No abstract

No abstract

Not all queries in relational calculus can be answered sensibly when disjunction, negation, and universal quantification are allowed. The class of relation calculus queries or formulas that have sensible answers is called the domain independent class which is known to be undecidable. Subsequent research has focused on identifying large decidable subclasses of domain independent formulas. In this paper we investigate the properties of two such classes: the evaluable formulas and the allowed formulas. Although both classes have been defined before, we give simplified definitions, present short proofs of their main properties, and describe a method to incorporate equality. Although evaluable queries have sensible answers, it is not straightforward to compute them efficiently or correctly. We introduce relational algebra normal form for formulas from which form the correct translation into relational algebra is trivial. We give algorithms to transform an evaluable formula into an equivalent allowed formula and from there into relational algebra normal form. Our algorithms avoid use of the so-called Dom relation, consisting of all constants appearing in the database or the query. Finally, we describe a restriction under which every domain independent formula is evaluable and argue that the class of evaluable formulas is the largest decidable subclass of the domain independent formulas that can be efficiently recognized.

To support the reuse and combination of ontologies in Semantic Web applications, it is often necessary to obtain smaller ontologies from existing larger ontologies. In particular, applications may require the omission of certain terms, e. g., concept names and role names, from an ontology. However, the task of omitting terms from an ontology is challenging because the omission of some terms may affect the relationships between the remaining terms in complex ways. We present the first solution to the problem of omitting concepts and roles from knowledge bases of description logics (DLs) by adapting the technique of forgetting, previously used in other domains. Specifically, we first introduce a model-theoretic definition of forgetting for knowledge bases (both TBoxes and ABoxes) in DL-Lite N bool , which is a non-trivial adaption of the standard definition for classical logic, and show that our model-based forgetting satisfies all major criteria of a rational forgetting operator, which in turn verifies the suitability of our model-based forgetting. We then introduce algorithms that implement forgetting operations in DL-Lite knowledge bases. We prove that the algorithms are correct with respect to the semantic definition of forgetting. We establish a general framework for defining and comparing different definitions of forgetting by introducing a parameterized family of forgetting operators called query-based forgetting operators. In this framework we identify three specific query-based forgetting operators and show that they form a hierarchy. In particular, we show that the model-based forgetting coincides with one of these query-based forgetting operators.

No abstract