If … is used to represent a simple proposition with definite truth value, it is said that … is a propositional constant, and the truth value of the propositional constant is certain and unchangeable, either 1 or 0.

If … is used to refer to a simple statement, it is said that … is a propositional variable. At this time, … is a variable whose value is 1 or 0.

A propositional formula is a symbol string consisting of propositional constants, propositional variables, conjunctions and brackets. , but not all symbol strings composed of these symbols are propositional formulas. Therefore, a strict definition of propositional formula must be given.

Definition 1.6

(1) Constant or variable of a single proposition is a compound formula;

(2) If A is compound, it is also compound;

(3) If A and B are combined formulas, then,, and are also combined formulas;

(4) Only the symbol string consisting of (1) ~ (3) is a compound formula.

In the future, we will call the combination formula the propositional formula, or simply the formula.

For convenience, brackets are specified, etc. Can be omitted. In the definition of formula, symbols such as A and B are introduced to express any propositional formula, which is called metalanguage symbol.

According to the definition,,, etc. are propositional formulas, but they are not propositional formulas.

The so-called metalanguage refers to the language used to explain the object language, and the object language refers to the language used to describe the studied object (referring to mathematical logic).

The definition of an example shows that it is a formula.

Solution ① is that the formula consists of (1)

② Does the formula come from (1)

③ Formula consists of ①, ② and (3).

④ Formula consists of ①, ③ and (3).