Discoverable Agent Knowledge -- A Formal Framework for Agentic KG Affordances (Extended Version)

# Discoverable Agent Knowledge — A Formal Framework for Agentic KG Affordances (Extended Version)††thanks: A version of this paper has been submitted to EKAW 2026. This manuscript is an extended version including additional formalisation and a worked example.
Source: [https://arxiv.org/html/2605.19186](https://arxiv.org/html/2605.19186)
11institutetext:School of Computer Science and Informatics, University of Liverpool, UK11email:\{T\.R\.Payne,V\.Tamma\}@liverpool\.ac\.uk22institutetext:Open University: Milton Keynes, Milton Keynes, UK22email:enrico\.daga@open\.ac\.uk###### Abstract

Two decades ago, the Semantic Web Services community was asked how agents with different ontological commitments could discover, compose, and invoke web services coherently\. The response was OWL\-S and WSMO: formally grounded capability descriptions specifying what a service could do, what the agent must already know for invocation to be epistemically sound, and how ontological mismatches could be formally bridged\. Current KG metadata standards such asVoIDandDCATdescribe what a KG*contains*yet say nothing about what a specific agent can*prove*from it, what closure assumptions govern empty results, or whether the agent’s task vocabulary is grounded in the schema\. Furthermore, in deployed KGs the governing schema DL and the operative entailment regime can diverge: an epistemic failure mode invisible to current metadata\. We revisit and extend these insights for the KG setting with a four\-dimensional formal framework from which we derive the*Agentic Affordance Profile \(AAP\)*: a semantic layer aboveVoIDandDCATenabling principled KG selection, composition, and failure diagnosis at agent planning time\. A five\-point research agenda identifies the formal, computational, and engineering work needed to realiseAAP\-based affordance matching at scale\.

## 1Introduction

LLM\-based agents that collaborate to solve composite tasks through the discovery and integration of knowledge\-based resources\[[1](https://arxiv.org/html/2605.19186#bib.bib1),[36](https://arxiv.org/html/2605.19186#bib.bib34)\]have driven a growing interest in*Agentic AI*\. This raises open challenges around the autonomy and governance of agents reasoning over Knowledge Graphs \(KGs\)\[[7](https://arxiv.org/html/2605.19186#bib.bib7),[17](https://arxiv.org/html/2605.19186#bib.bib17)\]\. Structured knowledge supports their reasoning and decision making\[[37](https://arxiv.org/html/2605.19186#bib.bib35)\], constrains query interpretation via ontological vocabularies, and provides factual content for agent conclusions; yet the means by which an agent*assesses*whether a given KG is fit for a given task remains largely informal, either assumed at design time or conducted as an offline activity\. Current KG metadata standards such asVoID\[[2](https://arxiv.org/html/2605.19186#bib.bib2)\]orDCAT\[[20](https://arxiv.org/html/2605.19186#bib.bib20)\]describe what a KG*contains*\(triple counts, entity types, schema references, licensing\), yet they do not describe its*knowledge affordance*\[[9](https://arxiv.org/html/2605.19186#bib.bib9)\]: what task\-relevant queries are guaranteed to return meaningful results, what reasoning is supported, or whether the vocabulary is intelligible to the agent without mediation\. An LLM\-orchestrated agent querying a KG without this assessment risks drawing unsound conclusions from mismatched or incomplete content\.

The parallels with the Semantic Web Services community\[[3](https://arxiv.org/html/2605.19186#bib.bib3),[6](https://arxiv.org/html/2605.19186#bib.bib6),[12](https://arxiv.org/html/2605.19186#bib.bib13),[22](https://arxiv.org/html/2605.19186#bib.bib26),[23](https://arxiv.org/html/2605.19186#bib.bib21),[24](https://arxiv.org/html/2605.19186#bib.bib22),[34](https://arxiv.org/html/2605.19186#bib.bib33),[35](https://arxiv.org/html/2605.19186#bib.bib32)\]from two decades ago are striking; frameworks such as OWL\-S\[[22](https://arxiv.org/html/2605.19186#bib.bib26),[23](https://arxiv.org/html/2605.19186#bib.bib21)\]and WSMO\[[12](https://arxiv.org/html/2605.19186#bib.bib13),[35](https://arxiv.org/html/2605.19186#bib.bib32)\]utilised ontologies for formally describing how web services could be discovered, composed and queried\. Polleres et al\.\[[30](https://arxiv.org/html/2605.19186#bib.bib29)\]characterise many of these similarities, noting that current descriptions of agents are specified in natural language \(with input and output parameters appearing in JSON Schema or via content types\), and that such descriptions*“…are prone to ambiguity as the semantics of the functionality or capability is not precisely captured with natural language descriptions alone…”*\.

Given this convergence, we revisit the key structural insights from the OWL\-S/WSMO tradition and extend them formally to the KG setting, focusing on the*inter\-agent epistemic coherence problem*\[[32](https://arxiv.org/html/2605.19186#bib.bib31)\]: how a community of heterogeneous agents, each grounded in its own ontology, can determine whether the knowledge required for a given KG interaction is coherent and meaningful\. We specify a four\-dimensional formal framework for agentic KG affordance characterisation, and from it derive the*Agentic Affordance Profile \(AAP\)*for KGs: a semantic layer aboveVoIDandDCATenabling principled KG selection, composition, and failure diagnosis at agent planning time\. Essentially, an*Agentic Affordance Profile*is a task\-relative semantic description of what a specific class of agent can soundly retrieve, prove, and conclude from a given KG, structured along four dimensions:*Semantic Expressivity*,*Agentic Discoverability*,*Task\-Relative Grounding*, and*Epistemic Trust Scope*\. We then present a research agenda identifying the formal, computational, and engineering challenges required to makeAAP\-based affordance matching deployable in practice\.

