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Navigating Taxonomic Expansions of Entity Sets Driven by Knowledge Bases

Pietro Cofone, Giovanni Amendola, Marco Manna, Aldo Ricioppo

TL;DR

The paper extends entity set expansion by introducing taxonomic expansion graphs derived from knowledge bases to reveal hierarchical generalizations beyond linear expansion. It formalizes three local navigation primitives (SIM, PREC, INC) and three core tasks (can, core, ess) within the NCF/SKB framework, enabling efficient local exploration without full graph materialization. A rigorous complexity landscape is developed under broad, medium, and handy assumptions, showing intractability in broad settings but tractability in the handy setting, with concrete reductions and algorithms linking canonical/core/essential expansions to navigation tasks. These results provide a principled foundation for practical, real-time navigation of taxonomic expansion graphs and point to future work on approximation, alternative explanation languages, and richer summaries.

Abstract

Recognizing similarities among entities is central to both human cognition and computational intelligence. Within this broader landscape, Entity Set Expansion is one prominent task aimed at taking an initial set of (tuples of) entities and identifying additional ones that share relevant semantic properties with the former -- potentially repeating the process to form increasingly broader sets. However, this ``linear'' approach does not unveil the richer ``taxonomic'' structures present in knowledge resources. A recent logic-based framework introduces the notion of an expansion graph: a rooted directed acyclic graph where each node represents a semantic generalization labeled by a logical formula, and edges encode strict semantic inclusion. This structure supports taxonomic expansions of entity sets driven by knowledge bases. Yet, the potentially large size of such graphs may make full materialization impractical in real-world scenarios. To overcome this, we formalize reasoning tasks that check whether two tuples belong to comparable, incomparable, or the same nodes in the graph. Our results show that, under realistic assumptions -- such as bounding the input or limiting entity descriptions -- these tasks can be implemented efficiently. This enables local, incremental navigation of expansion graphs, supporting practical applications without requiring full graph construction.

Navigating Taxonomic Expansions of Entity Sets Driven by Knowledge Bases

TL;DR

The paper extends entity set expansion by introducing taxonomic expansion graphs derived from knowledge bases to reveal hierarchical generalizations beyond linear expansion. It formalizes three local navigation primitives (SIM, PREC, INC) and three core tasks (can, core, ess) within the NCF/SKB framework, enabling efficient local exploration without full graph materialization. A rigorous complexity landscape is developed under broad, medium, and handy assumptions, showing intractability in broad settings but tractability in the handy setting, with concrete reductions and algorithms linking canonical/core/essential expansions to navigation tasks. These results provide a principled foundation for practical, real-time navigation of taxonomic expansion graphs and point to future work on approximation, alternative explanation languages, and richer summaries.

Abstract

Recognizing similarities among entities is central to both human cognition and computational intelligence. Within this broader landscape, Entity Set Expansion is one prominent task aimed at taking an initial set of (tuples of) entities and identifying additional ones that share relevant semantic properties with the former -- potentially repeating the process to form increasingly broader sets. However, this ``linear'' approach does not unveil the richer ``taxonomic'' structures present in knowledge resources. A recent logic-based framework introduces the notion of an expansion graph: a rooted directed acyclic graph where each node represents a semantic generalization labeled by a logical formula, and edges encode strict semantic inclusion. This structure supports taxonomic expansions of entity sets driven by knowledge bases. Yet, the potentially large size of such graphs may make full materialization impractical in real-world scenarios. To overcome this, we formalize reasoning tasks that check whether two tuples belong to comparable, incomparable, or the same nodes in the graph. Our results show that, under realistic assumptions -- such as bounding the input or limiting entity descriptions -- these tasks can be implemented efficiently. This enables local, incremental navigation of expansion graphs, supporting practical applications without requiring full graph construction.

Paper Structure

This paper contains 19 sections, 12 theorems, 17 equations, 2 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Context
  3. Working Example
  4. Motivation
  5. Contribution
  6. Preliminaries
  7. Basics on Relational Structures
  8. Knowledge Bases and Conjunctive Formulas
  9. Computational Complexity
  10. Framework Overview
  11. Navigating Taxonomic Expansions of Entity Sets
  12. Computing Characterizations and Essential Expansions
  13. Canonical Characterizations (can problem)
  14. Core Characterizations (core problem)
  15. Essential Expansion (ess problem)
  16. ...and 4 more sections

Key Result

proposition 1

Let $\tau_1$ and $\tau_2$ be two $n$-ary tuples. It holds that $\mathit{ess}(\mathbf{U}\cup{\tau_1},\mathcal{S})\subseteq\mathit{ess}(\mathbf{U}\cup{\tau_2},\mathcal{S})$ if, and only if, $\mathit{core}(\mathbf{U}\cup{\tau_2},\mathcal{S})\longrightarrow\mathit{core}(\mathbf{U}\cup{\tau_1},\mathcal{S

Figures (2)

  • Figure 1: Knowledge graph $\mathcal{G}_0$ underlying the selective knowledge base $\mathcal{S}_0$ of our Example.
  • Figure 2: Expansion graph $\mathit{eg}(\mathbf{U}_0,\mathcal{S}_0)$, where $\mathsf{tp} = \mathsf{theme\_park}$, $\mathsf{ap} = \mathsf{amusement\_park}$, and $\mathit{conj}(\varphi)$ is the conjunction of atoms of $\varphi$.

Theorems & Definitions (25)

  • proposition 1: AMENDOLA2024120331
  • definition 1: AMENDOLA2024120331
  • proposition 2
  • proof
  • proposition 3
  • proof
  • theorem 1
  • proof
  • Corollary 5.1
  • proof
  • ...and 15 more