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This paper shows that several propositional satisfiability algorithms compute approximations of fixed points using lattice-based abstractions. The Boolean Constraint Propagation algorithm (bcp) is a greatest fixed point computation over a lattice of partial assignments. The original algorithm of Davis, Logemann and Loveland refines bcp by computing a set of greatest fixed points. The Conflict Driven Clause Learning algorithm alternates between overapproximate deduction with bcp, and underapproximate abduction, with conflict analysis. Thus, in a precise sense, satisfiability solvers are abstract interpreters. Our work is the first step towards a uniform framework for the design and implementation of satisfiability algorithms, static analysers and their combination.