The logic of statements

To determine the term "propositional logic", it is necessary to clearly understand what "utterance" is.

So, a statement is a sentence that is grammatically correct, and is false or true. This concept should express a certain meaning. For example, the expression "canary is a bird" includes such components: "canary" and "bird".

That is why one of the key, original concepts of logic is statements. These concepts should describe a specific situation in which there will be either a statement of something or a negation.

The statement is considered to be true if the reality of the situation is described when describing it. By themselves, "lies" and "truth" determine the truth of statements.

The logic of statements consists of simple and complex expressions. So, a simple statement that does not include other expressions in its composition is considered simple. And to complex are expressions that are derived from simple, logically related statements.

The classical logic of propositions can be represented by a general theory of deduction. This is exactly the part of logic in which the logical connections of simple expressions that are independent of the structure of utterances are described.

It is impossible not to mention the conjunction - a complex statement, obtained by combining two simple expressions with the word "and". The truth of the conjunction is confirmed by the reliability of all the statements included in its structure. In the case when at least one of its members is false, the entire conjunction has a "lie" sign.

The conjunction itself serves to form those complex statements that are based on such assumptions:

- any expression (both simple and complex) can be either true or false;

- the truth of a complex statement directly depends on the truth of the statements and logical connections in it.

When two sentences are combined using the word "or", a disjunction is obtained. In everyday life this concept can be considered from the standpoint of two different meanings. First, it is a non-exclusive meaning, which implies the truth of the expression, whether one of the two expressions is true or both. Secondly, the exclusive meaning states that one of the expressions is true, and the other is false.

Formulas of propositional logic contain special symbols. Thus, in the disjunction, the symbol V denotes that the expression is true with at least one of the statements true, and it is false if both its terms are false.

In determining the implication, there is an assertion that the basis of the utterance can not be true with a false consequence. In other words, this concept assumes the dependence of the truth or falsity of the expression on the meaning of its components and the ways of their connections.

Despite the fact that the implication is useful enough for some purposes, it is not very consistent with the understanding of the conditional relationship in its general form. Thus, in encompassing many important features of the logical behavior of an utterance, this concept can not be its adequate description.

The logic of statements is aimed at solving such a central task as the separation of correct and incorrect schemes of reasoning and the systematization of the former. To get the right result, you need to focus your attention on special symbols that can represent one or another form. Hence the interest in such words as "or", "and", etc., which are insignificant at first glance, is indicated.

The logic of statements has even its own language, consisting of the following elements:

- initial symbols - variables, logical constants and technical signs;

- formulas.

For a better understanding of what has been said, we need to go over to concrete examples. For example, the conjunction uses the & symbol, the disjunction - \ / or \ º /.