Living with inconsistency and taming nonmonotonicity

In this paper we consider rule-based query languages with negation in bodies and heads of rules, traditionally denoted by Datalog¬¬. Tractable and at the same time intuitive semantics for Datalog¬¬ has not been provided even though the area of deductive databases is over 30 years old. In this paper we identify sources of the problem and propose a query language, which we call 4QL. The 4QL language supports a modular and layered architecture and provides a tractable framework for many forms of rule-based reasoning both monotonic and nonmonotonic. As the underpinning principle we assume openness of the world, which may lead to the lack of knowledge. Negation in rule heads may lead to inconsistencies. To reduce the unknown/inconsistent zones we introduce simple constructs which provide means for application-specific disambiguation of inconsistent information, the use of Local Closed World Assumption (thus also Closed World Assumption, if needed), as well as various forms of default and defeasible reasoning.

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