Contextual Deviation Information: An Information-Theoretic Measure of Protocol Violation and Semantic Falsity in Multi-Agent Communication

This paper introduces Contextual Deviation Information (CDI), a novel information-theoretic measure that quantifies, in bits, how sharply an observed output departs from the behavior prescribed by a normative context. Unlike Shannon information, which measures statistical surprise relative to a descriptive source distribution, CDI measures normative deviation from an agreed protocol or expected behavior. The paper formalizes context as a conditional probability distribution over outputs, defines CDI, and proves fundamental properties including non-negativity, monotonicity, additivity, context relativity, and decomposition into Shannon entropy and Kullback-Leibler divergence. It shows that Shannon information emerges as a special case when the contextual distribution coincides with the actual behavior distribution. The framework is further extended to semantic falsity by introducing a truth-conditional distribution and Semantic Deviation Information (SDI), along with combined contextual-semantic measures and a classification of deceptive behavior. A multi-agent network simulation demonstrates that CDI can detect protocol-violating nodes solely from their observable communication behavior. The work bridges information theory, protocol conformance, and the formal semantics of deception.