Incremental Closure of Variable Splitting Tableaux

Incremental closure is a proof search technique for free variable analytic tableaux where partial solutions are updated along with tableaux expansion. In this paper we address possible adaptations of the incremental closure technique to variable splitting tableaux. Variable splitting tableaux provide a sound way to instantiate occurrences of the same variable in different branches differently by imposing additional constraints on closing substitutions. We show how these constraints can be formulated as graph theoretical problems and suggest incremental methods for calculating solutions.