Abstract In Minker and Rajasekar (J Log Program 9(1):45–74, 1990), proposed a semantics for negation-free disjunctive logic programs that offers natural generalisation of the fixed point definite programs. We show this can be further generalised with classical negation, in constructive modal-theoretic framework where rules are built from claims hypotheses , namely, formulas form $$\Box \varphi ...