The remainder of the paper is structured as follows\. Section[2](https://arxiv.org/html/2605.19186#S2)revisits the structural insights of OWL\-S and WSMO, namely the*Profile*/*Process Model*/*Grounding*decomposition and the mediator\-as\-first\-class\-object move, and identifies which of them transfer to the KG setting and which require formal extension\. This motivates Section[3](https://arxiv.org/html/2605.19186#S3), which introduces the four dimensions of*Semantic Expressivity*,*Agentic Discoverability*,*Task\-Relative Grounding*, and*Epistemic Trust Scope*; specifies how each is evaluated against a task signature; and characterises their pairwise interactions\. The section closes by deriving a single feasibility predicate that the four dimensions jointly compute, together with the affordance gap signal that this factorisation makes available for failure diagnosis\. Section[4](https://arxiv.org/html/2605.19186#S4)grounds the framework in a worked example drawn from a scholarly\-search task, showing how three superficially comparable KGs yield distinct planner verdicts and how each dimensional shortfall maps to a specific remedial action\. Section[5](https://arxiv.org/html/2605.19186#S5)sets out the five\-point research agenda required to makeAAP\-based affordance matching deployable in practice \(spanning ontology formalisation, computational tractability, compositional semantics, knowledge\-service specification, and engineering integration\), before Section[6](https://arxiv.org/html/2605.19186#S6)concludes\.

## 2Agents, Knowledge and the SWS tradition

Two of the most influential formalisms to emerge from the work on Semantic Web Services, OWL\-S\[[3](https://arxiv.org/html/2605.19186#bib.bib3),[23](https://arxiv.org/html/2605.19186#bib.bib21),[22](https://arxiv.org/html/2605.19186#bib.bib26)\]and WSMO\[[6](https://arxiv.org/html/2605.19186#bib.bib6),[12](https://arxiv.org/html/2605.19186#bib.bib13)\], embody structural insights about the formal description of resource and service capability for agents\[[29](https://arxiv.org/html/2605.19186#bib.bib28)\]that equally hold for KGs, thus motivating our vision of an*Agentic Affordance Profile*\. OWL\-S organised service descriptions around three components addressing three distinct questions an agent must answer at different stages of interaction\. The*Profile*answered*“What does this service do?”*, enabling*discovery*by formal reasoning over the shared ontologies of the requester and service provider\[[28](https://arxiv.org/html/2605.19186#bib.bib27)\]\. The*Process Model*answered*“How does it work internally?”*, enabling workflow composition\. The*Grounding*answered*“How do I invoke it?”*, mapping formal descriptions to protocol bindings\. These same three questions arise for KGs:

1. 1\.*“What can I do with this KG?”*– what queries return results, what reasoning is supported, what task\-relevant concepts are present;
2. 2\.*“How does querying work?”*– what are the inference rules, update protocols, access constraints; and
3. 3\.*“How do I query it?”*– SPARQL endpoints, authentication, federation\.

Whilst current KG metadata frameworks answer the third question adequately, they only answer the first at a content level, falling short of the OWL\-S*Profile*\-level question:*what can this KG do for an agent with a specific task?*Answering this requires knowing what reasoning is supported, whether the agent’s task vocabulary is grounded in the KG’sTBox, and what inferences can be formally trusted\.

A KG’s agentic affordance profile therefore needs to describe, for a given task type, three things from the agent’s epistemic perspective: first, what the agent must already have grounded before engaging the KG \(the epistemic preconditions for coherent interaction\); second, what it can reliably conclude from query results, and under what closure assumptions those conclusions hold; and third, how its knowledge base is extended by the interaction, expressed in the KG’s vocabulary\. Specifying these against shared domain ontologies enables formal affordance matching, replacing the exploratory querying that agents must currently perform\.

Whereas OWL\-S primarily addressed capability descriptions, WSMO,*inter alia*, contributed a complementary insight: a typed taxonomy of*mediators*, treated as formally specified bridges between ontologically mismatched components\[[12](https://arxiv.org/html/2605.19186#bib.bib13)\]\. These mediators were first\-class objects: discoverable, composable, and describable using the same vocabulary as services\. For KG interoperability, the WSMO mediator concept maps onto a formally specified KG\-to\-KG bridge: not just a functional adapter, but a transformation with a defined preservation specification, against which the agent can assess whether the transformed content remains adequate for its task\. However, registering a mediator simply as a static bridge is insufficient for an agent operating under task\-relative ontological constraints, since it needs to determine if the mediator will close the specific semantic gap for the task at hand*before*it is invoked\. Mediators therefore need to declare formal input and output signatures, grounded in shared ontologies, so that their suitability can be assessed at plan formation rather than discovered through invocation\. Mediation must therefore be a planning object, not merely a resolution mechanism\.

