Agents' beliefs can be incomplete and partially inconsistent. The process of agents' belief formation in such contexts has to be supported by suitable tools allowing one to express a variety of inconsistency resolving and nonmonotonic reasoning techniques.

In this paper we discuss 4QL*, a general purpose rule-based query language allowing one to use rules with negation in the premises and in the conclusions of rules. It is based on a simple and intuitive semantics and provides uniform tools for lightweight versions of well-known forms of nonmonotonic reasoning. In addition, it is tractable w.r.t. data complexity and captures PTIME queries, so can be used in real-world applications.

Reasoning in 4QL* is based on well-supported models. We simplify and at the same time generalize previous definitions of well-supported models and develop a new algorithm for computing such models.