To define the term "propositional logic", you need to clearly understand what is the "statement."
So the statement is a suggestion, ranked grammatically correct, and is false or true.This notion must express a certain meaning.For example, the phrase "canary birds have" includes the following components: "canary" and "Bird".
That is why one of the key initial concepts of logic and is saying.These concepts are to describe the specific situation in which the statement is either something or denial.
True considered to be saying, if traced line reality of the situation when it is circumscribing.Themselves "false" and "true" define a true statement.
logic statements consists of simple and complex expressions.So, just think the statement that does not include in its composition other expressions.And to the complex include expressions that are derived from the simple, logically interrelated statements.
classical propositional logic can be represented by the general theory of deduction.It is that part of the logic, which describes not depend on the structure of sentences logical connections simple expressions.
Not to mention the conjunctions - a complex statement, obtained by combining two simple expressions using the word "and".The truth of the conjunction confirms the accuracy of all statements included in its structure.In the case where at least one of its members is false, the whole conjunction is a sign of "a lie."
conjunction itself serves to form the complex statements, which are based on these assumptions:
- any expression (both simple and complex) can be either true or false;
- the truth of the complex utterances depends on the truth of the statements contained in it and the logical links in it.
When joining two statements with the word "or" has already obtained a disjunction.In everyday life, this concept can be viewed from the perspective of two different meanings.First, it is non-exclusive sense, which implies the validity of expression, regardless of the true expression of one or two such, they are both.Second, eliminating the sense asserts that one of the expressions is true, and the other - is false.
formulas of propositional logic contain special characters.Thus, in the disjunction symbol V denotes the fact that the expression is true at the truth of at least one of the statements, and false if both of its members are false.
In determining the implication there is a statement saying that the base can not be true at the wrong investigation.In other words, this concept implies dependence truth or falsity of the expression of the value of its components and methods of their relations.
Despite the fact that the implication is quite useful for some purposes, it is not very consistent with the understanding of the conditioned connection in general.Thus, in many important traits surrounds the device logical behavior saying this concept can not be an adequate description of it.
logic of statements aimed at addressing this central problem, as the separation of right and wrong reasoning schemes and systematization of the first.To get the correct result, you must focus on the special characters that can represent one or another form.Hence the designated interest in such seemingly insignificant words like "and", "and," etc.
logic statements even has its own language, which consists of the following elements:
- the original characters - variables, constants and logical technical signs;
- formulas.
To understand what has been said must go to specific examples.For example, using the conjunction symbol & amp ;, disjunction - \ / or \ ยบ /.
