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arxiv: 2605.01442 · v1 · submitted 2026-05-02 · 💻 cs.AI · math.LO

Rethinking Explanations: Formalizing Contrast in Description Logics

Yasir Mahmood , Arnab Sharma , Axel-Cyrille Ngonga Ngomo , Balram Tiwari This is my paper

Pith reviewed 2026-05-09 14:29 UTC · model grok-4.3

classification 💻 cs.AI math.LO
keywords contrastive explanationsdescription logicsknowledge basesABox assertionsjustificationsELALC
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The pith

Description logic knowledge bases can explain a true fact by contrasting it directly against a similar but absent foil.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes contrastive explanations to answer why one axiom P holds instead of another expected axiom Q in description logic knowledge bases. Existing justification and abduction methods only trace reasoning steps for individual true or missing axioms without addressing user surprise or the differences between alternatives. By formalizing facts as ABox assertions such as C(x) and possible foils as C(y) or D(x), the work defines a contrast relation that isolates the distinguishing axioms. This approach is developed for the DL fragments EL and ALC, with properties analyzed and an implementation tested on knowledge bases of different sizes.

Core claim

Contrastive explanations are defined by relating a fact assertion to a foil assertion and identifying the minimal differences in the supporting axioms or reasoning steps that entail the fact but do not entail the foil, thereby answering the question why P holds instead of Q over description logic knowledge bases.

What carries the argument

The contrast relation, which takes a fact assertion and a foil assertion as input and outputs the set of axioms that support the fact but not the foil.

Load-bearing premise

Users will find direct contrasts between similar facts and foils more useful than separate explanations for each, and the contrast relation can be computed efficiently while keeping the same soundness as standard description logic reasoning.

What would settle it

A direct comparison on a large knowledge base showing whether computing the contrast relation takes significantly longer than standard entailment checks or produces explanations that users rate no better than separate why and why-not answers.

read the original abstract

There has been a growing interest in explaining entailments over description logic (DL) knowledge bases. The existing explanation formalisms focus on justifications to explain true axioms, and abductive reasoning to explain missing axioms in a knowledge base. However, these formalisms only point out the reasoning steps behind a (missing) entailment and lack a user-centered approach as they do not consider an inquirer's needs, level of understanding, or prior knowledge. We propose contrastive explanations, aiming at answering "why an axiom P (fact) is true instead of another axiom Q (foil)" over description logic knowledge bases. The motivation arises from the observation that when a user discovers that P has occurred, they are often surprised because they anticipated the occurrence of another similar event Q. Furthermore, individual explanations for "why P" and "why not Q" are unsatisfactory since a user expects to see the difference between P and Q. In this work, we first present formal foundations of contrasting questions and then define contrastive explanations within description logics. To this end, facts include ABox assertions of the form C(x) for a concept C and individual x. Possible foils for such facts are assertions C(y) (contrasting against an individual y), or D(x) (contrasting against a concept D). Additionally, we explore the properties of contrastive explanations in the DL EL and ALC. We also provide an implementation of our definition and an experimental evaluation on KBs of varying sizes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes contrastive explanations for description logic knowledge bases to answer why an axiom P (fact) holds instead of a foil Q. Facts are ABox assertions C(x); foils are C(y) (different individual) or D(x) (different concept). It presents formal foundations for contrasting questions, defines the contrastive explanations using DL entailment differences, explores their properties in EL and ALC, and reports an implementation with runtime experiments on KBs of varying sizes.

