  We formulate a Boolean algebra in the set of idempotents of Clifford algebra
Cl($R^{n,n}$) and within this frame we examine different formulations of the
Boolean Satisfiability Problem in Clifford algebra. Exploiting the isomorphism
between null subspaces of $R^{n,n}$ associated to simple spinors and the
orthogonal group O(n) we ultimately give a continuous formulation of the
Boolean Satisfiability Problem within this group that opens unexplored
perspectives.
