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Propositional formula
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=== Definitions === A definition creates a new symbol and its behavior, often for the purposes of abbreviation. Once the definition is presented, either form of the equivalent symbol or formula can be used. The following symbolism =<sub>Df</sub> is following the convention of Reichenbach.<ref>Reichenbach p. 20-22 and follows the conventions of PM. The symbol =<sub>Df</sub> is in the [[metalanguage]] and is not a formal symbol with the following meaning: "by symbol ' s ' is to have the same meaning as the formula '(c & d)' ".</ref> Some examples of convenient definitions drawn from the symbol set { ~, &, (, ) } and variables. Each definition is producing a logically equivalent formula that can be used for substitution or replacement. :* definition of a new variable: (c & d) =<sub>Df</sub> s :* OR: ~(~a & ~b) =<sub>Df</sub> (a ∨ b) :* IMPLICATION: (~a ∨ b) =<sub>Df</sub> (a β b) :* XOR: (~a & b) ∨ (a & ~b) =<sub>Df</sub> (a β b) :* LOGICAL EQUIVALENCE: ( (a β b) & (b β a) ) =<sub>Df</sub> ( a β‘ b )
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