In database theory and knowledge representation, the certain answers is the set of answers to a given query consisting of the intersection of all the complete databases that are consistent with a given knowledge base. The notion of certain answer, investigated in database theory since the 1970s, is indeed defined in the context of open world assumption, where the given knowledge base is assumed to be incomplete.
Intuitively, certain answers are the answers that are always returned when querying a given knowledge base, considering both the extensional knowledge that the possible implications inferred by automatic reasoning, regardless of the specific interpretation.
Definition.
In literature, the set of certain answers is usually defined as follows:
formula_1
where:
In description logics, such set may be defined in a similar way as follows:
Given an ontology formula_8 and a query formula_9 on formula_10, formula_11 is the set of tuples formula_12 such that, for each model formula_13 of formula_10, we have that formula_15.
Where: