The physical foundations for the geometric structure of relativistic
  theories of gravitation. From General Relativity to Extended Theories of
  Gravity through Ehlers-Pirani-Schild approach
  We discuss in a critical way the physical foundations of geometric structure
of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild
formalism. This approach provides a natural interpretation of the observables
showing how relate them to General Relativity and to a large class of Extended
Theories of Gravity. In particular we show that, in such a formalism, geodesic
and causal structures of space-time can be safely disentangled allowing a
correct analysis in view of observations and experiment. As specific case, we
take into account the case of f(R) gravity.
