As a recognition method, neural network is superior and powerful, especially in image-recognition, but as a well-known method whether neural network can solve the causality reasoning or not? If not, why?
one requirement for causality is the existence of a temporal sequence because in order to be recognizable as such, the cause has to appear before the effect.
So, during the recognition of single static images, causality cannot be involved. You could argue that there is still room for reasoning like "Because a tree is in front of it there are not really two halves of a horse but it's a whole horse, only partially visible." But first, I think current ANNs do not have enough capacity for reasoning, and second, I would not call the relationship between elements in a static image "causality".
There are, of course, ANNs for predicting the development of temporal series, e. g. of stock prices; here causality is certainly involved, though partially irrational (as far as stock prizes go). But those ANNs do just pattern recognition without "knowing" or regarding any causes.
Speaking pictorially, I would compare today's ANNs to students who are good willing and industrious but do not really understand anything. They have a chance of finishing (officially) successfully by just collecting clues on what to do. ("In tasks which look similar to those we had in autumn, I have to add all resistance values.")
From my point of view, in order to recognize causal relations you need the ability either to interact with the objects you are observing, or to build up an internal model of some part of the outer world, and to simulate the evolution of this model under different circumstances. In principle, you could come to the same conclusions by just watching, but without interacting or simulating, there is only a slim chance that the objects answer your questions.
Since today's usual ANNs do not interact with the sources of their input, and do not have the capacity to simulate these sources, my answer to your question is: No.
My viewpoint is that neural network , in naturally, is a method of statistics mathematically, and it is, in naturally again, is belong to an inductive method mathematically, and in an error-optimized, so neural network is not easy to reason by causality reasoning.