Proving Musical Properties using a temporal Concurrent Constraint Calculus

We show how the ntcc calculus, a model of temporal concurrent constraint programming with the capability of modeling asynchronous and non-deterministic timed behavior, can be used for modeling real musical processes. We use the nondeterminism facility of ntcc to build weaker representations of musical processes that greatly simplifies the formal expression and analysis of its properties. We argue that this modeling strategy provides a ”runnable specification” for music problems that eases the task of formally reasoning about them. We show how the linear temporal logic associated with ntcc gives a very expressive setting for formally proving the existence of interesting musical properties of a process. We give examples of musical specifications in ntcc and use the linear temporal logic for proving properties of a real musical problem.