Existing linked\-data quality and fitness\-for\-use frameworks\[[10](https://arxiv.org/html/2605.19186#bib.bib12),[33](https://arxiv.org/html/2605.19186#bib.bib39),[38](https://arxiv.org/html/2605.19186#bib.bib38)\]characterise completeness, consistency and interpretability as intrinsic properties of the KG\. TheAAPdiffers in two respects: it is*relational*\(scored against a task signature rather than the resource alone\) and*planning\-actionable*\(each dimensional shortfall maps to a specific remedial action\), not merely an audit score\. Gibson’s ecological psychology\[[15](https://arxiv.org/html/2605.19186#bib.bib16)\]defines an affordance not as a property of an environment alone but of its relationship with an agent: what the environment*offers*relative to the agent’s capacities and goals\. Applied to knowledge resources, a KG’s affordance is not what it contains in the abstract but what it enables a*specific agent*to do on a*specific task*\. Celino\[[9](https://arxiv.org/html/2605.19186#bib.bib9)\]formalised this intuition as a*Knowledge Affordance \(KA\)*for knowledge resources, defined relative to a requester’s context, goals, and competency questions\. This separates an affordance from a capability advertisement: a VoID description describes the resource from the publisher’s perspective whereas an affordance describes it from the agent’s; e\.g\., the same KG may have high affordance for a SNOMED\-CT\-grounded medical agent and zero for a legal agent with no published alignment\.

## 3Agentic Affordances: A Four\-Dimension Framework

The*agentic affordance*of a knowledge graph is characterised across four dimensions, each a property of the KG relative to a specific agent and task rather than of the KG in isolation\. This distinguishes theAAPfrom a capability advertisement: not what the resource*is*but what it*offers*a specific requester\.

Semantic Expressivity \(ℰ\\mathcal\{E\}\):represents the description logic \(DL\) expressivity of the ontology governing the KG’s schema, and the degree to which KG content is schema\-compliant\. Without knowing the governing DL, an agent cannot determine what it can prove: transitivity reasoning requires support for transitive property chains, while sound query rewriting requiresOWL\-QL\. This dimension is evaluated by determining the*DL fragment*of the governing ontology, located on a partial order from schema\-freeRDFthroughRDFS, theOWL2 profiles \(EL,QL,RL\),OWL2 DL, andOWL2 Full\[[4](https://arxiv.org/html/2605.19186#bib.bib4),[25](https://arxiv.org/html/2605.19186#bib.bib23)\], paired with the proportion of KG content whose typing is entailed by the governingTBoxunder that fragment’s standard entailment regime\. The latter component aligns with the consistency\-status reading inℛ\\mathcal\{R\}below:ℰ\\mathcal\{E\}characterises what the schema*licenses*;ℛ\\mathcal\{R\}characterises what the deployed endpoint*actually*returns\.

Agentic Discoverability \(𝒟\\mathcal\{D\}\):reflects the degree to which an agent can autonomously assess a KG’s fitness for a specific task from its metadata and capability description alone, without querying the KG content\. It is used to assess the cost of KG discovery: a KG at the lower end requires exploratory queries before the agent can assess its fitness for the desired task, whereas one at the upper end can be evaluated at planning or composition time from its metadata alone, enabling rational KG selection without committing to engage a resource\.

This dimension can be evaluated by determining the proportion of a set𝒬\\mathcal\{Q\}of an agent’s task types \(where𝒬\\mathcal\{Q\}is defined at agent design time against a shared task ontology, itself a prerequisite identified in Sec\.[5](https://arxiv.org/html/2605.19186#S5)\) for which, given some KG, it can determine the KG’s fitness*purely from declared metadata*, without querying the KG itself\. A score of 1 means the KG’s metadata is rich enough to pre\-assess suitability for every task type; a score of 0 means the metadata is silent on all of them\. The characteristics for this dimension span from no description \(rawSPARQLendpoint\)→\\tosyntactic metadata \(VoID\[[2](https://arxiv.org/html/2605.19186#bib.bib2)\],DCAT\[[20](https://arxiv.org/html/2605.19186#bib.bib20)\]\)→\\tonatural language documentation→\\toa fullAAPprofile: formal affordance scores over supported task types, grounded in shared domain ontologies\.

LetM​\(𝐾𝐺\)M\(\\mathit\{KG\}\)denote the set of metadata assertions about𝐾𝐺\\mathit\{KG\}\(endpoint declarations,VoID/DCATdescriptors, and any declaredAAPprofile\), and let𝑓𝑖𝑡𝑛𝑒𝑠𝑠​\(𝐾𝐺,t\)\\mathit\{fitness\}\(\\mathit\{KG\},t\)abbreviate the conjunction of the𝒢\\mathcal\{G\}\- andℛ\\mathcal\{R\}\-conditions required by task typett\(coverage oftt’s signature and an entailment regime at least equal tott’s minimum\)\. We then define:

𝒬D​\(𝐾𝐺\)=\{t∈𝒬∣𝑓𝑖𝑡𝑛𝑒𝑠𝑠​\(𝐾𝐺,t\)​is entailed by​M​\(𝐾𝐺\)\}\\mathcal\{Q\}\_\{D\}\(\\mathit\{KG\}\)\\;=\\;\\bigl\\\{\\,t\\in\\mathcal\{Q\}\\;\\mid\\;\\mathit\{fitness\}\(\\mathit\{KG\},\\,t\)\\text\{ is entailed by \}M\(\\mathit\{KG\}\)\\bigr\\\}\(1\)Unlikeℰ\\mathcal\{E\},𝒢\\mathcal\{G\}, andℛ\\mathcal\{R\}, the dimension𝒟\\mathcal\{D\}is a*meta\-dimension*: it scores the metadata’s capacity to*report*the other three at planning time, and approaches its upper bound once anAAPis published over a representative task set𝒬\\mathcal\{Q\}\. It thus captures the*maturity gap*between populations of KGs that do and do not commit toAAP\-style description, and is the only dimension that an individual KG’s publisher can raise without altering the KG itself\.

