Executable First-Order Queries in the Logic of Information Flows

TL;DR

This paper introduces a new variant of the logic of information flows called forward LIF (FLIF), which models executable first-order queries with a graph-navigational approach, enabling effective query processing under access limitations.

Contribution

It proposes FLIF, a novel first-order logic variant that aligns with executable query fragments and facilitates translation into algebraic plans respecting access constraints.

Findings

FLIF is equivalent to the executable fragment of first-order logic.

io-disjoint FLIF expressions enable transparent algebraic query plan translation.

Any FLIF expression can be transformed into io-disjoint form.

Abstract

The logic of information flows (LIF) has recently been proposed as a general framework in the field of knowledge representation. In this framework, tasks of procedural nature can still be modeled in a declarative, logic-based fashion. In this paper, we focus on the task of query processing under limited access patterns, a well-studied problem in the database literature. We show that LIF is well-suited for modeling this task. Toward this goal, we introduce a variant of LIF called "forward" LIF (FLIF), in a first-order setting. FLIF takes a novel graph-navigational approach; it is an XPath-like language that nevertheless turns out to be equivalent to the "executable" fragment of first-order logic defined by Nash and Lud\"ascher. One can also classify the variables in FLIF expressions as inputs and outputs. Expressions where inputs and outputs are disjoint, referred to as io-disjoint FLIF expressions, allow a particularly transparent translation into algebraic query plans that respect the access limitations. Finally, we show that general FLIF expressions can always be put into io-disjoint form.