Non-commutative quantales for many-valuedness in applications

Abstract

In this paper we show how the diversity of properties for quantales is well suited for describing multivalence in many-valued logic. Tensor products of quantales will play an important role in showing how more simple valuation scales can be tensored together to provide more complex valuation scales. In health care applications, this is typically seen for disorders and functioning. Classification of disorder is typically quite bivalent, whereas scales used in functioning classifications are multivalent. The role ‘not specified’ or ‘missing’ is shown to be of importance.