The truth condition is embedded in the analysis of propositional knowledge; if S knows that p then p is true.
Whilst a straightforward condition given a classical bivalent system with values true and false, bringing truth value gluts into the picture raises some novel matters.
In a classical framework, ‘true’ is equivalent to ‘not false’, so the condition could simply be rephrased as: if S knows that p then p is not false.
But when the possibility of propositions which are both true and false is introduced, there are three plausible knowledge operators (K):
- Kp is true if and only if p is true
- Kp is true if and only if p is not false
- Kp takes the value of p, so it could be both true and false
The main question is, if one knows that p, does this require that p is true or that p is not false?