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REVIEW 4 major objections 3 minor 43 references

Counterfactual Explanations as Plans

T0 review · 4 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Counterfactual explanations of plans are minimally different alternative plans that flip the outcome, and model reconciliation is the same idea in epistemic form.

desk verdict A clean conceptual framework for counterfactual explanations in planning, but the central unification claim rests on under-specified minimality conditions that need to be made precise before the definitions are implementable. read the letter →

arxiv 2502.09205 v1 pith:I5RNUQHO submitted 2025-02-13 cs.AI cs.LO

Vaishak Belle (University of Edinburgh) This is my paper · ORCID
classification cs.AIcs.LO MSC 68T2703B4568T20
keywords counterfactualexplanationsexplainableplanningmodelreconciliationepistemiclogicsituationcalculusonly-knowingactionsequencessensingactions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that a counterfactual explanation of a plan's outcome is another executable plan that flips the outcome and is minimally different from the original plan. Once truth is distinguished from what the agent knows, the same definition covers model reconciliation: the missing knowledge or false belief the user corrects is the smallest addition or replacement that makes the plan achieve its goal. The formalization uses a modal epistemic logic of actions and knowledge, and the paper argues that existing notions of contrastive explanations, discrepancy, and skeptical or credulous reconciliation are variations of this one recipe. If right, this gives a single logical account for 'why' and 'what if' questions in sequential decision making.

What carries the argument

The load-bearing object is the counterfactual plan $\delta'$ of Definition 1, chosen to be minimally distant from the original $\delta$ while making the goal false; distance is made concrete by length-based minimality (Definition 2), fluent-based minimality (Definition 4), or the joint plan-and-effect measure (Definition 6). In the reconciliation settings the same counterfactual template is applied with epistemic goals: the missing ingredient is a formula $\alpha$ added to the agent's initial theory (or a false belief $\beta$ removed) such that the agent comes to know $\varphi$, with 'smallest such $\alpha$' playing the role of minimal distance. The supporting machinery is the modal logic ES—a situation-calculus-style language with action modalities $[a]$, 'always' $2$, knowledge $K$, and only-knowing $O$—together with basic action theories, successor state and sensing axioms, and the distinction between the real world $\Sigma_0$ and the agent's believed theory $\Sigma'_0$.

What would settle it

Build a basic action theory where achievable plan distances have no minimum (for example, an infinite descending chain generated by inserting ever-shorter no-op sequences) or where two incomparable formulas both restore the agent's knowledge of the goal; either case would show the definitions do not always pick out a unique explanation.

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Extended reading notes

Core claim

The paper's central claim is that counterfactual explanations generalize from single decisions to action sequences: given a plan $\delta$ that entails goal $\varphi$, a counterfactual explanation is a plan $\delta'$ with $\Sigma \models \mathrm{Exec}(\delta') \land [\delta']\neg\varphi$ and $\mathrm{dist}(\delta',\delta)$ minimal (Definition 1). The paper then shows that model reconciliation is the same counterfactual idea once one separates truth from belief: the user either supplies a missing formula $\alpha$ or replaces a false belief $\beta$ so that, after a minimally distant plan, the agent knows the goal (Definitions 13, 16, 18, 21). This is formalized in the modal epistemic logic ES, where the agent's uncertainty is modeled by a set of possible worlds and the only-knowing operator $O$ captures both beliefs and non-beliefs.

Load-bearing premise

The framework assumes that for every explanation query there is a well-defined 'closest' alternative plan or 'smallest' piece of missing knowledge, but the definitions do not fix a distance metric or an ordering on formulas, so in some cases no unique explanation exists.

Editorial extensions

If this is right

  • Contrastive explanations in planning—where the answer to 'why this action rather than that one' is an altered action sequence—become a special case of Definition 1.
  • Model reconciliation, where the user corrects the agent's model or suggests actions, is captured by the same counterfactual template, with the smallest missing formula or false belief as the explanation.
  • Because sensing actions are allowed, a counterfactual explanation can be a plan that gains information rather than only changing the world.
  • The paper's claim implies that existing discrepancy and skeptical/credulous reconciliation accounts can be re-expressed as variations of Definitions 13 through 21.
  • Since reasoning in ES can reduce to non-modal reasoning, the definitions are in principle implementable with standard planning and regression techniques.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The choice of distance metric is decisive: length, affected fluents, and action costs can rank the same pair of plans differently, so the framework predicts that what counts as a good explanation depends on the user's implicit notion of closeness; this is testable by user studies.
  • The paper treats the user's knowledge as a proxy for ground truth in a single-agent setting, which suggests a natural extension to genuine multi-agent counterfactual explanations by adding separate epistemic operators for each agent.
  • In machine learning, a 'plan' could be an ordered sequence of feature changes, which would connect this framework to algorithmic recourse; the paper does not explore that application.
  • One could derive concrete algorithms by instantiating the distance metric with plan cost and using a planner to search for the minimally distant goal-flipping sequence, then compare the generated explanations with human judgments.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. The paper develops a formal account of counterfactual explanations in the modal situation calculus ES. It defines a counterfactual explanation of a goal φ after an executable plan δ as an alternative executable plan δ′ that makes ¬φ true and is minimally distant from δ (Definition 1), and then extends this to epistemic goals (Definition 11), missing actions, missing knowledge, weakened truths, false beliefs (Definitions 13, 16, 18, 21), and diverse explanations (Definitions 8 and 10). The paper claims that contrastive explanations and model reconciliation become instances of this single counterfactual-plan framework. The formal content is definitional and example-driven; there are no theorems or proofs.

