Propositional Formula - Propositional Connectives

Propositional Connectives

Arbitrary propositional formulas are built from propositional variables and other propositional formulas using propositional connectives. Examples of connectives include:

• The unary negation connective. If is a formula, then is a formula.
• The classical binary connectives . Thus, for example, if and are formulas, so is .
• Other binary connectives, such as NAND, NOR, and XOR
• The ternary connective IF ... THEN ... ELSE ...
• Constant 0-ary connectives ⊤ and ⊥ (alternately, constants { T, F }, { 1, 0 } etc. )
• The "theory-extension" connective EQUALS (alternately, IDENTITY, or the sign " = " as distinguished from the "logical connective" )