Task\-Relative Grounding \(𝒢\\mathcal\{G\}\):the degree to which a KG’s vocabulary covers the agent’s*task signature*𝒮\\mathcal\{S\}\(i\.e\. the set of ontological concepts required by the task\), where coverage includes not only explicit presence in the KG’s vocabulary but also implicit definability via the KG’s ontology axioms\. As different ontologies model the same domain at different granularities, the required concepts may not appear directly in a third\-party KG but may be expressible as complex fragments or be derivable through its axiom structure\. In a knowledge\-based agent framework, coverage is therefore a question of formal inference over the KG’s theory, not lexical name matching\. For example, two KGs may both expose an IRI named𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\}and return populated query results, yet those results carry different epistemic weight\. In one KG, governed byConference\.owl,111Part of the OAEI conference dataset \([https://oaei\.ontologymatching\.org](https://oaei.ontologymatching.org/)\); extended in the worked example \(Sec\.[4](https://arxiv.org/html/2605.19186#S4)\)\.the concept𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\}is fixed by surroundingTBoxaxioms\[[13](https://arxiv.org/html/2605.19186#bib.bib14)\]: any instance returned is provably an invited speaker in the schema’s intended sense\. In a second KG using the same IRI only in itsABox, the name is present but its meaning is unconstrained by the schema; the results match the label, but the KG makes no commitment about what the label denotes\. Dimension𝒢\\mathcal\{G\}captures this distinction: a KG groundsCCif and only ifCCis explicitly axiomatised or implicitly definable from aTBoxsub\-signature\.

A conceptC∈𝒮C\\in\\mathcal\{S\}is*implicitly definable*from restricted signatureΣ⊆Sig​\(𝒯\)\\Sigma\\subseteq\\mathrm\{Sig\}\(\\mathcal\{T\}\)under TBox𝒯\\mathcal\{T\}if any two models of𝒯\\mathcal\{T\}agreeing on all entities inΣ\\Sigmamust also agree onCC\(Beth definability\[[5](https://arxiv.org/html/2605.19186#bib.bib5)\]\)\. Intuitively,CCis implicitly definable fromΣ\\Sigmaif the axioms in𝒯\\mathcal\{T\}leaveCCno freedom once the meanings of theΣ\\Sigma\-symbols are fixed\. Letℛ=𝑆𝑖𝑔​\(𝒯𝐾𝐺\)\\mathcal\{R\}=\\mathit\{Sig\}\(\\mathcal\{T\}\_\{\\mathit\{KG\}\}\)be the*resident signature*of the KG \(all names in its TBox𝒯𝐾𝐺\\mathcal\{T\}\_\{\\mathit\{KG\}\}\)\. The*coverage problem*asks whether everyC∈𝒮C\\in\\mathcal\{S\}is explicitly inℛ\\mathcal\{R\}or implicitly definable fromℛ\\mathcal\{R\}via𝒯𝐾𝐺\\mathcal\{T\}\_\{\\mathit\{KG\}\}in the Beth sense\[[13](https://arxiv.org/html/2605.19186#bib.bib14),[14](https://arxiv.org/html/2605.19186#bib.bib15)\]\. We therefore define:

𝒢=\|\{C∈𝒮:C∈ℛ\+\}\|\|𝒮\|\\mathcal\{G\}=\\frac\{\|\\\{C\\in\\mathcal\{S\}:C\\in\\mathcal\{R\}^\{\+\}\\\}\|\}\{\|\\mathcal\{S\}\|\}\(2\)whereℛ\+\\mathcal\{R\}^\{\+\}is the*signature closure*\[[14](https://arxiv.org/html/2605.19186#bib.bib15)\]: the set of concept and role names either explicitly inℛ\\mathcal\{R\}or implicitly definable fromℛ\\mathcal\{R\}via𝒯𝐾𝐺\\mathcal\{T\}\_\{\\mathit\{KG\}\}in the Beth sense\. While Beth definability provides the*semantic*criterion for membership inℛ\+\\mathcal\{R\}^\{\+\}, the*computational*route is DL\-dependent: inOWL\-QL/DL\-Lite, coverage is verified via perfect query rewriting\[[8](https://arxiv.org/html/2605.19186#bib.bib8)\]; inOWL\-EL, via module extraction\[[16](https://arxiv.org/html/2605.19186#bib.bib10),[11](https://arxiv.org/html/2605.19186#bib.bib11)\]; in more expressive fragments, uniform interpolation provides the general machinery\[[19](https://arxiv.org/html/2605.19186#bib.bib19)\]\. Empirically, definition\-pattern catalogues offer a complementary, largely DL\-independent route that covers many real\-world cases without invoking these general techniques\[[13](https://arxiv.org/html/2605.19186#bib.bib14)\]\. This dimension is task\- and agent\-relevant: the same KG may have𝒢=1\\mathcal\{G\}=1for one task and𝒢=0\\mathcal\{G\}=0for another\. When𝒢<1\\mathcal\{G\}<1, the gap identifies exactly which concepts require mediation or knowledge acquisition, connecting the framework directly to on\-demand alignment\[[13](https://arxiv.org/html/2605.19186#bib.bib14),[31](https://arxiv.org/html/2605.19186#bib.bib30)\]\.𝒢\\mathcal\{G\}is a schema\-level metric: it assesses whether the KG’s vocabulary can ground the task concepts, not whether relevant instances exist; instance\-level relevance is only partially addressed byVoIDentity statistics\.

Epistemic Trust Scope \(ℛ\\mathcal\{R\}\):a structured profile characterising the conditions under which an agent can treat query results as actionable inferences, determined by the KG’s world\-closure assumptions, completeness declarations, and consistency status\. In OWL\-S and WSMO, service descriptions were grounded in explicit formal semantics, enabling agents to reason about capabilities prior to invocation and to determine what they could soundly*conclude*after invocation; current KG metadata standards carry no analogous account of entailment or closure\. The critical question forℛ\\mathcal\{R\}is therefore not only what the KG can express \(Dimensionℰ\\mathcal\{E\}\) but what can be inferred from an*empty or partial*result, which depends on the KG’s*world\-closure assumption*and any*predicate\-level completeness declarations*\.

