Negative Knowledge for Certain Query Answers

Abstract

Abstract. Querying incomplete data usually amounts to finding answers we are certain about. Standard approaches concentrate on positive information about query answers, and miss negative knowledge, which can be useful for two reasons. First, sometimes it is the only type of knowledge one can infer with certainty, and second, it may help one find good and efficient approximations of positive certain answers. Our goal is to consider a framework for defining both positive and negative certain knowledge about query answers and to show two applications of it. First, we demonstrate that it naturally leads to a way of representing certain information that has hitherto not been used in querying incomplete databases. Second, we show that approximations of such certain information can be computed efficiently for all first-order queries over relational databases.

Coping with Incomplete Data: Recent Advances

“…The framework of [49] presented in Section 3.2 has been used to define certain answers as objects, but there is more to it and we believe it should be further developed. One example of the use the use of the framework is [50], which defined negative and possible answers with the help of certain knowledge. It can also be used to handle semantically opaque object identifiers, a problem which is especially relevant in data integration and OBDA, where object identifiers are retrieved from multiple sources and are often encoded using different conventions.…”

Earliest Query Answering for Deterministic Stepwise Hedge Automata

“…The open end of a stream can be instantiated continuously. Therefore, streams can be seen as incomplete databases, for which the notion of certain query answers (CQAs) was widely studied [9]. An element is a certain query answer if it is selected by all completions of the incomplete database.…”

Universal (and Existential) Nulls

“…◂ Another area of applications of "*"-nulls relates to intuitionistic, or constructive database logic. In the constructive four-valued approach of [15] and the three-valued approach of [13,22] the proposition A ∨ ¬A is not a tautology. In order for A ∨ ¬A to be true, we need either a constructive proof of A or a constructive proof of ¬A.…”

“…In order for A ∨ ¬A to be true, we need either a constructive proof of A or a constructive proof of ¬A. Therefore both [15] and [22] assume that the database I has a theory of the negative information, i.e. that I = (I + , I − ), where I + contains the positive information and I − the negative information.…”

“…that I = (I + , I − ), where I + contains the positive information and I − the negative information. The papers [15] and [22] then show how to transform an FO-query ϕ(x) to a pair of queries (ϕ + (x), ϕ − (x)) such that ϕ + (x) returns the tuples ā for which ϕ(ā) is true in I + , and ϕ − (x) returns the tuples ā for which ϕ(ā) is true in I − (i.e. ϕ(ā) is false in I).…”