Abstract We study the notion of strong equivalence between two disjunctive logic programs under the G3-stable model semantics, also called the P-stable semantics, and we show how some particular cases of testing strong equivalence between programs can be reduced to verify if a formula is a theorem in some paraconsistent logics or in some cases in classical logic. We also present some program transformations for disjunctive programs which can be used to reduce the size of a program.