Reconstructing a single-head formula to facilitate logical forgetting

Abstract

Abstract Logical forgetting is removing some variables from a formula while maintaining its consequences on the remaining variables. This removal may require exponential time on arbitrary propositional Horn formulae, but it only takes polynomial time on single-head propositional definite Horn formulae. Single-head means that no variable is the head of multiple clauses. An algorithm to make a formula single-head if possible is shown. It enlarges the set of formulae admitting polynomial-time forgetting by making them single-head if possible and then running the usual algorithm for forgetting.