{"id":"cd18a6ba-a9ee-4c8d-bdaf-0cff85a53268","arxiv_id":"2502.09205","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A formal account in modal situation calculus that defines counterfactual explanations as minimally distant alternative plans which toggle a goal, including reconciliation through added knowledge or corrected beliefs.","lead":"This paper defines counterfactual explanations for sequential AI planning as alternative action plans that change an outcome, and extends the idea to cases where an agent has partial or false beliefs. It formalizes these definitions in a modal situation calculus logic and argues that this unifies several existing accounts of explainable planning.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The definitions of counterfactual and reconciliation explanations presuppose a minimal solution ('dist minimal' / 'smallest α') without specifying an ordering or proving existence, so the central unification claim is not yet a well-posed formal statement.","rationale":"Read in good faith, the paper's aim is to define, in the modal logic ES, a general notion of counterfactual explanations as plans and to show that model reconciliation is a special case. The central load-bearing assertion is that Definitions 1, 13, 16, 18 and 21 are well-posed formal definitions. The reader's weakest-assumption analysis identifies the right spot: minimality and 'smallest α' are used without an explicit well-founded ordering or existence proof. I agree with that assessment. In my own reading, the most concrete manifestation is the single-α restriction and the absence of a defined ordering in the reconciliation definitions; this makes the claimed subsumption of prior reconciliation accounts impossible to check. A secondary indicator of the same under-specification is Definition 13's 'Σ̸|= [δ]Kφ, that is, Σ |= [δ]¬Kφ', which is not a logical equivalence in general; this suggests the definitions have not yet been tightened to the point of being formal. None of this is fatal: the framework is coherent, the examples illustrate the intended semantics, and the distance measures of Section 4 show the author is aware of the need to choose metrics. The paper is a promising definitional starting point, not a fully verified theory. Therefore the conditional verdict stands; the concrete test I propose would force the missing ordering and existence conditions into the open.","tokens_in":15333,"tokens_out":16867,"duration_ms":165692,"concrete_test":"Use a finite propositional blocks-world instance of Definition 16 in which the required missing knowledge is a conjunction of two facts: let Σ0−Σ′0 contain Glass(d) and Metal(d), neither alone sufficient to make the agent know Broken(d) after pickup(d)·drop(d), but their conjunction sufficient. Check whether Definition 16, which quantifies over a single α ∈ Σ0−Σ′0, yields an explanation. If it does not, the reconciliation definition is under-inclusive in the paper's own intended settings; if it does, the intended reading of 'some α' must be stated explicitly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Definition 1 makes 'dist(δ′,δ) is minimal' the defining property of a counterfactual explanation, but the metric is left as an uninstantiated parameter; Definitions 13, 16, 18 and 21 reuse 'dist(δ′,δ) is minimal' and 'the smallest such α' without fixing a metric or an ordering on formulas. This is not a harmless convenience. In Definition 16, α must be a single formula from Σ0−Σ′0; if the missing knowledge that would make Σ entail [δ]Kφ is a conjunction of two facts, no such α exists and the definition is empty. If 'smallest' is interpreted as logically weakest, the set of sufficient α is upward closed under entailment and in a first-order theory can have infinite descending chains, so no minimum is guaranteed. Likewise, no existence theorem is supplied for the plan-minimization step: for arbitrary Σ, δ, φ, the set {δ′ : Σ |= Exec(δ′) ∧ [δ′]¬φ} may be empty or, with real-valued costs, may have an infimum that is not attained. Because the paper's central claim is that contrastive and reconciliation explanations are instances of one counterfactual-plan framework, an ill-defined optimization means that claim is not actually a formal statement. The reviewer's conditional verdict is appropriate, but the definitions as written cannot be implemented or checked.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":15598,"tokens_out":10310,"duration_ms":101523,"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":[{"comment":"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.","section":"Section 4, Definition 1 (and Definitions 11, 13, 18)"},{"comment":"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).","section":"Section 5.1, Definition 16 (and Definitions 18, 21)"},{"comment":"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.","section":"Sections 1 and 5.4"},{"comment":"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.","section":"Section 5.1, Definition 13"}],"minor_comments":[{"comment":"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.","section":"Section 4, Example 9"},{"comment":"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.","section":"Section 4, Definition 10"},{"comment":"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'.","section":"Section 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is best read as a formalization proposal rather than a completed theory. If the authors close the well-definedness gaps and add at least one explicit correspondence theorem, even for a restricted fragment, the result would be a solid contribution. The breadth of settings is attractive, but the absence of any existence or correspondence proofs makes a strong acceptance hard to justify at this stage."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper is a definitional contribution to explainable planning, and it is a reasonably good one. What is actually new is the epistemic part: Definitions 16, 18, and 21, which frame model reconciliation as a counterfactual over missing knowledge or false beliefs, using the ES logic's only-knowing semantics. The objective-level Definition 1 is close to contrastive explanations and cost-based minimality in prior work, as the reader says, but the bundled treatment of missing actions, partial truths, weakened beliefs, and false beliefs under one vocabulary is a useful organizing step. The examples are clear and the use of ES semantics is consistent throughout.