Bivalent logic assigns either true or false as the unique truth value of every proposition. A primitive interrogative, i.e. boolean-valued primitive, is stable iff it reliably answers either true or false for a given set of arguments.
The three classical laws of thought are:
- The law of identity: P → P. For every stable primitive interrogative
prim A, B, C = prim A, B, C.
- The law of noncontradiction: ¬(P ∧ ¬P). For every stable primitive interrogative
(prim A, B, C ∧ ¬prim A, B, C) = false.
- The law of excluded middle: P ∨ ¬P. For every primitive interrogative
((prim A, B, C = true) ∨ (prim A, B, C = false)) = true.
unknown. Implementation of this system would proceed directly from creation of an atom to represent
unknownand the formation of a new enumeration that contained the standard true and false atoms and also the
unknownatom. New logical operations could then be written in terms of this new enumeration.