Consider a medical agent querying for contraindications between two drugs\. Under the closed world assumption \(CWA\), as in a relational database, an empty result is a sound negative conclusion: no contraindication exists\. Under the open world assumption \(OWA\), as in anOWLKG with no completeness assertion, an empty result means only that no contraindication is*recorded*; the agent cannot safely conclude absence, and any plan predicated on that conclusion is epistemically unsound\. Between these lies the Locally Closed World Assumption \(LCWA\)\[[26](https://arxiv.org/html/2605.19186#bib.bib24)\], under which theCWAis applied selectively to specific predicates;SHACLClosed Shapes\[[18](https://arxiv.org/html/2605.19186#bib.bib18)\]provide an operationally equivalent mechanism, meaning many deployed KGs already operate under a form ofLCWAwithout explicitly declaring it\.ℛ\\mathcal\{R\}must therefore characterise not only whether a KG operates globally underOWAorCWA, but which predicates or shapes are locally closed\. This dimension is thus a structured, three\-component profile characterising which closure assumptions apply: \(a\) consistency status \(uncertified / TBox\-consistent / jointly consistent\); \(b\) declared entailment regime \(none /RDFS/OWL\-EL/OWL\-QL/OWL\-DL\); and \(c\) completeness scope, expressed as the set of task\-relevant predicates for which closure is declared, together with the formal semantics of that declaration: globalCWA, predicate\-levelLCWA\[[26](https://arxiv.org/html/2605.19186#bib.bib24)\], or shape\-levelSHACLclosure\[[18](https://arxiv.org/html/2605.19186#bib.bib18)\]\.

ℛ\\mathcal\{R\}determines what an agent can*infer*from a KG, not merely what it can retrieve\. Safety\-critical or regulatory reasoning requires an entailment regime of at leastOWL\-DLand completeness declarations for the relevant predicates; scientific classification may require onlyOWL\-ELwith consistency certification; and factual retrieval operates soundly underSPARQLSimple entailment, provided the agent draws no negative conclusions\. Critically, whenℛ\\mathcal\{R\}is undeclared, an agent that conflates the open and closed world assumptions may produce plans that are locally coherent but globally unsound: an epistemic failure invisible to the other three dimensions\. A KG may have anOWL\-DLgoverning schema but be deployed as a plain triple store whose content does not satisfy the schema axioms, leaving its operative entailment regime atSPARQLSimple entailment only; conversely, a plainRDFSKG whose publishers declare completeness over a restricted predicate set provides a well\-defined, non\-trivial affordance profile for queries over that set\. In practice, many real\-world KGs carry expressive schemas but operate without engaging their reasoning capacity or making the completeness declarations that would make query results epistemically actionable\[[10](https://arxiv.org/html/2605.19186#bib.bib12)\]\.

These four dimensions form a partially ordered affordance space, not a simple scale\. Three interactions are particularly important, as illustrated in Figure[1](https://arxiv.org/html/2605.19186#S3.F1):

1. 1\.ℰ\\mathcal\{E\}*constrains*ℛ\\mathcal\{R\}*and the computability of*𝒢\\mathcal\{G\}, but in different ways\. Forℛ\\mathcal\{R\}, the constraint is on*scope*: the reasoning regime cannot exceed the vocabulary expressivity, so the maximumℛ\\mathcal\{R\}a KG can declare is bounded by itsℰ\\mathcal\{E\}\. For𝒢\\mathcal\{G\}, the constraint is on*cost*: module extraction and uniform interpolation are tractable only for specificDLfragments, so the efficiency of the coverage check varies with the governing schema\. The eligibility to assess coverage is unaffected: the task signature𝒮\\mathcal\{S\}carries no DL level of its own, so𝒢\\mathcal\{G\}is expressivity\-agnostic from the task side\.
2. 2\.𝒟\\mathcal\{D\}depends on𝒢\\mathcal\{G\}*and*ℛ\\mathcal\{R\}, but again in different ways\. With respect to𝒢\\mathcal\{G\}, the dependency is a*precondition*: an agent that cannot assess coverage of its task signature cannot use even a richly described KG, so𝒢\\mathcal\{G\}must hold for𝒟\\mathcal\{D\}to be informative at all\. With respect toℛ\\mathcal\{R\}, the dependency is on*publication*: without closure declarations being part of whatM​\(𝐾𝐺\)M\(\\mathit\{KG\}\)records, the agent cannot determine at planning time whether negative conclusions will be sound, so the value of𝒟\\mathcal\{D\}is bounded by the fraction ofℛ\\mathcal\{R\}\-relevant facts the metadata actually publishes\.
3. 3\.𝒢\\mathcal\{G\}andℛ\\mathcal\{R\}*jointly determine task feasibility*, but in two layers\. The baseline requirement is straightforward: an agent needs coverage of task concepts \(𝒢=1\\mathcal\{G\}=1\)*and*an entailment regime at least equal to that required by the task\. A second layer applies to tasks requiring*sound negative conclusions*: the corresponding predicates must be declared closed underℛ\\mathcal\{R\}, since a grounding alone is insufficient if the KG’s closure assumptions do not permit absence reasoning\.

