geometric formulae and axioms

Dear category theorists, Recently I came across geometric formulae (built up from atomic formulae using only conjunction, disjunction and existential quantification). I would know like to know whether there is any way to decide whether an arbitrary given first order formula is (classically) equivalent to a geometric formula (or geometric axiom: phi -> psi where phi and psi are both geometric formulae). I've looked in the book by Mac Lane and Moerdijk but didn't discover a general decision method. Any hints or references to relevant literature would be much appreciated. Best regards, Karel Stokkermans