T2B2T Paradigm: RDF & BDI Integration

• T2B2T paradigm is an architectural framework that converts RDF triples into BDI mental states and vice versa, ensuring clear semantic mapping.
• It employs formal BDI ontologies and dual mapping functions to guarantee soundness and completeness in multi-agent cognitive systems.
• The Semas platform operationalizes this framework by integrating an RDF triplestore, BDI reasoner, and LLM-powered logic augmentation for dynamic agent behavior.

The Triples-to-Beliefs-to-Triples (T2B2T) paradigm is an architectural approach for the bidirectional integration of structured Knowledge Graph data (RDF triples) and cognitive agent mental states (Beliefs, Desires, Intentions—BDI). As formalized in the Semas platform, this paradigm mediates the transformation of declarative world knowledge into agent beliefs, supports multi-level BDI agent reasoning, and re-materializes the resulting enriched agent mental states back into RDF triples, enforcing semantic interoperability and explainability across agent and knowledge graph layers (Zuppiroli et al., 21 Nov 2025).

1. Formal Foundation: BDI Ontology and Semantic Representation

The T2B2T paradigm is grounded in a modular BDI Ontology that provides semantic definitions for the agent's cognitive architecture. The ontology employs Description-Logic (DL) axioms (expressed in OWL 2) to characterize the relationships between agents, their mental states, and the causal and referential structure of beliefs, desires, and intentions. The key DL axioms are:

• $$\mathrm{MentalState} \sqsubseteq \mathrm{MentalEntity}$$
• $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$
• $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$
• $$\mathrm{Desire} \sqsubseteq \mathrm{MentalState} \sqcap \exists\,\mathrm{isMotivatedBy.Belief} \sqcap \exists\,\mathrm{isFulfilledBy.Intention}$$
• $$\mathrm{Intention} \sqsubseteq \mathrm{MentalState} \sqcap \exists\,\mathrm{fulfills.Desire} \sqcap \exists\,\mathrm{isSupportedBy.Belief}$$

These semantics are instantiated in RDF/Turtle via canonical patterns where an agent node is linked to its current beliefs, desires, and intentions, each described by their type and interrelations (e.g., bdi:motivates, bdi:isSupportedBy). This formalization underpins both the conversion functions and the reasoning cycle.

2. T2B2T Bidirectional Mapping: Functions $f$ and $g$

The core of the T2B2T paradigm is a dual-mapping pipeline:

2.1 Triples-to-Beliefs (T2B):

Let $\mathcal{T}$ denote the set of input RDF triples and $\mathcal{B}$ the set of belief assertions. The mapping is defined as: $f: \mathcal{T} \;\to\; \mathcal{B}$ For every triple $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$0 representing a percept (e.g., property :perceives or :observes), $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$1 yields a belief entity $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$2 that

• is typed as a bdi:Belief,
• refers to $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$3 (the perceived world state),
• and records $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$4 as its validity or value.

This is concretely realized as: $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$5

2.2 Beliefs-to-Triples (B2T):

After the BDI reasoning cycle (internal rules evolving $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$5, desires $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$6, intentions $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$7), mental entities are projected back to RDF via

$$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$8

Each mental state yields a triple-set (subgraph) reifying its type, referent, validity, and links to other mental entities (e.g., bdi:motivates, bdi:fulfills). Soundness (every belief reflects a valid triple) and completeness (all mental entities are exported) are guaranteed by construction. The feedback property $$\mathrm{Agent} \sqsubseteq \exists\, \mathrm{hasMentalState.MentalState}$$9 (with $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$0 the internal reasoning operator) ensures that the T2B2T cycle preserves isomorphism up to fresh identifiers.

3. Semas Platform Architecture and Dataflow

T2B2T is operationalized in the Semas platform—an agent system featuring a Prolog-style BDI reasoner integrated with an RDF triplestore. Its architecture comprises:

• RDF Triplestore: Persistent storage of domain/world knowledge and exported mental snapshots.
• T2B Importer: Polls perceptual triples, applying $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$1 to initialize or update the agent's Belief Base.
• BDI Reasoner (Semas Core): Applies BDI rules of the form $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$2, where $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$3 (e.g., a bdi:Belief) triggers a sequence of desire/intention manipulations.
• Logic-Augmented-Generation (LAG) Layer: At critical points (e.g., intention formation), invokes an LLM using prompts that include BDI axioms and the current mental state, returning validated enrichments such as justifications.
• B2T Exporter: Applies $$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$4 to export all new/updated beliefs, desires, intentions, justifications back to the RDF store.

Linearized dataflow:

$$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$6

This architecture enforces a principled feedback loop between declarative representations and procedural mental state evolution.

4. Canonical BDI and RDF Patterns in T2B2T

The paradigm’s mappings leverage BDI and RDF patterns to ensure transparency and explainability. Canonical relationships are:

Mental Entity	Key Properties	RDF Example Snippet
Belief	refersTo, hasValidity, motivates	:B1 a bdi:Belief ; bdi:refersTo :WS1 ; bdi:hasValidity ...
Desire	isMotivatedBy, isFulfilledBy, label	:D1 a bdi:Desire ; bdi:isMotivatedBy :B1 ; rdfs:label ...
Intention	fulfills, isSupportedBy, isJustifiedBy, label	:I1 a bdi:Intention ; bdi:fulfills :D1 ; ...
Justification	justifies, comment	:Just1 a bdi:Justification ; bdi:justifies :I1 ; ...

This alignment facilitates modular extension, reusability, and semantic interoperability across interacting agents and external systems.

5. Illustrative Scenario: Pipeline Execution

A concrete scenario demonstrates the dynamic execution of T2B2T. Given triples encoding world state, agent information, and task requirements:

$$\mathrm{Belief} \sqsubseteq \mathrm{MentalState} \sqcap \exists\, \mathrm{refersTo.WorldState} \sqcap \exists\, \mathrm{motivates.Desire} \sqcap \exists\,\mathrm{supports.Intention}$$7

• T2B Mapping: The system detects a percept (ex:WS1) and instantiates ex:B1 as a belief that the agent is at home.
• BDI Reasoning: Rule triggers create a desire (ex:D1: "Do a home task") based on the belief; intention formation rules check preconditions and generate an intention (ex:I1) to avoid a hotel check-in with an explicit justification (ex:Just1).
• B2T Mapping: The finalized beliefs, desires, intentions, and justifications are exported as enriched RDF subgraphs and merged into the RDF Store, closing the cycle.

6. Properties and Significance in Multi-Agent and Neuro-Symbolic Contexts

The T2B2T paradigm establishes cognitive and operational bridges between declarative and procedural intelligence, especially relevant in settings where multi-agent and neuro-symbolic systems require both symbolic explainability and interoperable representation. The feedback mechanism and proof of soundness/completeness ensure that knowledge cycles are lossless within their semantic domain. The Logic-Augmented-Generation layer further facilitates augmentation of internal reasoning with LLM-powered validation, making the knowledge exported both cognitively grounded and robustly justified (Zuppiroli et al., 21 Nov 2025).

A plausible implication is that T2B2T, through formal modular design and alignment with foundational semantic web principles, positions BDI-based cognitive architectures as first-class citizens within the broader Web of Data, addressing both explainability and operational integration.