Domain–Action Taxonomy Framework

• Domain–Action Taxonomy is a hierarchical framework that categorizes fields and actions through both abstract mathematical models and empirical analysis.
• It integrates rigorous methods like indexed monoidal actions, weighted limits, and data-driven induction to align theoretical constructs with observed behaviors.
• The taxonomy underpins adaptive systems in robotics, conversational AI, and video analytics by ensuring structured knowledge representation and robust generalization.

A domain–action taxonomy is a multi-dimensional, hierarchical framework that systematizes the relationships between domains (fields, contexts, environments, or entity universes) and the actions (tasks, behaviors, representations, or procedural steps) that occur within them. Its scope extends from abstract category-theoretic formulations to empirical approaches analyzing user intent or robotic execution. Across research fields, domain–action taxonomies provide essential structure for knowledge representation, generalization, qualitative evaluation, action detection, and adaptive behavior in both human and artificial agents.

1. Conceptual Foundations and Formal Structures

Domain–action taxonomies originate from both mathematical abstraction and empirical categorization. The category-theoretic perspective, as in indexed monoidal actions (Pisani, 2012), defines a family of categories parametrized by a base category $\Cat$, organizing "left" and "right" actions as covariant and contravariant functors enriched over a symmetric monoidal closed category $\mathcal{V}$. For each object $X \in \Cat$, one considers pairs $(\mathcal{L} X, \mathcal{R} X)$ as categories of actions on $\mathcal{V}$, with key constructions involving weighted (co)limits and Kan extensions. Actions in this formalism reflect morphisms internal (pointwise) and external (weighted), establishing rigorous principles for compositionality, substitution, and adjointness.

Empirically grounded taxonomies—such as TiFi (Chu et al., 2019), which induces hierarchies for fictional or specialized domains—apply lexical, graph, and semantic criteria to noisy category systems, mapping entities and their actions into clean hierarchical structures. TUNA (Shelby et al., 7 Oct 2025) advances this by stratifying observed user actions in conversational AI into a three-level model: modes (e.g., information seeking, procedural guidance), strategies (e.g., retrieval, clarification), and atomic request types (e.g., direct fact, summarization, creative content generation).

2. Classification Criteria and Taxonomical Dimensions

Taxonomies define granular criteria along which domains and actions are organized. In robotics, the taxonomy of action representations (Zech et al., 2018) distinguishes between action models (covering perception, abstraction, learning, and effect) and computational models (including mathematical formulation, feature extraction, and evaluation):

Dimension	Subgroups (Sample Criteria)
Action Model	Perceptual input, attention, abstraction, learning modality, effect grounding (bidirectional/unidirectional)
Computational Model	Mathematical or biomimetic formulation, supervised/unsupervised training, evaluation context

Conversational and user behavior taxonomies, such as TUNA (Shelby et al., 7 Oct 2025), resolve actions into nested layers. For instance, a user’s domain–action could be categorized as Mode 1 (Information Seeking) > Strategy: Retrieval > Request Type: ReqDirectFactQuestion.

Hierarchical similarity matrices (as in TSDA (Liu et al., 2023)) encode domain relationships using distance matrices $A$, allowing adaptation mechanisms to exploit structured relationships within and across domains.

3. Methodologies for Taxonomy Construction

Construction methodologies vary by domain specificity and data modalities:

• Data-driven induction: TiFi (Chu et al., 2019) uses supervised models (logistic regression) and features (lexical, syntactic, graph-based) for "category cleaning" and "edge cleaning," mapping nodes and edges to valid class–subclass pairs. Top-level classes connect to ontological roots (e.g., WordNet synsets), enabling cross-domain queries.
• Theoretical formulation: Indexed monoidal actions (Pisani, 2012) use pairwise category constructions and substitution laws to internalize enriched functorial structures. Weighted (co)limits are defined via external homs $\{A,B\}$ and colimits via actions $A * M$.
• Empirical/qualitative mapping: In "Qualitative Judgement of Research Impact" (Murtagh et al., 2016), contributions are mapped to taxonomy nodes, and innovation is measured by the taxonomic rank of nodes transformed or created, with normalized scores calculated to reflect strategic depth.
• Instance-based approaches: DA-AIM (Lu et al., 2022) operates at the instance level, using mixed sampling of annotated action instances from source video to target domain, enabling finer-grained mappings in spatiotemporal action detection.
• Sequence-based generalization: SeqDG (Nasirimajd et al., 21 Jun 2025) employs action sequence reconstruction, mixing actions from multiple domains to ensure learned features correspond to domain-invariant user intent, not environmental specifics.

