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Executable First-Order Queries in the Logic of Information Flows

Heba Aamer, Bart Bogaerts, Dimitri Surinx, Eugenia Ternovska, Jan Van den Bussche

TL;DR

This work introduces FLIF, a forward-only graph-navigation fragment of the Logic of Information Flows, and proves its expressive equivalence with executable FO for queries under limited access patterns. FLIF provides a simple, compositional language with atomic edges representing information accesses and three operators for path construction, enabling declarative modeling of data sources with restricted inputs. The paper develops io-disjoint FLIF and shows how any FLIF can be rewritten into this fragment, yielding transparent translations to executable FO and enabling straightforward relational-algebra plans for query processing. The results offer a direct, efficiency-conscious bridge between navigational graph querying and first-order logic within access-constrained settings, with implications for information integration and web-like data sources.

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 Ludäscher. 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.

Executable First-Order Queries in the Logic of Information Flows

TL;DR

This work introduces FLIF, a forward-only graph-navigation fragment of the Logic of Information Flows, and proves its expressive equivalence with executable FO for queries under limited access patterns. FLIF provides a simple, compositional language with atomic edges representing information accesses and three operators for path construction, enabling declarative modeling of data sources with restricted inputs. The paper develops io-disjoint FLIF and shows how any FLIF can be rewritten into this fragment, yielding transparent translations to executable FO and enabling straightforward relational-algebra plans for query processing. The results offer a direct, efficiency-conscious bridge between navigational graph querying and first-order logic within access-constrained settings, with implications for information integration and web-like data sources.

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 Ludäscher. 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.
Paper Structure (55 sections, 13 theorems, 70 equations, 3 figures, 2 tables)

This paper contains 55 sections, 13 theorems, 70 equations, 3 figures, 2 tables.

Table of Contents

  1. Preliminaries
  2. Forward LIF
  3. Syntax and semantics of FLIF: atomic expressions
  4. Syntax and semantics of FLIF: operators
  5. The evaluation problem for FLIF expressions
  6. Executable FO
  7. $\mathcal{V}$-executable Formulas
  8. From Executable FO to FLIF
  9. From FLIF to executable FO
  10. Inputs and outputs of forward LIF
  11. Io-disjoint FLIF
  12. From FLIF to io-disjoint FLIF
  13. Complications of Translation
  14. Statement of the theorem
  15. Variable renaming
  16. ...and 40 more sections

Key Result

Theorem 3.5

Let $\varphi$ be a $\mathcal{V}$-executable formula over a schema $\mathcal{S}$. There exists an FLIF expression $\alpha$ over $\mathcal{S}$ and a set of variables $\mathbb{V} \supseteq \mathit{fvars}(\varphi) \cup \mathcal{V}$ such that for every $D$, $\mathcal{V}$-valuation $\nu_{\rm in}$, and $\m

Figures (3)

  • Figure 1: Part of graph view of the database considered in Example \ref{['ex:bustrain1']}.
  • Figure 2: Table view for the expressions considered in Example \ref{['ex:bustrain1']}.
  • Figure 3: Summary of the translations shown in the paper, where a dashed arrow denotes an input-respecting translation, a double arrow denotes a simple translation, and finally, a double dashed arrow denotes both.

Theorems & Definitions (47)

  • Remark 1.1
  • Definition 2.1
  • Example 2.2
  • Example 2.3
  • Remark 2.4
  • Example 2.5
  • Remark 2.6
  • Definition 2.7: The evaluation problem $\mathit{Eval}_{\alpha}^{\mathbb{V}}(D,\nu_{\rm in})$ for FLIF expression $\alpha$ over $\mathbb{V}$
  • Example 2.8
  • Example 3.1
  • ...and 37 more