- Symbolic logic
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 philosophicallogic . 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 andpredicate logic . Other logics of interest includetemporal logic ,modal logic andfuzzy logic . See alsomodel theory .Modern mathematical areas arising out of
formal logic are grouped under the headingmathematical logic .Propositional logic
The area of symbolic logic called
propositional logic , originally called "propositional calculus" but not to be confused with the school subjectcalculus , studies the properties of sentences formed from constants, usually designated A, B, C, ... and fivelogical operator s, AND, OR, IMPLIES, EQUALS and NOT. The corresponding logical operations are known, respectively, as conjunction, disjunction,material conditional ,biconditional , andnegation . These five operators are sometimes denoted as keywords, especially incomputer language s, and sometimes by special symbols (seeTable of logic symbols ). All except NOT are binary operators; NOT is a unary operator which precedes its operand. The values of these operators are given bytruth table s.Predicate logic
Predicate logic , originally called "predicate calculus", expands on propositional logic by the introduction of variables, usually denoted by "x", "y", "z", or other lowercase letters, and also by the introduction of sentences containing variables, called predicates, usually denoted by an uppercase letter followed by a list of variables, such as P("x") or Q("y","z"). In addition, predicate logic allows so-calledquantifiers , representing ALL and EXISTS.ee also
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Table of logic symbols
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