Operationalising Extended Cognition: Formal Metrics for Corporate Knowledge and Legal Accountability

Corporate responsibility turns on notions of corporate textitmens rea, traditionally imputed from human agents. Yet these assumptions are under challenge as generative AI increasingly mediates enterprise decision-making. Building on the theory of extended cognition, we argue that in response corporate knowledge may be redefined as a dynamic capability, measurable by the efficiency of its information-access procedures and the validated reliability of their outputs. We develop a formal model that captures epistemic states of corporations deploying sophisticated AI or information systems, introducing a continuous organisational knowledge metric SS(varphi) which integrates a pipeline's computational cost and its statistically validated error rate. We derive a thresholded knowledge predicate mathsfKS to impute knowledge and a firm-wide epistemic capacity index KS,t to measure overall capability. We then operationally map these quantitative metrics onto the legal standards of actual knowledge, constructive knowledge, wilful blindness, and recklessness. Our work provides a pathway towards creating measurable and justiciable audit artefacts, that render the corporate mind tractable and accountable in the algorithmic age.