How are propositions concerning spacetime curvature constructed explicitly in terms of coincidences? Is Einstein's insight [1] that 

All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more [...] material points.

and [2] his (so recognized)

[...] view, according to which the physically real consists exclusively in that which can be constructed on the basis of spacetime coincidences, spacetime points, for example, being regarded as intersections of world lines

applicable to propositions concerning spacetime curvature ?
How, for instance, is the proposition    
"spacetime containing the worldline of material point A is curved"   
constructed and expressed explicitly on the basis of spacetime coincidences (in which the "material point" identified as A or suitable other "material points" took part) ?

Edit in response to the answers and comments presently provided (Sept. 12th, 2013):


*

*Trying to put my question more formally,     


given that there is the set $S$ of any and all distinct "spacetimes" imaginable,
and that there is the function (or proposition)
$\kappa : S \rightarrow \{ true, false, undetermined \}$
which for any spacetime under consideration represents whether it is "curved", or "not curved", or not an eigenstate of "possessing any curvature" at all,
and further given a set of sufficiently many distinct names $W := \{ A, B, M, M', ... \}$,
and that there is the function
$coinc : S \rightarrow \text{ powerset}[ \text{ powerset}[ \, W \, ] \, ]$
which for any spacetime under consideration represents the set of (distinguishable) coincidences of (different, and distinctly named) "worldlines",
I'd like to know the explicit expression of the function (or proposition)
$f : \text{ powerset}[ \text{ powerset}[ \, W \, ] \, ] \rightarrow \{ true, false, undetermined \}$,
for which
$\forall s \in S: f( coinc( s ) ) = \kappa( s )$.
Looking at the above quotes it may be expected that $f$ has been worked out and written down long ago already; therefore, please write it down in an answer here, or point me to the corresponding reference. However, here are


*

*Considerations which answers would be acceptable otherwise:


either a proof that such a requested function $f$ doesn't exist at all; presumably by exhibiting two distinct spacetimes $s_a$ and $s_b$ for which 
$coinc( s_a ) = coinc( s_b )$ but $\kappa( s_a ) \ne \kappa( s_b )$.
(But recall the hole argument discussion relating to the difficulty of distinguishing spacetimes at all.)
Finally, if such a requested function $f$ can neither be explicitly stated, nor refuted, then
define the notion "geodesic" (which has already been used/presumed in answers below) or at least the notion "null geodesic" explicitly in terms of $coinc( s )$.
 A: Nice question. In addition to coincidences, you also need the notion of geodesics. Here are a couple of simple examples.
Example #1: In a vacuum spacetime, say we have electrically test particles A and B. Their world-lines are geodesics. Suppose these two geodesics coincide twice. Then we are guaranteed that this spacetime is not flat.
Example #2: The Gravity Probe B experiment can be expressed in terms of coincidences. This experiment involved sending a gyroscope into orbit around the earth and detecting its precession. Suppose, in a simplified conceptual version of the experiment, that the axis of the gyroscope has a mark on it, and we also mark the point on the housing that is initially right next to it. After a while, we observe that the two marks no longer coincide. Then at some still later time, we observe that the two marks again coincide, because we've had one full cycle of precession.
A: If you make a change of coordinates $x \to x'=x'(x)$, and if $x_0$ is a coincidence, then, in the new coordinates, $x'_0=x'(x_0)$ is a coincidence. Now, you can obtain the value of the new curvature tensor $R_{\alpha'\beta'\gamma'\delta'}$ from the old curvature tensor $R_{\alpha\beta\gamma\delta}$ by using transformation laws for tensors ($R_{\alpha'\beta'\gamma'\delta'} = \large \frac{\partial x^\alpha}{\partial x'^{\alpha'}}\frac{\partial x^\beta}{\partial x'^{\beta'}}\frac{\partial x^\gamma}{\partial x'^{\gamma'}}\frac{\partial x^\delta}{\partial x'^{\delta'}} R_{\alpha\beta\gamma\delta}$). If one of the components $R_{\alpha\beta\gamma\delta}(x_0)$ is different of  zero, then there will exist one of the components $R_{\alpha'\beta'\gamma'\delta'}(x'_0)$ which will be different of  zero.
