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Symbolic logic
From Wikipedia, the free encyclopedia
Symbolic logic is the area of mathematics which studies the purely formal properties of strings of symbols. The interest in this area springs from two sources. First, the symbols used in symbolic logic can be seen as representing the words used in philosophical logic. Second, the rules for manipulating symbols found in symbolic logic can be implemented on a computing machine.
Symbolic logic is usually divided into two subfields, propositional logic and predicate logic.
Modern mathematical areas arising out of formal logic are grouped under the heading mathematical logic.
The area of symbolic logic called propositional logic, originally called propositional calculus but not to be confused with the school subject calculus, studies the properties of sentences formed from constants, usually designated A, B, C, ... and five logical operators, AND, OR, IMPLIES, EQUALS and NOT. These five operators are sometimes denoted .AND., especially in computer science, and sometimes by special symbols called cap, cup, arrow, double arrow, and tilde. All except NOT are binary operators, NOT is a unary operator which precedes its operand. The values of these operators are given by truth tables.
Predicate logic, originally called predicate calculus, expands on propositional logic by the introduction of variables, usually denoted x, y, z, or with other lower case letters, and also sentences which contain variables, called predicates, usually denoted by a capital letter, followed by a list of variables, such as P(x) or Q(y,z). In addition, predicate logic allows so-called quantifiers, to represent ALL and EXISTS.
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