Traditional or BooleanLogic treats purely binary logical states: a statement can only be either 100% true or 100% false.

BooleanLogic connectives are defined by truth tables where 1 is**true** and 0 is **false**, i.e.,
For "and" symbolized as "&" or "^" or "∧" (or "&&" in CeeLanguage/CeePlusPlus/JavaLanguage, etc.)

See also FuzzyLogic, FirstOrderLogic, SymbolicLogic, TheoremProving, ThreeValuedLogic, TetralemmicLogic, MultiValuedLogic

CategoryLogic

BooleanLogic connectives are defined by truth tables where 1 is

^ | A B ---+------ 0 | 0 0 0 | 1 0 0 | 0 1 1 | 1 1For "or" symbolized as "|" or "v" or "∨" (or "||" in the languages above)

v | A B ---+------ 0 | 0 0 1 | 1 0 1 | 0 1 1 | 1 1"Not" is "~" (or "!" or "¬")

~ | A ---+--- 1 | 0 0 | 1and "implication" (see LogicalImplication) or "If..then.." is "->" or "⇒" (conditional)

-> | A B ----+------ 1 | 0 0 0 | 1 0 1 | 0 1 1 | 1 1"Iff" or "If and only if" is "<->" or "⇔" (biconditional) is the same as (A -> B) ^ (B -> A) There are many axioms of BooleanLogic, including DeMorgansLaws, and some deduction rule, such as

A^(A->B) -> BThis means, when doing proofs in logic or mathematics, in any step if A (which can be a complex expression) is true (or an assumption) and there is a definition, assumption, axiom or previously proved theorem of the form A->B, then B can be introduced into the proof chain. For more truth tables, see It should be noted that implication in BooleanLogic does not model the way the human mind does implication; it's a rather forced fit. This continues to cause theoretical and pragmatic issues that motivate a continuing search for a more suitable model.

See also FuzzyLogic, FirstOrderLogic, SymbolicLogic, TheoremProving, ThreeValuedLogic, TetralemmicLogic, MultiValuedLogic

CategoryLogic

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