Explainable Goal Recognition (XGR)

• Explainable Goal Recognition (XGR) is a framework that infers and explains an agent’s goals by mapping observed action sequences to probabilistic hypotheses with clear causal insights.
• It leverages the Weight of Evidence and contrastive reasoning to quantify support for goals, identifying key observational markers and counterfactual cues.
• By integrating planning-based, probabilistic, and neural techniques, XGR enhances transparency and trust in automated decision-making across diverse domains.

Explainable Goal Recognition (XGR) comprises algorithmic, statistical, and user-centric frameworks for making the inference process behind goal recognition in artificial agents transparent, interpretable, and actionable for human observers. The core of XGR is to map sequences of observations to probabilistic hypotheses about an agent's goal, while simultaneously deriving explanations for these hypotheses—typically addressing both the "why?" (why this goal) and "why not?" (why not alternative goals) questions. Recent work, notably the Weight of Evidence (WoE)-based approach, formalizes this process to produce explanations that are quantitatively grounded, empirically validated, and in close alignment with human explanatory discourse (Alshehri et al., 2023, Alshehri et al., 2024, Sado et al., 2020).

1. Formal Foundations of Explainable Goal Recognition

Goal Recognition (GR) is cast as the inference of an unobserved agent goal $g \in G$ from a sequence of observable actions, typically within a classical planning domain $\Xi = \langle F, A \rangle$:

• $F$: finite set of facts (fluents)
• $A$: set of actions with deterministic transition structure
• $I \subseteq F$: initial state
• $O = \langle o_1, o_2, ..., o_n \rangle$: sequence of observed (action, state) pairs $o_i = (\alpha_i, \varphi_i)$
• $G = \{g_1, ..., g_m\}$: set of candidate goals (each a fluent or conjunction thereof)

The recognition task is to compute the posterior $P(g_j \mid O)$ over $G$, typically under the assumptions of agent rationality (optimal or near-optimal actions) and conditional independence of observations (Markov property given goal). Planning-based and model-agnostic recognizers assign likelihoods by comparing observed trajectories to optimal and counterfactual plans, deriving $P(g \mid O)$ via likelihood functions such as Boltzmann rationality (Alshehri et al., 2023, Alshehri et al., 2024).

2. Theoretical Basis: Cognitive Alignment and Information Theory

XGR approaches are grounded in cognitive and social-psychology theories that describe how humans explain agency and intention:

• Causal and Contrastive Reasoning: Malle's model posits contrast as central to human explanations ("Why $g$ rather than $g'$?") (Alshehri et al., 2024).
• Observational Markers: Human explanations focus on discriminative events or "markers"—key observed actions that shift belief toward a particular goal.
• Weight of Evidence (WoE): Inference is explicated via the information-theoretic quantity $$woe(g/g': o_i \mid O_{i-1}) = \log P(g \mid O_i) - \log P(g' \mid O_i)$$, measuring the differential evidential support for $g$ over $g'$ by observation $o_i$ (Alshehri et al., 2023, Alshehri et al., 2024).

This cognitive alignment is further reinforced by empirical studies that code and analyze human-generated explanations for artificial agents across domains such as Sokoban and StarCraft (Alshehri et al., 2024).

3. The Weight of Evidence (WoE) Framework

WoE serves as the principal mechanism for quantifying and expressing explanatory relevance in XGR:

• Definition: For uniform priors, the WoE at observation $o_i$ for $g$ over $g'$ is $woe(g/g': o_i \mid O_{i-1})$. Positive values indicate support for $g$, negative for $g'$.
• Computationally: Each observed action incrementally updates the WoE, yielding a cumulative, additive explanation: $$\sum_{k=1}^i woe(g/g': o_k \mid O_{k-1}) = \log P(g \mid O_i) - \log P(g' \mid O_i)$$.
• Contrastive and Counterfactual Reasoning: The most positive WoE identifies "why" observations; the most negative signals counterfactual markers (those that would have spoken for an alternative goal) (Alshehri et al., 2023, Alshehri et al., 2024).

This framework elegantly supports algorithmic explanation selection mimicking human discourse.

4. XGR Architecture and Explanation Generation

The modern XGR architecture is modular, wrapping around any GR engine supplying $P(g \mid O)$:

• Inputs: The full observation sequence $O$, current posteriors over $G$, predicted top-ranked goals $G_p$, and lower-probability counterfactuals $G_c$.
• Stage 1—Complete Explanans Construction: For each $(g, g') \in G_p \times G_c$ and observation $o_i$, compute and store $(g, g', \omega_i, o_i)$ tuples, with $\omega_i = woe(g/g': o_i \mid O_{i-1})$.
• Stage 2—Explanation Selection:
  • Why $g$?: Choose $o_i$ of maximum $\omega_i$ as the Observational Marker.
  • Why not $g'$?: Choose $o_j$ of minimum $\omega_j$ (Counterfactual Marker) and compute the counterfactual action $a_j'$ via replanning.
• Language Generation: Explanations are verbalized as:
  • "The recognizer chose goal $g$ rather than $g'$ mainly because, at step $i$, the agent performed $o_i$, which increases the log-likelihood in favor of $g$ by $\Delta_i = \omega_i$."
  • For counterfactuals: "Had the goal been $g'$, the agent should have taken action $a_j'$ instead."

