17. A method comprising: receiving, over a communication network, by a processing device, first information in natural language text from a user indicating statements and arguments, and which statement of the statements is an intended result of a given argument; receiving, over the communication network, by the processing device, second information in natural language text from the user indicating challenges to the statements or the arguments; establishing, by the processing device, a correspondence between the statements and the arguments to generate nodes in an argument graph; when a new first node is added to the argument graph based on new node information received over the communication network, automatically rating, by the processing device, all of the nodes in the argument graph in order of increasing EDepth to update the argument graph and cause transmission, over the communication network, the argument graph as updated, wherein the EDepth of a given node of the nodes in the argument graph is a length of a longest path in said argument graph ending at the given node and extending only over challenge, argument, assumption and citation edges, wherein each first node of the nodes in the argument graph determined to have a same first EDepth is rated before each second node of the nodes determined to have a same second EDepth greater than the same first EDepth, wherein a node to be rated of the nodes is established using only arguments of the argument graph that are not validly challenged, and wherein the node to be rated of the argument graph is rated as established based on status of verification of validity of an inference corresponding to the node to be rated and by determining whether the node to be rated has an established proof; and providing to the user the updated argument graph indicating the status of verification of validity of the inference corresponding to the rated node and whether the rated node has an established proof.
18. The method of claim 17 , wherein the first information indicates which statement of the statements is an assumption of a second given argument, and wherein the rating whether the node to be rated of the nodes is established by the argument graph is by using only assumptions that are not validly challenged and the arguments that are not validly challenged.