Contextual Information Allocation in Shared-State Cognitive Models: An Information-Theoretic Bound

Abstract

Context-sensitive behavior can be modeled by enriching an internal state, by allowing a response rule to access context directly, or by preserving a shared state while introducing an auxiliary criterion or control variable. This paper isolates an information-theoretic constraint on the third architecture. Let $C$ denote context, $S$ a candidate internal or latent state, $O$ an observable response, and $M$ an auxiliary variable such that $O\perp C\mid(S,M)$. Then \[ I(C;O\mid S)\le I(C;M\mid S)\le H(M\mid S). \] Once a shared state has been specified, residual context dependence in behavior therefore lower-bounds both the context information and the conditional entropy that an auxiliary context-mediating mechanism must carry. The bound is representation-relative rather than a measure of state-space size or a universal contextuality measure. A worked recognition-memory example shows how the quantity can be computed for payoff-induced criterion shifts and compared across alternative representational allocations. Ontological contextuality and quantum probability are treated as a separate specialization rather than as prerequisites for the cognitive interpretation. More broadly, the framework provides a basis for analyzing context-memory-control trade-offs in cognitive models and artificial agents that must maintain coherent behavior across changing contexts under bounded internal representations.