In order to define the term “propositional logic”, it is necessary to clearly understand what “utterance” is.
So, a statement is a sentence that is built grammatically correctly, and is false or true. This concept should express a certain meaning. For example, the expression “canary is a bird” includes the following components: “canary” and “bird”.
That is why one of the key, initial concepts of logic are statements. These concepts should describe a specific situation in which there will be either an affirmation of something or a denial.
A statement is considered to be true if the conformity of the reality of the situation is traced when describing it. By themselves, “false” and “truth” determine the truth of the statements.
The logic of statements consists of simple and complex expressions. So, a statement that does not include other expressions is considered simple. And to complex are expressions that are derived from simple, logically related statements.
The classical propositional logic can be represented by the general theory of deduction. This is precisely the part of the logic that describes the logical connections of simple expressions that are independent of the structure of sentences.
It is impossible not to mention the conjunction - a complex statement obtained by combining two simple expressions using 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 whole conjunction has the sign of “false”.
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 its statements and the logical connections in it.
When two statements are combined using the word “or,” a disjunction is already obtained. In everyday life, this concept can be considered from the perspective of two different meanings. Firstly, this is a non-exclusive meaning, which implies the truth of an expression, regardless of whether one of the two is true or whether they are both. Secondly, the exclusive meaning states that one of the expressions is true and the other is false.
The propositional logic formulas contain special characters. So, in a disjunction, the symbol V means that the expression is true if at least one of the statements is true , and false if both its members are false.
In determining the implication, there is a statement that the basis of the statement cannot be true in a false investigation. In other words, this concept implies the dependence of the truth or falsity of an expression on the meaning of its components and the ways of their connections.
Despite the fact that the implication is quite useful for some purposes, it is not very consistent with the understanding of conditional relationships in a general way. So, while covering many important features of the logical behavior of the utterance, this concept cannot be an adequate description of it.
The logic of statements is aimed at solving such a central problem as the separation of right and wrong reasoning schemes and systematization of the former. To get the right result, you need to focus on special characters that can represent one form or another. Hence the interest in such seemingly insignificant words as “or”, “and”, etc. is indicated.
Statements logic even has its own language, consisting of the following elements:
- source symbols - variables, logical constants and technical signs;
- formulas.
For a better understanding of what has been said, it is necessary to go to specific examples. For example, the conjunction uses the & symbol, the disjunction is \ / or \ º /.