Significance. If the framework were made fully precise and the claimed links to model reconciliation and contrastive explanations were proved, this would be a useful unification: it gives an epistemic-logic account of counterfactual plans and clarifies how truth and belief interact in explanation. The use of ES and only-knowing is a good fit for distinguishing the user's model from the agent's beliefs, and the diversity and possibility variants show the approach has breadth. At present, however, the load-bearing notions of minimal distance and smallest knowledge addition are left unspecified, and the unification claims are asserted rather than proved. The paper is a promising formalization program rather than a completed formal result.

major comments (4)
  1. [Section 4, Definition 1 (and Definitions 11, 13, 18)] The defining condition 'dist(δ′,δ) is minimal' requires a fixed distance function and a guarantee that the minimization is attained, but neither is supplied. The metrics sketched in Definitions 2, 4, and 6 are presented only as examples, so every subsequent definition remains parameterized by an unspecified dist. For arbitrary Σ, δ, φ, the set of eligible δ′ may be empty, and with a real-valued cost the infimum may not be attained. Please state the definitions relative to a chosen metric with an explicit well-foundedness or existence condition, or prove that a minimizer exists under the stated assumptions.
  2. [Section 5.1, Definition 16 (and Definitions 18, 21)] The phrase 'the smallest such α' is not defined. Under the natural ordering by logical strength, a smallest α need not exist: if α is sufficient, any α′ logically stronger than α is also sufficient, so the set of sufficient formulas is upward closed and may have no least element in a first-order setting. Moreover, restricting α to a single sentence in Σ0−Σ′0 makes the definition empty when the missing knowledge is a conjunction of two facts. The paper should specify an ordering on formulas, allow finite conjunctions or sets, and prove existence (or state conditions under which a minimum exists).
  3. [Sections 1 and 5.4] The central claim that existing accounts of discrepancy, contrastive explanations, and credulous/skeptical reconciliation are variations of this framework is not made precise. No theorem or translation shows that, for example, the reconciliation definitions of Section 5 correspond to the discrepancy notion of [37] or that the B-based variant of Section 5.4 corresponds to credulous entailment in [42]. Without an explicit correspondence result, the claimed unification is an informal analogy rather than a formal contribution.
  4. [Section 5.1, Definition 13] The step from 'Σ ̸|= [δ]Kφ' to 'Σ |= [δ]¬Kφ' is not justified by the semantics in Section 2. In general, failure of entailment means there is a model where Kφ is false, not that Kφ is false in every model. The only-knowing operator can yield negative knowledge under suitable conditions, but the paper does not state or prove the needed property for formulas of the form [δ]Kφ. This makes the trigger condition of Definition 13, and the analogous reasoning in Examples 14 and 15, unsupported as written.
minor comments (3)
  1. [Section 4, Example 9] Example 9 is inconsistent with Definition 8. If φ = ∃x¬Broken(x), then ¬φ = ∀xBroken(x), so α ∧ ¬φ is ∃xGlass(x) ∧ ∀xBroken(x), not ∃x(Glass(x) ∧ Broken(x)). The proposed δ′ = pickup(c) · drop(c) does not make all objects broken in the example domain. Please modify either φ, α, or the example so that the formal condition and the worked scenario agree.
  2. [Section 4, Definition 10] Definition 10 is titled 'diverse CF explanations' but contains no diversity condition: it merely collects sequences satisfying the distance bound. As written, the set could contain one element or many identical elements, so the term 'diverse' is not justified by the formal condition. A diversity measure or an explicit constraint on the set should be added.
  3. [Section 3] There is a typo in the sentence 'We will included an extended report with some examples'; it should read 'We will include an extended report'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the counterfactual/reconciliation definitions are stipulated formalizations, not fitted predictions, and the few self-citations are not load-bearing.

