A constructive valuation semantics for classical logic
The goal is to find a witness for \(x\) from a classical proof of \(\exists xP(x)\) from Horn assumptions \(\forall y(Q_1(Y)\&\cdots\& Q_n(y)\to Q_{n+1}(y))\). For this fragment classical and intuitionistic provability coincide, and it is difficult to invent a classical proof which is not already intuitionistic (if obvious redundancies are deleted).
scientific article; zbMATH DE number 1011146