One possible development of the present work is towards the analysis of reasoning about minimal belief and negation as failure in a first-order setting: in particular, it should be interesting to see whether it is possible to extend the techniques developed for the propositional case to a more expressive language. A first attempt in this direction is reported by Donini et al. (1997a).

## Acknowledgments

This research has been partially supported by Consiglio Nazionale delle Ricerche, grant 203.15.10.

## References

Beringer, A., & Schaub, T. (1993). Minimal belief and negation as failure: a feasible approach. In Proc. of the 11th Nat. Conf. on Artificial Intelligence (AAAI'93), pp.

400 405.

Bochman, A. (1995). On bimodal nonmonotonic modal logics and their unimodal and nonmodal equivalents. In Proc. of the 14th Int. Joint Conf. on Artificial Intelligence
(IJCAI'95), pp. 1518 1524.
Chen, J. (1994).  The logic of only knowing as a unified framework for non-monotonic reasoning. Fundamenta Informaticae, 21, 205 220.

Donini, F. M., Nardi, D., & Rosati, R. (1997a). Autoepistemic description logics. In Proc.

of the 15th Int. Joint Conf. on Artificial Intelligence (IJCAI'97), pp. 136 141.

Donini, F. M., Nardi, D., & Rosati, R. (1997b). Ground nonmonotonic modal logics. J. of Logic and Computation, 7 (4), 523 548.

Eiter, T., & Gottlob, G. (1992). Reasoning with parsimonious and moderately grounded expansions. Fundamenta Informaticae, 17 (1,2), 31 54.
Eiter, T., & Gottlob, G. (1993). Propositional circumscription and extended closed world reasoning are Π 2 -complete. Theoretical Computer Science, 114, 231 245.

Eiter, T., & Gottlob, G. (1995). On the computational cost of disjunctive logic programming: propositional case. Annals of Mathematics and Artificial Intelligence, 15 (3,4).

Gelfond, M., & Lifschitz, V. (1988). The stable model semantics for logic programming.

In Proceedings of the Fifth Logic Programming Symposium, pp. 1070 1080. The MIT
Press.
Gelfond, M., & Lifschitz, V. (1990). Logic programs with classical negation. In Proceedings of the Seventh International Conference on Logic Programming, pp. 579 597. The MIT Press.

Gelfond, M., & Lifschitz, V. (1991). Classical negation in logic programs and disjunctive databases. New Generation Computing, 9, 365 385.