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natural deduction : FOLDOC
natural deduction
A set of rules expressing how valid proofs may be constructed in predicate logic.
In the traditional notation, a horizontal line separates {premises} (above) from {conclusions} (below). Vertical ellipsis (dots) stand for a series of applications of the rules. "T" is the constant "true" and "F" is the constant "false" (sometimes written with a LaTeX perp).
"^" is the AND (
conjunction) operator, "v" is the inclusive OR ({disjunction}) operator and "/" is NOT (negation or complement, normally written with a LaTeX {neg}).
P, Q, P1, P2, etc. stand for propositions such as "Socrates was a man". P[x] is a proposition possibly containing instances of the variable x, e.g. "x can fly".
A proof (a sequence of applications of the rules) may be enclosed in a box. A boxed proof produces conclusions that are only valid given the assumptions made inside the box, however, the proof demonstrates certain relationships which are valid outside th


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