Thus, the four dimensions yield principled, computable answers to*“can this agent use this KG?”*and*“to what degree?”*

![Refer to caption](https://arxiv.org/html/2605.19186v1/x1.png)Figure 1:Dimension interaction diagram\.Novelty over OWL\-S/WSMO:The three contributions of theAAPdiffer in weight\.*Primary:*coverage in𝒢\\mathcal\{G\}is*definability*\-based, not alignment\-based; implicitly derivable concepts are admitted via signature closure and Beth definability, a criterion not captured in OWL\-S and WSMO, which rely on explicit alignment or asserted\-equivalence matching\[[13](https://arxiv.org/html/2605.19186#bib.bib14),[14](https://arxiv.org/html/2605.19186#bib.bib15)\]\.*Secondary:*ℰ\\mathcal\{E\}andℛ\\mathcal\{R\}are*independently variable*: OWL\-S and WSMO grounded expressivity and entailment in a single formal model, whereas in deployed KGs the two routinely diverge; a KG may declareOWL DLyet be queried without inference or closure guarantees, with consequences invisible to expressivity alone\.*Tertiary:*all scores are*agent\- and task\-relative*in a dimensionally decomposed, operationalised sense not made explicit in service profile matching: a score of zero on𝒢\\mathcal\{G\}is an actionable planning precondition, not a quality judgement, in the Gibsonian sense\[[9](https://arxiv.org/html/2605.19186#bib.bib9),[15](https://arxiv.org/html/2605.19186#bib.bib16)\]\.

Feasibility predicate\.The two\-layer structure above is captured by a single planning\-actionable predicate\. Given taskttwith signature𝒮t\\mathcal\{S\}\_\{t\}and a minimum epistemic requirementℛtmin\\mathcal\{R\}\_\{t\}^\{\\min\}\(an entailment regime together with the set of predicates over which closure must hold fortt’s inferences to be sound\),ttis*feasible*against𝐾𝐺\\mathit\{KG\}iff

𝒢​\(𝐾𝐺,𝒮t\)=1andℛ​\(𝐾𝐺\)⊧ℛtmin\.\\mathcal\{G\}\(\\mathit\{KG\},\\mathcal\{S\}\_\{t\}\)=1\\quad\\text\{and\}\\quad\\mathcal\{R\}\(\\mathit\{KG\}\)\\models\\mathcal\{R\}\_\{t\}^\{\\min\}\.The roles ofℰ\\mathcal\{E\}and𝒟\\mathcal\{D\}are indirect but essential:ℰ\\mathcal\{E\}bounds the*computability*of the𝒢\\mathcal\{G\}check \(via the DL fragment of𝒯𝐾𝐺\\mathcal\{T\}\_\{\\mathit\{KG\}\}\) and the maximum regime expressible inℛ\\mathcal\{R\}, while𝒟\\mathcal\{D\}determines whether feasibility can be decided*at planning time*fromM​\(𝐾𝐺\)M\(\\mathit\{KG\}\)alone, or only by exploratory querying\.

This factorisation is what gives the affordance gap signal its diagnostic power: a feasibility failure is always attributable to a specific dimensional shortfall, and the dimension identifies the class of remedy \(vocabulary mediation, KG re\-selection, or schema/content repair\) before the agent commits to invocation\.

## 4Agentic Affordance Profile in Practice

We envisage utilising this four\-dimension framework via a concrete artefact: an*Agentic Affordance Profile*\(AAP\) for KGs, functioning as a semantic layer aboveVoIDandDCAT\. AnAAPdescribes, for a given KG and a family of agent task types, the values ofℰ\\mathcal\{E\},𝒟\\mathcal\{D\},𝒢\\mathcal\{G\}, andℛ\\mathcal\{R\}using a vocabulary defined inOWLand grounded in shared domain ontologies\. Publishing anAAPin a KG registry would enable formal affordance matching at agent planning time\. AnAAPis thus not a capability advertisement: it does not describe what the KG*contains*from the publisher’s perspective, but what a specific class of agent can*do*with the KG: what it can prove, what it can safely conclude from an empty result, and where mediation is required before interaction is epistemically sound\.

TheAAPassumes that agents behave*rationally*with respect to KG discovery: before committing to engage, an agent evaluates whether a KG can further its goals in a pre\-invocation phase we term the*knowledge cycle*\. The cycle has three phases: discovery, plan formation, and \(when multiple KGs are involved\) composition\. We adoptBDIas the reference deliberation model\[[37](https://arxiv.org/html/2605.19186#bib.bib35)\], asBDImakes the belief\-update, goal\-checking, and intention\-commitment steps in whichAAPscores are consumed explicit\. The framework is, however, architecture\-agnostic: an LLM\-orchestrated planner can consumeAAPscores directly via a registry tool wrapper, treating them as preconditions on tool\-use without a classicalBDIloop\[[21](https://arxiv.org/html/2605.19186#bib.bib37)\]\. At*discovery*time, an agent queries anAAP\-enabled registry for KGs whose expressivity meets the task minimum,𝒢​\(𝑡𝑎𝑠𝑘\)=1\\mathcal\{G\}\(\\mathit\{task\}\)=1, and whose entailment regime is sufficient, enabling principled KG selection at planning time without requiring content access\. This is analogous to OWL\-S*Profile*matching\[[28](https://arxiv.org/html/2605.19186#bib.bib27)\]applied to KGs\.

