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

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 as VoID and DCAT describe 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; Semantic Expressivity, Agentic Discoverability, Task-Relative Grounding, and Epistemic Trust Scope, from which we derive the Agentic Affordance Profile (AAP): a semantic layer above VoID and DCAT enabling principled KG selection, composition, and failure diagnosis at agent planning time. The four dimensions operationalise the affordance structure of the Ontological Continuum at the individual-agent level, specifically for kg selection, composition, and failure diagnosis. A worked example drawn from a scholarly-search task concretely grounds the framework, and identifies the formal, computational, and engineering work needed to realise AAP-based affordance matching at scale though a five-point research agenda.