full rationale

The paper's central move is to define counterfactual explanations as minimally distant alternative action sequences that toggle a goal (Definition 1) and then to reuse the same schema, with epistemic goals and model updates, in Definitions 13, 16, 18 and 21. This is an act of definitional unification rather than a derivation of an empirical result from fitted inputs: the reconciliation accounts are stipulated to be instances of the counterfactual schema, and the paper explicitly claims the relationship 'can be seen as a counterfactual' rather than deriving it from independent premises. No parameter is fitted to data and then renamed as a prediction; no quantity is defined in terms of the quantity it is claimed to explain. The logic ES is imported from prior work by Lakemeyer and Levesque ([23]), not from the author's own papers, and the paper explicitly says 'Our ideas do not hinge on this language, and so any planning language that helps us reason about truth, knowledge, actions and sensing should suffice.' The only self-citations ([3], [30]) are pointer-style references to multi-agent extensions and epistemic-planning implementations; they do not carry the load of the formal definitions. The reviewer-identified weakness—that 'dist minimal' and 'smallest such alpha' are left with unspecified metrics or orderings and no existence proof—is a well-definedness and completeness gap, not circularity: an ill-posed optimization does not make the definition equivalent to its inputs. Likewise, the omitted proof of regression and representation theorems (Section 3, 'We omit the details but refer readers to [23]') is an external citation to independent prior work, and the paper's own admission that an extended report with examples is pending is a presentation gap. Overall, the derivation chain is self-contained at the level of definitions; the main risk is formal adequacy, not circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

Most of the machinery is imported from the ES logic of Lakemeyer and Levesque [23] and the only-knowing operator of Levesque [26]. The paper's own additions are the choice of distance metrics, the diversity bound k, and the definitions of smallest α. No numerical data are fitted. The main unstated assumptions are epistemic: the user's knowledge proxies for ground truth, the agent believes the dynamics correctly, and minimal explanations exist.

free parameters (3)
  • distance metric (dist) = unspecified; candidates: length, fluent-set, plan-and-effect
    Definitions 1, 11, 13 and 18 require minimal distance, but the metric is chosen by hand and left as a parameter of the definitions.
  • diversity bound k = positive integer, user-specified
    Definitions 8 and 10 use k as an upper bound on closeness; no principled choice is given.
  • "smallest α" ordering = undefined
    Definitions 16, 18, 21 require the smallest formula α extending the agent's knowledge, but no ordering on formulas is defined.
assumptions (6)
  • domain assumption User knowledge can stand in for ground truth in the real world
    Footnote 2: 'the user's knowledge can serve as proxy for truth in the real world.' This collapses multi-agent discrepancy to a single-agent account; if the user is also fallible, the reconciliation definitions lose their target.
  • domain assumption Agent believes the dynamics exactly as the real world does
    Section 2, Eq 1: agents are assumed to only-know Σ'0 ∧ Σdyn, i.e., they believe the successor state, precondition, and sensing axioms. This rules out false beliefs about dynamics, which the paper does not handle.
  • domain assumption Initial agent knowledge is a subset or weakening of world facts (except false belief section)
    Section 5.1 assumes Σ'0 ⊆ Σ0, Section 5.2 assumes Σ0 |= Σ'0; these constrain when explanations apply.
  • ad hoc to paper Existence of minimal distances and smallest knowledge additions
    Definitions 1, 13, 16, 18, 21 invoke minimality and 'smallest α' without specifying a well-founded ordering or proving existence.
  • standard math Standard first-order logic with equality, unique names, standard names and infinitary domain closure
    Section 2 semantics of ES relies on substitutional quantification over standard names.
  • standard math Modal logic ES properties, including Barcan formula and only-knowing characterization
    The paper uses properties (a)-(e) from Section 2 and Oα |= Kβ iff α |= β, citing Lakemeyer and Levesque [23, 26].

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Pith. "Pith review of Counterfactual Explanations as Plans." pith.science (2026). https://pith.science/paper/I5RNUQHO

@misc{pith2026250209205,
  author       = {Pith},
  title        = {Pith review of: Counterfactual Explanations as Plans},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I5RNUQHO}},
  note         = {Machine review of arXiv:2502.09205}
}
read the original abstract

There has been considerable recent interest in explainability in AI, especially with black-box machine learning models. As correctly observed by the planning community, when the application at hand is not a single-shot decision or prediction, but a sequence of actions that depend on observations, a richer notion of explanations are desirable. In this paper, we look to provide a formal account of ``counterfactual explanations," based in terms of action sequences. We then show that this naturally leads to an account of model reconciliation, which might take the form of the user correcting the agent's model, or suggesting actions to the agent's plan. For this, we will need to articulate what is true versus what is known, and we appeal to a modal fragment of the situation calculus to formalise these intuitions. We consider various settings: the agent knowing partial truths, weakened truths and having false beliefs, and show that our definitions easily generalize to these different settings.

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