ЛОГИЧЕСКИЕ СИМВОЛЫ
Logical Symbols
Modern formal logic makes extensive use of a language of symbols to achieve a precise and simple interpretation of the object and to enable the investigator to apply the formal mathematical method. The symbols used for constructing, according to definite rules, the formulas of a system in formal logic are of three basic types: (1) those denoting the elementary logical objects of the system; (2) those denoting logical connections or operations; (3) auxiliary symbols, e.g., brackets and stops.
Several systems of symbolic notation are accepted in modern logic, as a result of which different symbols may represent the same logical concepts. The meanings of the most important of these symbols are given below:
- A, B, C ... X, Y, Z ... (also used with indices) denote variable propositions.
a, b, c ... x, y, z ... (also used with indices) denote variable objects.
P(.), R(.,.), S(.,.,.) (also used with indices) denote variable predicates.
- ¬, ~, → —symbols of negation (read as "not")
∨, + —symbols of disjunction (read as "or")
·, ∧ —symbols of conjunction (read as "and")
⊃, → —symbols of implication (read as "if ... then")
≡, ↔ —symbols of equivalence (read as "if and only if ... then")
∃, E —symbols of the existential quantifier
∀, (x) —symbols of the universal quantifier