A theory of modeling semantic uncertainty in label representation

A new theory of modeling the uncertainty associated with vague concepts is introduced. We consider the problem of quantifying an agents uncertainty concerning which labels are appropriate to describe a given observation. This can be regarded as a simplified model of natural language communication. Semantic meaning conveyed by high-level knowledge representation is often inherently uncertain. Such uncertainty is referred to semantic uncertainty and dominated by fuzzy modeling. In this framework, from an epistemic point of view, labels are precise and uncertainty comes from the undecidable boundary between labels in agents conceptual space. In this framework the boundary is regarded as a random variable and it can be modeled by a probability distribution. We also propose a functional calculus to measure how appropriate of using a certain label to describe an observation. In this way, a vague concept can be represented by a distribution on the labels. The new theory is verified by applying it to the vague category game.