We present the semantic foundations for computing the least fix-point semantics of definite logic programs using only standard operations over boolean functions. More precisely, we propose a representation of sets of first-order terms by boolean functions and a provably sound formulation of intersection, union, and projection (an operation similar to restriction in relational databases) using conjunction, disjunction, and existential quantification. We report on a prototype implementation of a logic solver using Binary Decision Diagrams (BDDs) to represent boolean functions and compute the above-mentioned three operations. This work paves the way for efficient solvers for particular classes of logic programs e.g., static program analyses, which leverage BDD technologies to factorise similarities in the solution space.