During*plan formation*, the agent performs a reachability check to determine whether every concept in its task signature𝒮\\mathcal\{S\}is covered by the KG’s signature closureℛ\+\\mathcal\{R\}^\{\+\}\(𝒢=1\\mathcal\{G\}=1\)\. If not, the agent determines which concepts in𝒮\\mathcal\{S\}lie outsideℛ\+\\mathcal\{R\}^\{\+\}and searches for knowledge\-producing services \(such as PSMs\[[27](https://arxiv.org/html/2605.19186#bib.bib25)\]\) that can supply the missing knowledge\. These may include dynamic ontology alignment procedures, SPARQL CONSTRUCT queries over external KGs, or inference services grounded in the KG’s axioms\. Invocation results update the agent’s epistemic state and the reachability check is repeated\. Once coverage is confirmed, the agent can proceed to contact the KG\. Composition introduces a further consideration\. If an agent’s tasks involve querying multiple KGs, or if a pre\-registered mediator is used to address a conceptual gap, anAAP\-based composition check determines whether the composite task signature𝒮\\mathcal\{S\}is covered by the union of signature closuresℛ\+\\mathcal\{R\}^\{\+\}\. Where gaps exist, the framework identifies which concepts require alignment or mediation; both classical andLLM\-driven approaches to on\-demand alignment are applicable\[[13](https://arxiv.org/html/2605.19186#bib.bib14),[31](https://arxiv.org/html/2605.19186#bib.bib30),[39](https://arxiv.org/html/2605.19186#bib.bib36)\]\. The composition case poses a particular efficiency challenge: naively, every correspondence in every aligned ontology is a candidate for closing the gap\. Module extraction over the task signature\[[11](https://arxiv.org/html/2605.19186#bib.bib11)\]provides a pre\-invocation filter: only correspondences whose source entities lie within the task\-scoped module are candidates for gap resolution, and where no such correspondences exist, alignment failure can be predicted without invoking any negotiation service\. A registered mediator can thus be evaluated against the specific gap𝒮∖ℛ\+\\mathcal\{S\}\\setminus\\mathcal\{R\}^\{\+\}before any invocation is committed:*mediation as a planning object*, not merely a resolution mechanism\.

When*troubleshooting*task failure, current frameworks typically offer no structured account of why a task failed: the agent receives no result, or an unexpected one, with no information about which property of the knowledge source was insufficient\. The affordance framework transforms task failure into principled diagnosis by attributing it to a specific dimensional gap:

1. 1\.where task concepts lie outside the KG’s signature closureℛ\+\\mathcal\{R\}^\{\+\}\(a𝒢\\mathcal\{G\}\-failure\), the KG lacks the vocabulary to ground the task; the remedy is vocabulary mediation or the invocation of a knowledge\-producing service to supply the missing grounding;
2. 2\.if the KG’s entailment regime or closure assumptions fall short of what the task requires \(aℛ\\mathcal\{R\}\-failure\), the issue lies not in the KG’s content but in its epistemic commitments, pointing to KG selection revision rather than repair;
3. 3\.where the governing schema is inconsistent or KG content is non\-compliant \(anℰ\\mathcal\{E\}\-failure\), content repair or schema revision is indicated\.

This constitutes an*affordance gap*signal: unlike abstract quality metrics\[[33](https://arxiv.org/html/2605.19186#bib.bib39),[38](https://arxiv.org/html/2605.19186#bib.bib38)\], it characterises fitness for a specific agentic use and directly prescribes the remedial action required\.

To illustrate the framework through an example, imagine that an LLM\-orchestrated assistant is asked by an EKAW programme chair to compile an*emerging\-voices*shortlist: researchers who have published recently on knowledge engineering, yet who have*never*been invited speakers at a major conference\. The agent’s task signature is defined as:

𝒮=\{𝖱𝖾𝗌𝖾𝖺𝗋𝖼𝗁𝖾𝗋,𝖯𝖺𝗉𝖾𝗋,𝖺𝗎𝗍𝗁𝗈𝗋𝖮𝖿,𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋,𝖢𝗈𝗇𝖿𝖾𝗋𝖾𝗇𝖼𝖾,𝗀𝗂𝗏𝖾𝗇𝖠𝗍\}\\mathcal\{S\}=\\\{\\mathsf\{Researcher\},\\mathsf\{Paper\},\\mathsf\{authorOf\},\\mathsf\{Invited\\\_speaker\},\\mathsf\{Conference\},\\mathsf\{givenAt\}\\\}and its plan requires a*sound*negative inference on𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\}: underOWAan empty result means only “no record of being invited”, which would silently admit prior invited speakers into the shortlist\. Three KGs advertise themselves as candidates:

- •KG1is a legacySPARQLendpoint exposingOAEI\-style IRIs inABoxtriples with a minimalRDFSschema declaring only𝖱𝖾𝗌𝖾𝖺𝗋𝖼𝗁𝖾𝗋\\mathsf\{Researcher\},𝖯𝖺𝗉𝖾𝗋\\mathsf\{Paper\}, and𝖺𝗎𝗍𝗁𝗈𝗋𝖮𝖿\\mathsf\{authorOf\}, and aVoIDdescription giving only triple counts;
- •KG2is a deployment ofConference\.owl\(Sec\.[3](https://arxiv.org/html/2605.19186#S3)\) at anOWL 2 ELendpoint, withVoID\+DCATmetadata but no completeness declarations;
- •KG3is a deployment of anOWL 2 DLextension ofConference\.owlcarrying a fullAAPprofile in which𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\}is declared closed via aSHACLClosed Shape\[[18](https://arxiv.org/html/2605.19186#bib.bib18)\]\.

