OaK builds a task-specific ontology on the fly and refines it from judge feedback

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OaK is an ontology-as-a-kernel framework that constructs a task-oriented ontology and knowledge graph from task requirements and training data, generates task-adaptation functions for graph reasoning over it, then uses judge feedback to iteratively refine both. The premise is that an automatically built ontology can look semantically plausible while lacking the relational structures decisions actually need, so refinement is driven by task outcome rather than by plausibility. Evaluated on TravelPlanner, CRMArenaPro and ToolQA, it improves evidence grounding and multi-step reliability over standard LLM agents.