true proposition. For example, "the opposite sides of a parallelogram are equal" is a theorem in plane geometry. Generally speaking, only important or interesting statements are called theorems in mathematics. Proving theorem is the central activity of mathematics. A mathematical statement that is considered true but not proved is a conjecture. When it is proved to be true, it is a theorem. It is the source of the theorem, but it is not the only source. A mathematical statement derived from other theorems can become a theorem without going through the process of becoming a conjecture. As mentioned above, theorems need some logical framework, and then form a set of axioms (axiom system). At the same time, the reasoning process allows new theorems and other previously discovered theorems to be derived from axioms.