\n\nThe paper also does some things well that are easy to underrate. It is honest about what it is not: no proofs, no implementation, and the reduction to first-order reasoning is cited rather than shown. That is acceptable for a framework paper, provided the definitions are at least well-posed. Here the stress-test note lands. Definition 1, and the epistemic definitions derived from it, all depend on 'dist(δ', δ) is minimal' or 'the smallest such α' without specifying the metric, the ordering on formulas, or proving existence. This is not a cosmetic gap. In Definition 16, α must be a single formula from Σ0 − Σ'0; if the missing knowledge is a conjunction, the definition is empty. If 'smallest' means logically weakest, the set of sufficient α is upward closed under entailment and may have no minimum. The plan-minimization step can also fail: for arbitrary Σ, δ, φ, the set of alternative plans may be empty or the infimum may not be attained. So the central claim that contrastive and reconciliation explanations are instances of one counterfactual-plan framework is, as written, not yet a formal statement. It is a promising research program, but the definitions need an explicit distance metric (even a parameterized one) plus existence conditions, or a proof that minimal explanations exist for the intended domains.\n\nThe subsumption claims about prior work are asserted, not proved. That is a minor issue for a paper of this type; the bigger issue is the ill-defined optimization. I am not convinced the unification claim is wrong; I just think the paper has not yet earned it.\n\nWho is this for? Researchers in explainable AI planning who want a logical framework for thinking about counterfactual explanations and model reconciliation. It could also be useful in a graduate seminar on knowledge representation. A serious referee should see it; the author should be asked to fix the definitional gaps, not to abandon the idea. The core intuition is sound and worth building on. I would accept it for peer review with the expectation of major revision.","headline":"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.","tokens_in":814,"tokens_out":1710,"would_cite":true,"duration_ms":28710,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T27","03B45","68T20"],"pacs":[],"model":"deepseek-v4-flash","headline":"Counterfactual explanations of plans are minimally different alternative plans that flip the outcome, and model reconciliation is the same idea in epistemic form.","keywords":["counterfactual explanations","explainable planning","model reconciliation","epistemic logic","situation calculus","only-knowing","action sequences","sensing actions"],"falsifier":"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.","tokens_in":15117,"feed_emoji":"🤖","tokens_out":9971,"duration_ms":83992,"temperature":0.7,"pith_summary":"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.","feed_headline":"One counterfactual definition explains plans and reconciles models","feed_subtitle":"The 'why' of a plan is a minimally different plan; model reconciliation is just added knowledge.","key_machinery":"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 $\\Sigma'_0$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the modal epistemic logic ES, the language in which all the paper's definitions are stated.","marker":"[23]"},{"why":"Provides the situation-calculus basic action theories (successor state, precondition, sensing axioms) used to model plans and executability.","marker":"[34]"},{"why":"Frames the discrepancy problem in epistemic planning that the paper recasts as a variation of its counterfactual-explanation definition.","marker":"[37]"},{"why":"Gives the skeptical and credulous entailment semantics for reconciliation-based explanations that the paper links to possibility vs knowledge.","marker":"[42]"},{"why":"Introduces the machine-learning notion of counterfactual explanations that the paper adapts from data points to action sequences.","marker":"[43]"},{"why":"Defines model reconciliation in human-aware planning, the target phenomenon the paper's reconciliation definitions formalize.","marker":"[40]"}],"fun_headline_variants":["Counterfactual explanations are minimal alternative plans","Reconciling models via counterfactual plans","Plan counterfactuals unify explanation and reconciliation","Why plans: counterfactuals as minimal deviations","Counterfactuals in plans: from explanation to model repair"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Counterfactual explanations are minimal alternative plans","Reconciling models via counterfactual plans","Plan counterfactuals unify explanation and reconciliation","Why plans: counterfactuals as minimal deviations","Counterfactuals in plans: from explanation to model repair"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000193,"raw_usage":{"total_tokens":1319,"prompt_tokens":882,"completion_tokens":437,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":498,"completion_tokens_details":{"reasoning_tokens":364}},"tokens_in":498,"tokens_out":437,"duration_ms":4433,"temperature":1.0,"reasoning_tokens":364,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T22:17:13.604906+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Lakemeyer & Hector J","cited_arxiv_id":null,"evidence_quote":"Supplies the modal epistemic logic ES, the language in which all the paper's definitions are stated."},{"cited_title":"In: Proceedings of the International Conference on Automated Planning and Scheduling, 32, pp","cited_arxiv_id":null,"evidence_quote":"Frames the discrepancy problem in epistemic planning that the paper recasts as a variation of its counterfactual-explanation definition."},{"cited_title":"Journal of Artificial Intelligence Research 73, pp","cited_arxiv_id":null,"evidence_quote":"Gives the skeptical and credulous entailment semantics for reconciliation-based explanations that the paper links to possibility vs knowledge."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the machine-learning notion of counterfactual explanations that the paper adapts from data points to action sequences."},{"cited_title":"In: Proceedings of the International Conference on Automated Planning and Scheduling, 28, pp","cited_arxiv_id":null,"evidence_quote":"Defines model reconciliation in human-aware planning, the target phenomenon the paper's reconciliation definitions formalize."}],"review_version":1}