System, apparatus and method may permit users to collaboratively engage in inference on a computer and visualize structure of that inference, and provide a formal verification system for informal argumentation and inference. The system and method may generate and allow for modification of graphical structures that represent sequences of structured rational argumentation; and automatically monitor, compute and represent ratings or scores of nodes within the structure; indicate whether a node is supported by a chain of argumentation that has not been validly rebutted. The graphical structures may be displayed to bring into focus contentious and significant underlying points within an argument, and simulate the effects of alternative resolutions of these contentious points. The graphical displays may provide a transparent verification to other users of the state of what can be demonstrated and refuted, allow discovery of weak or missing points in a logical argument, and allow rational inference by users.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. An apparatus comprising: a processing device configured to: receive first information indicating statements and arguments, and which statement of the statements is an intended result of an argument; receive second information indicating challenges to the statements or the arguments; establish a correspondence between the statements and the arguments to nodes in a graph; and rate whether a first node of the nodes is established by an argument graph using only arguments that are not validly challenged. 2. The apparatus of claim 1, wherein the first information indicates which statement of the statements is an assumption of an argument, and wherein the processing device rates whether the first node of the nodes is established by the argument graph using only assumptions that are not validly challenged and the arguments that are not validly challenged. 3. The apparatus of claim 1, wherein the first node is validly challenged when a challenge node exists that is established by an argument graph using only assumptions and arguments that are not validly challenged. 4. The apparatus of claim 1, wherein the first node is validly challenged when a challenge node exists for the first node. 5. The apparatus of claim 1, wherein the first node is not validly challenged when every challenge to the first node is validly rebutted by a counter challenge to said challenge or an argument graph thereof. 6. The apparatus of claim 1, wherein the processing device is further configured to receive third information indicating which of the statements or the nodes is designated as a citation, and wherein the first node is not rated as established unless the first node is a citation node or an argument for the first node exists from another node of the nodes that is rated as established. 7. The apparatus of claim 1, wherein the processor is further configured to receive third information indicating which of the statements, nodes or edges is designated as a suggested edit, and wherein, when a first edge of the edges is designated as the suggested edit, the first edge is not considered as an argument, assumption or challenge in rating the nodes. 8. The apparatus of claim 1, wherein the processor is further configured to: receive third information indicating a set of choice nodes, rate at most one of each set of choice nodes as established, and rate a first choice node of the choice nodes as established, when an argument graph exists for the first choice node such that no node in an argument graph thereof is validly challenged and no argument exists for other of the choice nodes in the set of choice nodes to which the first choice node belongs. 9. An apparatus comprising: a processing device configured to: receive first information indicating nodes in a graph and directed edges, said edges indicating which first node of the nodes provides an argument for another node of the nodes, which second node of the nodes provides an assumption for another second node of the nodes, and which third node of the nodes provides a challenge to another third node of the nodes; receive second information indicating text or data associated with the nodes; rate a first edge of the edges as established when the first edge originates at an established node of the nodes; and rate a node of the nodes as established (i) in a case when each incoming assumption edge thereof is established and no incoming challenge edge is established, and (ii) in a case when at least one incoming argument edge exists, at least one of the at least one incoming argument edge exists is established. 10. The apparatus of claim 9, wherein the nodes in the graph are rated in order of increasing EDepth, and wherein the EDepth is a length of a longest path in said graph ending at said node corresponding thereto extending only over challenge, argument, assumption and citation edges. 11. The apparatus of claim 9, wherein the processing device is further configured to: receive third information indicating which of the nodes is a citation node, and wherein a second node of the nodes is only rated as established when the second node is a citation node or has an established incoming argument edge. 12. The apparatus of claim 9, wherein the processing device is further configured to: select a node of the nodes and a statement associated therewith is designated as axiomatized, and rate other nodes of the nodes in the graph as the other nodes would be rated when an axiomatized node is established. 13. The apparatus of claim 9, wherein the processing device is further configured to: select a edge of the edges and attach a challenge to or insert a node within the selected edge and attach a challenge edge to the selected edge. 14. An apparatus comprising: a processing device configured to: receive first information indicating nodes and directed edges of a graph, said edges indicating which first node of the nodes provides an argument for another node of the nodes, which second node of the nodes provides an assumption for another second node of the nodes and which third node of the nodes provides a challenge to another third node of the nodes; receive second information indicating text or data associated with the nodes; and determine a belief for each respective node estimating (i) a likelihood that each incoming assumption edge thereof is from a true node, (ii) when the node has at least one argument edge, at least one of the at least one argument edge is from a true node, and (iii) no incoming challenge edge thereof is from a true node. 15. The apparatus of claim 14, wherein the processing device is configured to: determine which node of the nodes provides a test for a fourth node, and receive third information indicating a likelihood a result of the test implies the fourth node is true when the test node itself is true and determine a numerical belief for all of the nodes in said graph. 16. The apparatus of claim 14, wherein the processing device is configured to: receive third information indicating a new node entered by a user selecting an existing node of the nodes, selecting an edge type and providing text or data as a declaration for said new node, connect said new node to said existing node using an edge of said edge type. 17. The apparatus of claim 14, wherein the processing device is configured to: display an indication of a reward in association with display of the graph for a successful or non-trivial challenges. 18. A method comprising: receiving, by a processing device, first information indicating statements and arguments, which statement of the statements is an intended result of an argument; receiving, by the processing device, second information indicating challenges to the statements or the arguments; establishing, by the processing device, a correspondence between the statements and the arguments to nodes in a graph; and rating, by the processing device, whether a first node of the nodes is established by an argument graph using only arguments that are not validly challenged. 19. The method of claim 18, wherein the first information indicates which statement of the statements is an assumption of an argument, and wherein the rating whether the first node of the nodes is established is by the argument graph using only assumptions that are not validly challenged and the arguments that are not validly challenged.