4. Taxonomy in Adaptive and Robust Systems

Domain–action taxonomies directly support system adaptation and generalization:

• Domain and viewpoint agnosticism: Hand action recognition frameworks (Sabater et al., 2021) use scale-invariant motion descriptors, contrastive metric learning, and multi-perspective data augmentations to map heterogeneous domain actions into a unified embedding space, yielding domain-agnostic classification. Such structuring is critical for systems operating under environmental variability.
• Generalization in sequential contexts: SeqDG (Nasirimajd et al., 21 Jun 2025) demonstrates that sequential relationships among actions are more robust than isolated visual cues, enabling domain-agnostic action categorization and knowledge transfer in egocentric vision systems.
• Instance-level taxonomy for detection: DA-AIM (Lu et al., 2022) improves action detection across domains by mixing annotated instances and supplementing supervision with auxiliary data, establishing taxonomies that are local (action instance-specific) rather than aggregated across entire images.
• Taxonomy-Structured Domain Adaptation: TSDA (Liu et al., 2023) formalizes adaptation as a four-player minimax game (encoder, discriminator, taxonomist, predictor). The taxonomist ensures representations retain hierarchical domain similarities; the discriminator enforces domain invariance, balanced by hyperparameters, with the equilibrium preserving structured taxonomy information.

5. Applications Across Domains

Domain–action taxonomies are foundational in diverse applications:

• Research evaluation: The qualitative impact of innovative research is assessed via taxonomy mapping (Murtagh et al., 2016); the creation or transformation of taxonomy nodes by academic output reflects deeper discipline-shaping contributions than flat citation metrics.
• Conversational AI: TUNA (Shelby et al., 7 Oct 2025) enables multi-scale evaluation, policy harmonization, and interface design by providing a systematic, extensible vocabulary for user actions and meta-conversational practices.
• Robotics and human–computer interaction: The taxonomy of action representations (Zech et al., 2018) is applied to manipulation, planning, effect prediction, and evaluation in robots, and is theoretically extensible to cognitive science and AI.
• Knowledge base induction: TiFi (Chu et al., 2019) constructs high-precision taxonomies for fictional or specialized universes, outperforming rule-based methods and facilitating semantic search and cross-domain entity alignment.
• Video analytics: DA-AIM (Lu et al., 2022) supports robust action detection across visually disparate or under-represented classes using instance-based taxonomy induction.

6. Limitations, Open Problems, and Future Directions

While domain–action taxonomies provide structure and transparency, several limitations persist:

• Subjectivity and ambiguity: Expert-driven mapping decisions introduce subjectivity; maintaining impartiality and reproducibility in taxonomy updates is essential (Murtagh et al., 2016).
• Taxonomy evolution and granularity: Fast-evolving domains require continuous maintenance; mismatched depth or structure complicates cross-domain comparability (Murtagh et al., 2016).
• Integration of relational and procedural layers: Many taxonomies neglect social or meta-conversational actions, which are crucial for comprehensive evaluation, especially in AI systems (Shelby et al., 7 Oct 2025).
• Correspondence and grounding: Robotics taxonomies show a lack of mechanisms to fully address the correspondence problem (transferring observed action representations into new embodiments) (Zech et al., 2018).
• Automated taxonomy induction: Current empirical frameworks require large annotated datasets and repeated validation; advancing automation may require coupled language–visual grounding and algorithmic insights from sequence-based and instance-centric methods.

Further research directions highlighted include:

• Enhancing effect–centric and hierarchical modeling in robotics (Zech et al., 2018)
• Developing intrinsically motivated, online learning across taxonomic structures
• Combining multi-modal sequence information for robust cross-domain generalization (Nasirimajd et al., 21 Jun 2025)
• Extending taxonomical frameworks into policy and safety domains for conversational systems (Shelby et al., 7 Oct 2025)
• Integrating formal mathematical constructs (Kan extensions, adjunctions) with empirical and algorithmic taxonomy induction for unified theory and practice

7. Comparative Frameworks and Significance

Domain–action taxonomies distinguish themselves from traditional flat category systems by their hierarchical structure, extensibility, and explicit encoding of both conceptual and procedural relationships. Compared to prior frameworks, they capture nuanced similarity, generalize across heterogeneous data sources, and support adaptive system design. The structuring of entities, actions, strategies, and context into layered models advances both theoretical understanding and empirical evaluation, facilitating robust, accountable, and transferable systems across research, industry, and interactive AI platforms.