Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Can You Tell the Difference? Contrastive Explanations for ABox Entailments

Patrick Koopmann, Yasir Mahmood, Axel-Cyrille Ngonga Ngomo, Balram Tiwari

TL;DR

This paper introduces contrastive ABox explanations (CEs) to answer why C(a) holds while C(b) does not, formalizing CPs and ABox patterns to capture the differences between fact and foil. It defines syntactic and semantic CEs and three optimality criteria—difference-minimal, conflict-minimal, and commonality-maximal—and analyzes their computational complexity across DLs from $\mathcal{EL}$ to $\mathcal{ALCI}$. It provides a first practical method for computing difference-minimal syntactic CEs and evaluates it on realistic knowledge bases, offering empirical insight into tractability and scalability. The work lays out a foundation for contrastive explanations in ontology reasoning, with implications for explainable AI in DL-based applications and future work to optimize algorithms and explore extended CE variants.

Abstract

We introduce the notion of contrastive ABox explanations to answer questions of the type "Why is a an instance of C, but b is not?". While there are various approaches for explaining positive entailments (why is C(a) entailed by the knowledge base) as well as missing entailments (why is C(b) not entailed) in isolation, contrastive explanations consider both at the same time, which allows them to focus on the relevant commonalities and differences between a and b. We develop an appropriate notion of contrastive explanations for the special case of ABox reasoning with description logic ontologies, and analyze the computational complexity for different variants under different optimality criteria, considering lightweight as well as more expressive description logics. We implemented a first method for computing one variant of contrastive explanations, and evaluated it on generated problems for realistic knowledge bases.

Can You Tell the Difference? Contrastive Explanations for ABox Entailments

TL;DR

This paper introduces contrastive ABox explanations (CEs) to answer why C(a) holds while C(b) does not, formalizing CPs and ABox patterns to capture the differences between fact and foil. It defines syntactic and semantic CEs and three optimality criteria—difference-minimal, conflict-minimal, and commonality-maximal—and analyzes their computational complexity across DLs from to . It provides a first practical method for computing difference-minimal syntactic CEs and evaluates it on realistic knowledge bases, offering empirical insight into tractability and scalability. The work lays out a foundation for contrastive explanations in ontology reasoning, with implications for explainable AI in DL-based applications and future work to optimize algorithms and explore extended CE variants.

Abstract

We introduce the notion of contrastive ABox explanations to answer questions of the type "Why is a an instance of C, but b is not?". While there are various approaches for explaining positive entailments (why is C(a) entailed by the knowledge base) as well as missing entailments (why is C(b) not entailed) in isolation, contrastive explanations consider both at the same time, which allows them to focus on the relevant commonalities and differences between a and b. We develop an appropriate notion of contrastive explanations for the special case of ABox reasoning with description logic ontologies, and analyze the computational complexity for different variants under different optimality criteria, considering lightweight as well as more expressive description logics. We implemented a first method for computing one variant of contrastive explanations, and evaluated it on generated problems for realistic knowledge bases.

Paper Structure

This paper contains 29 sections, 34 theorems, 36 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Description Logics
  4. Contrastive Explanations
  5. Syntactic and Semantic CEs
  6. Optimality Criteria
  7. Decision Problems
  8. Difference-Minimal Explanations
  9. Conflict-Minimal Explanations
  10. Commonality-Maximal Explanations
  11. Evaluation of a First Prototype
  12. A Practical Method for Computing CEs
  13. Benchmark
  14. Evaluation Results
  15. Conclusion and Future Work
  16. ...and 14 more sections

Key Result

Lemma 5

Let $P=\langle\langle\mathcal{T}\xspace,\mathcal{A}\xspace\rangle,C,a,b\rangle$ be an $\mathcal{L}$ CP. Then, one can compute in polynomial time, with access to an oracle that decides entailment for $\mathcal{L}$, an ABox $\mathcal{A}\xspace_e$ such that every semantic CE for $P$ is a syntactic CE f

Theorems & Definitions (78)

  • Definition 1
  • Example 2
  • Definition 3: Syntactic and Semantic CEs
  • Example 4
  • Lemma 5
  • proof
  • Definition 6: Preferred CEs
  • Definition 7
  • Lemma 7
  • Lemma 7
  • ...and 68 more