First-order logic Davis-Putnam-Logemann-Loveland procedure

The Davis-Putnam-Logemann-Loveland procedure (DPLL) was introduced in the early 1960s as a proof procedure for first-order logic. Nowadays, only its propositional logic core component is widely used in efficient propositional logic provers and respective applications. This success has motivated lifting DPLL to the first-order logic level in a more contemporary way, by exploiting successful first-order techniques like unification. Following this idea, in this chapter, a first-order logic version of DPLL, FDPLL, is presented.While propositional DPLL is based on a splitting rule for case analysis with respect to ground and complementary literals, FDPLL uses a lifted splitting rule--that is, the case analysis is made with respect to nonground and complementary literals now. To make this work, a new way of treating variables is employed. It comes together with a compact way of representing and reasoning with first-order logic interpretations, much like propositional DPLL reasons about propositional truth assignments. As a nice consequence, FDPLL naturally decides the class of Beruays-Schonfinkel formulas, which is notoriously difficult for most other calculi.

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