Analytic cut trees

Logic Journal of the IGPL 8:733-750 (2000)
Abstract
It has been maintained by Smullyan that the importance of cut-free proofs does not stem from cut elimination per se but rather from the fact that they satisfy the subformula property. In accordance with such a viewpoint in this paper we introduce <span class='Hi'>analytic</span> cut trees, a system from which cuts cannot be eliminated but satisfying the subformula property. Like tableaux <span class='Hi'>analytic</span> cut trees are a refutation system but unlike tableaux they have a single inference rule (a form of the <span class='Hi'>analytic</span> cut rule) and several branch closure rules. The main advantage of <span class='Hi'>analytic</span> cut trees over tableaux is efficiency: while <span class='Hi'>analytic</span> cut trees can simulate tableaux with an increase in complexity by at most a constant factor, tableaux cannot polynomially simulate <span class='Hi'>analytic</span> cut trees. Indeed <span class='Hi'>analytic</span> cut trees are intrinsically more efficient than any cut-free system.
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