Inference From Visible Information And Background Knowledge

TL;DR

This paper studies how to infer positive and negative information about queries in relational databases with visible and invisible relations, constrained by background theories, at both instance and schema levels.

Contribution

It provides a comprehensive analysis of inference problems involving visible and invisible relations under logical constraints, covering both instance and schema-level scenarios.

Findings

Characterizes conditions for positive inference of queries.

Analyzes the complexity of inference tasks.

Provides insights into schema-level inference capabilities.

Abstract

We provide a wide-ranging study of the scenario where a subset of the relations in a relational vocabulary are visible to a user --- that is, their complete contents are known --- while the remaining relations are invisible. We also have a background theory --- invariants given by logical sentences --- which may relate the visible relations to invisible ones, and also may constrain both the visible and invisible relations in isolation. We want to determine whether some other information, given as a positive existential formula, can be inferred using only the visible information and the background theory. This formula whose inference we are concered with is denoted as the \emph{query}. We consider whether positive information about the query can be inferred, and also whether negative information -- the sentence does not hold -- can be inferred. We further consider both the instance-level version of the problem, where both the query and the visible instance are given, and the schema-level version, where we want to know whether truth or falsity of the query can be inferred in some instance of the schema.