  The thesis of this paper is that truth-relevant logic is a better foundation
for mathematics than classical logic. It is a system proposed by Richard Diaz
in 1981. In a certain sense t-relevant logic is based on Kleene strong tables.
These define a system with three values: true, false, unknown. It turns out
that there exist tautologies with the following property: there exists a proper
subset of propositional variables (t-relevant variables) such that for all
combinations true/false the tautology will be true, that is, the rest of the
variables (redundant variables) occurring in the tautology can be unknown. We
consider such compound sentences as neither true nor false. Philosophical
justification is provided. Proof system based on tableaux is proposed. The
following theorem is proved: tautology L = (R1 v ~R1) & (R2 v ~R2) & ... & (Rm
v ~Rm), where {R1, R2, ... Rm} is a subset of t-relevant propositional
variables, and = is equivalence according to Kleene strong tables.