The architecture is agnostic to the underlying recognition algorithm, supporting planning-based (e.g., Mirroring), probabilistic, and hybrid methods (Alshehri et al., 2023, Alshehri et al., 2024).

5. Empirical Evaluation: Computational and Human-Centric Studies

XGR evaluation spans computational performance, ground-truth alignment, and effects on human users:

Computational Benchmarks: Eight IPC-style planning domains (Campus, Ferry, Kitchen, Intrusion, Rovers, Satellite, Miconic, Zeno-Travel) reveal:

Domain	XGR Overhead (%)	Overhead Due to Counterfactual Planning (%)	Avg. Runtime (s)
Miconic	≈ 1	70–99	0.14
Intrusion	≈ 45	70–99	Domain-variable
Zeno	≈ 4.2	>99	>200

In all domains, most additional computational cost arises from counterfactual planning rather than WoE scoring (Alshehri et al., 2023, Alshehri et al., 2024).

Human Studies and Ground-Truth Validation:

• Expert Annotation: In Sokoban, XGR's selected Observational Markers matched human-identified "why" observations in 73.3% and "why not" in 93.3% of cases (MAE~0.01–0.10).
• User Studies: With 60–65 participants across conditions, explanations provided by XGR improved:
  • Task prediction accuracy: Statistically significant improvement over baseline ($p\leq0.05$).
  • Explanation satisfaction: ~87–89% agreement on composite scales.
  • Trust: Increased "Reliable" and "Safe" subscales; no significant effect on "Confident" or "Predictable" (Alshehri et al., 2023, Alshehri et al., 2024).
• Decision Support (Maritime/Vessel Tracking): Addition of "why" and "why not" explanations reduced both over- and under-reliance on system recommendations, improved Brier scores for destination prediction, and led to higher trust and satisfaction (Alshehri et al., 2024).

6. Broader Methodological Landscape and Explanation Modalities

XGR encompasses a spectrum of approaches (Sado et al., 2020):

• Plan-Based and Library Recognition: Infer goals by matching observations to optimal/canonical plans; explanations derived from plan-differentiating actions.
• Inverse Reinforcement Learning: Explanations reference learned reward structure or feature expectations.
• Deep Neural Models: Explanations leverage saliency, attention, or layer-wise relevance metrics.
• Hybrid Techniques: Weight symbolic planning insights and neural predictions for both accuracy and multi-modal explanation support.
• Explanation Media: Natural language templates, visual storyboards, argument graphs, and Prolog-style traces are variously employed to fit domain and user expertise.

Explanatory sufficiency is an emerging focus, with ongoing work toward formal guarantees and dialog-based, interactive explanation systems.

7. Limitations, Open Problems, and Future Directions

• Scalability: Computational cost of planner-based counterfactuals limits real-time and large-scale deployment; promising solutions include domain-specialized or incremental planners (Alshehri et al., 2023, Alshehri et al., 2024).
• Partial Observability: Current XGR architectures assume full (noiseless) observation; extending to POMDP models is an open topic.
• Explanation Richness: Present XGR explanations prioritize observational markers and counterfactuals; ongoing studies seek to integrate policy preferences, belief attributions, causal histories, and user-adaptive abstraction levels (Alshehri et al., 2024, Sado et al., 2020).
• Task Complexity: Highly complex, multi-attribute tasks can reduce the explanatory benefit, indicating a need to calibrate explanation depth and information presentation.
• Interactive and Lifelong Systems: Future work aims at dialog-based refinement, continual learning of goal libraries, multi-agent reasoning, and formal explanation contracts (e.g., counterfactual completeness) (Sado et al., 2020).

A plausible implication is that human-centered XGR, grounded in WoE and contrastive reasoning, enables robust, scalable integration of autonomous goal-driven systems within human teams, laying the foundation for explainable, trustworthy agent behavior across a range of high-stakes applications.

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References:

• (Alshehri et al., 2023) Explainable Goal Recognition: A Framework Based on Weight of Evidence
• (Alshehri et al., 2024) Towards Explainable Goal Recognition Using Weight of Evidence (WoE): A Human-Centered Approach
• (Sado et al., 2020) Explainable Goal-Driven Agents and Robots -- A Comprehensive Review