Although𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\}is implicitly definable fromConference\.owl\[[13](https://arxiv.org/html/2605.19186#bib.bib14)\]and may*appear*as an IRI in KG1’sABox, the requiredTBoxaxioms are absent, so𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\},𝖢𝗈𝗇𝖿𝖾𝗋𝖾𝗇𝖼𝖾\\mathsf\{Conference\}, and𝗀𝗂𝗏𝖾𝗇𝖠𝗍\\mathsf\{givenAt\}are all outsideℛ\+​\(𝐾𝐺1\)\\mathcal\{R\}^\{\+\}\(\\mathit\{KG\}\_\{1\}\), giving𝒢=0\.5\\mathcal\{G\}=0\.5\(three of six task concepts are explicitly grounded, three depend on axiomatisation that is missing\)\. KG2admits a fully grounded query and correctly classifies recorded invited speakers, yet underOWAthe agent cannot conclude¬𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋​\(x\)\\neg\\mathsf\{Invited\\\_speaker\}\(x\)from an empty result:ℛ\\mathcal\{R\}’s closure scope is silent precisely on the predicate the task depends upon\. KG3’sSHACLClosed Shape on𝖨𝗇𝗏𝗂𝗍𝖾𝖽​\_​𝗌𝗉𝖾𝖺𝗄𝖾𝗋\\mathsf\{Invited\\\_speaker\}makes the closed\-world reading locally sound\[[18](https://arxiv.org/html/2605.19186#bib.bib18),[26](https://arxiv.org/html/2605.19186#bib.bib24)\]\.

Table 1:The three KGAAPs computed against𝒮\\mathcal\{S\}\.*Remedial actions\.*The KG1verdict recommends invocation of a knowledge\-producing service supplying the missingTBoxgrounding \(e\.g\., an alignment service projecting fromConference\.owl\); the KG2verdict recommends KG*re\-selection*rather than repair, since the shortfall is in epistemic commitment, not content\. This is the same dimension\-to\-action mapping as the failure\-diagnosis account above:𝒢\\mathcal\{G\}\-failures call for vocabulary mediation,ℛ\\mathcal\{R\}\-failures for selection revision,ℰ\\mathcal\{E\}\-failures for content or schema repair\. The same KG2would scoreℛ=1\\mathcal\{R\}=1for a task requiring only positive retrieval \(e\.g\.,*list current invited speakers*\), illustrating the agent\- and task\-relative character of every dimension\.

## 5Research Agenda

Realising theAAPas deployable infrastructure requires progress on five challenges spanning formal theory, computational methods, and engineering practice\.

AAP Ontology Formalisation:TheAAPvocabulary must be specified as anOWLontology enabling formal affordance matching at agent planning time\. Existing standards such asVoIDandDCATpartially constrainℰ\\mathcal\{E\}and𝒟\\mathcal\{D\}, but contribute nothing to𝒢\\mathcal\{G\}orℛ\\mathcal\{R\}, which require a new formal annotation vocabulary that is absent from current KG publishing practice\. A complementary prerequisite is a shared*task ontology*defining the agent task types against whichAAPscores are computed; this could initially be bootstrapped from existingMCPtool catalogues and agent capability schemas\.

Tractability of Task\-Relative Grounding:A number of tractable solutions exist forOWL\-QLviaOBDArewriting\[[8](https://arxiv.org/html/2605.19186#bib.bib8)\]and forOWL\-ELvia module extraction, but efficient computation of𝒢\\mathcal\{G\}for more expressiveDLschemas remains open\. The challenge is sound approximation: conservative coverage estimates that fail safely, makingAAPmatching practical without requiring uniform interpolation\. Whether approximate or defeasible matching provides stronger guarantees for real\-world tasks, however, remains an open question\.

Compositional Affordance Semantics:When agents federate across multiple KGs, union coverage ofℛ\+\\mathcal\{R\}^\{\+\}is necessary but not sufficient, since shared concept names may carry conflicting axioms and the KGs’ entailment regimes may not combine coherently \(e\.g\. when predicates fall under mutually incompatibleLCWAscopes\)\. Both composite coherence and mediator preservation under heterogeneous closure assumptions remain formally uncharacterised\.

Knowledge Service Specification:For PSMs and mediators to be evaluable as planning objects, each must declare its epistemic preconditions and the concepts it produces or bridges: the OWL\-S*Process Model*equivalent for knowledge services\. CurrentMCPtool descriptions andLLMtool schemas specify neither, so an agent cannot assess a tool’s fitness without invoking it\.

Engineering Integration and Adoption:A practical deployment requires tooling to assist KG publishers in computingAAPdimension values, and standard protocols for embedding affordance matching into current agent planning frameworks without framework\-specific adaptation\. Priority targets includeLLM\-driven frameworks in whichAAPregistry lookups serve directly as preconditions on tool use\. A further challenge is closing the feedback loop: translating dimensional failure signals into actionable repair guidance for KG maintainers, connecting affordance\-based diagnosis to KG lifecycle management\.

## 6Conclusions

Two decades ago, the Semantic Web Services community was asked how an agent can assess a web service resource’s fitness before committing to engage it\. This question applies directly to KGs, yet remains unanswered by current standards:VoIDandDCATdescribe what a KG contains, not what a specific agent can prove from it, what closure assumptions govern empty results, or whether its task vocabulary is grounded in the schema\. TheAAPframework addresses this formally, revisiting and extending the OWL\-S/WSMO insights for the KG setting\. Semantic Expressivity, Agentic Discoverability, Task\-Relative Grounding, and Epistemic Trust Scope together enable principled KG selection, composition, and failure diagnosis at planning time\. Unlike in 2005, matureSHACLtooling,OBDA\-aware triple stores, andLLM\-orchestrated agent frameworks make this substantially more tractable than at the time of OWL\-S and WSMO; the research agenda identifies the formal, computational, and engineering work that remains\.

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