Interpretive Entropy and the Linguanese Framework: Toward a Quantitative Theory of Semantic Ambiguity

Natural language is inherently ambiguous, yet no standard metric exists for quantifying the degree of ambiguity in a sentence or the amount of context required to resolve it. This paper introduces interpretive entropy H(s|c), a measure grounded in Information Theory that quantifies the dispersion of interpretations assigned by a competent speaker to sentence s in context c. Four formal properties of the measure are derived, including a compositionality bound (Theorem 3.5) and a monotonicity result for context enrichment (Theorem 3.7). The paper also presents Linguanese, a constructed language system designed to enable controlled experimentation on interpretive variability, together with its semantic lexicon, the Linguanary, which provides canonical definitions anchored to ten typologically diverse source languages. Drawing on underspecification theory, probabilistic semantics, and formal models of disambiguation, interpretive entropy is proposed as a quantitative framework connecting these approaches. Five falsifiable predictions are derived and translated into experimental protocols for independent replication. All Linguanese materials are publicly archived under a Creative Commons license.