A Quantum Approach to Vagueness and to the Semantics of Music

Quantum computational logics represent a suitable abstract environment for modelling semantic situations where vagueness and ambiguity play a relevant role. In this framework vague possible worlds can be described as a kind of abstract scenes, where individual concepts, relational concepts and events behave as quantum-like superpositions that ambiguously allude to a number of possibly antagonistic alternatives. The quantum semantics can be naturally applied to a formal analysis of musical compositions, where both musical ideas and extra-musical meanings are characterized by some essentially vague and ambiguous features. We investigate some examples.