: We give the main definitions and results of a new framework for algebraic specifications: the framework of label algebras. The main idea underlying our approach is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with range in terms instead of values. Surprisingly, there are several cases where even if two terms have the same value, it is possible that one of them is a suitable instance of a variable in an formula while the other one is not. It is for instance the case for algebraic specifications with exception handling or with observability features. We show that our approach is a useful tool for solving this problem.