We show several properties of the abstract interpretation settings regarding relationships between precision of semantic operators and abstract domains composition. Then, we apply these results to the framework for logic programs introduced in [CominiLM95], extended with the new class of operational observables. We prove that the classes of perfect, denotational and operational observables are complete lattices and we discuss some problems that arise studying them. Finally, we show how to use functional dependencies to systematically derive new domains in which our semantic operators enjoy desired precision properties.