Lattice-valued representation of the cut-elimination theorem (Q1192582)

Let \(L\) be a relatively pseudo-complemented complete lattice, \(F\) a set of formulas of a formal system (classical or intuitionistic). The author considers mappings \(m,M: F\to L\) satisfying a series of conditions. For such pairs of mappings he proves, as his main theorem: \(m(A)\leq M(B)\) for any provable sequent \(A\to B\). In the final section, he uses this result for a proof of the cut-elimination theorem.