Significance. If the contrast relation is shown to be computable while preserving standard DL soundness and entailment properties, the formalization offers a structured way to generate difference-focused explanations that could improve usability in ontology reasoning systems. The explicit treatment of foils and the EL/ALC properties are constructive contributions; however, the practical advantage over separate why-P and why-not-Q justifications remains an unverified assumption since no user model, satisfaction metric, or study is supplied.

major comments (2)
  1. [Abstract / Motivation] Abstract and motivation section: the central claim that separate explanations for 'why P' and 'why not Q' are unsatisfactory because users expect to see the difference is presented as motivation, yet no formal model of user priors, no contrast metric, and no user study or proxy evaluation appear; experiments report only KB size and runtime, leaving the user-centered advantage untested and therefore not derived from the formalism.
  2. [Definition of Contrastive Explanations] Definition of contrastive explanations (likely §3): the contrast relation is defined via entailment differences for foils C(y) and D(x), but without an explicit statement or derivation showing that the new relation introduces no additional inconsistencies or violates standard DL soundness, it is difficult to confirm that the formalism remains conservative over existing justification and abduction methods.
minor comments (2)
  1. [Formal Foundations] Notation for foils and contrast sets should be introduced with a small example immediately after the definition to improve readability.
  2. [Implementation and Evaluation] The experimental section would benefit from reporting the number of contrastive explanations generated per KB in addition to runtime, to give a sense of output size.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive feedback on our manuscript. We address each major comment below, indicating where revisions will be made to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract / Motivation] Abstract and motivation section: the central claim that separate explanations for 'why P' and 'why not Q' are unsatisfactory because users expect to see the difference is presented as motivation, yet no formal model of user priors, no contrast metric, and no user study or proxy evaluation appear; experiments report only KB size and runtime, leaving the user-centered advantage untested and therefore not derived from the formalism.

    Authors: We acknowledge that the motivation draws from cognitive science observations on contrastive explanations without providing a new user model or study in this work. The paper's primary contribution is the formalization in description logics, with experiments focused on computational feasibility. We will revise the abstract and motivation section to explicitly note that the user-centered advantage is hypothesized based on prior literature and that empirical validation via user studies is left for future work. revision: partial

  2. Referee: [Definition of Contrastive Explanations] Definition of contrastive explanations (likely §3): the contrast relation is defined via entailment differences for foils C(y) and D(x), but without an explicit statement or derivation showing that the new relation introduces no additional inconsistencies or violates standard DL soundness, it is difficult to confirm that the formalism remains conservative over existing justification and abduction methods.

    Authors: We agree that an explicit statement on conservativeness is needed for clarity. The contrastive explanation is defined as the symmetric difference of justifications for the fact and foil, which by construction relies solely on standard DL entailments. We will add a proposition in Section 3 with a brief proof that the definition preserves soundness, introduces no new inconsistencies, and remains conservative over existing justification methods. revision: yes

Circularity Check

0 steps flagged

No significant circularity; proposal is a new definitional framework

full rationale

The paper introduces formal foundations for contrasting questions and then defines contrastive explanations in description logics as a direct extension of standard DL semantics and entailment. Facts are ABox assertions C(x), with foils C(y) or D(x) identified via entailment differences; properties in EL and ALC follow from these definitions without any reduction of a derived object to fitted inputs or prior self-citations. The implementation and runtime experiments on KB sizes are independent of the formal claims. No load-bearing step matches the enumerated circularity patterns, as the central result is the definition itself rather than a prediction or theorem that collapses to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard DL semantics plus newly introduced contrast relations; no free parameters are mentioned. Axioms are the usual TBox and ABox entailment rules of EL and ALC. No new physical entities are postulated.

axioms (2)
  • standard math Standard description logic semantics for concept and role assertions
    Invoked when defining facts as ABox assertions C(x) and entailment.
  • domain assumption Users expect explanations that highlight differences between P and Q rather than separate why-P and why-not-Q answers
    Stated in the motivation paragraph of the abstract.
invented entities (1)
  • Contrastive explanation no independent evidence
    purpose: To answer why P holds instead of foil Q in DL knowledge bases
    Newly defined construct; no independent evidence outside the paper is provided.

pith-pipeline@v0.9.0 · 5576 in / 1411 out tokens · 20448 ms · 2026-05-09T14:29:40.112335+00:00 · methodology

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Reference graph

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