The 'Ah Ha!' Moment: When Possible, Answering the Currently Unanswerable using Focused Reasoning

The ‘Ah Ha! ’ Moment : When Possible, Answering the Currently Unanswerable using Focused Reasoning Daniel R. Schlegel and Stuart C. Shapiro Department of Computer Science and Engineering, and Center for Cognitive Science University at Buffalo, Buffalo, NY 14260 @buffalo.edu Abstract driven programs where events interact in complex ways, re- quiring complex state management, such as spreadsheets. In Section 2 we will discuss the issue of FR itself. In Sec- tion 3 2 we will discuss IGs in only the required amount of de- tail to further our discussion, and in Section 4 we will return to the issue at hand to discuss the different types of FR with examples, along with an algorithm to unify the three types of FR discussed. Finally, we will conclude with Section 5. Focused reasoning is a method for continuing a specific in- ference task as soon as rules or facts which may assist in the reasoning are added to the knowledge base without repeat- ing completed inference, re-posing queries, or performing un- necessary inference. Determining if focused reasoning should commence uses very few computational resources above those used normally to add a term to a knowledge base. We have developed three focused reasoning procedures – backward-in- forward, forward, and forward-in-backward – built upon Infer- ence Graphs, a graph-based concurrent reasoning mechanism. Introduction When an inference process has stopped before its natural con- clusion because of a lack of information, any new assertion which is relevant should immediately be used to continue that inference, but not derive anything unrelated to the inference task. Focused reasoning (FR) has been developed to do just this. Methods for performing focused reasoning have been developed for using forward, and bi-directional (Shapiro, Martins, & McKay, 1982) inference. To accomplish this, In- ference Graphs (IGs) (Schlegel & Shapiro, 2013b, 2014), a concurrent graph-based method for natural deduction reason- ing, are extended to recognize when new connections in the graph are relevant to incomplete inference procedures. Inference Graphs are propositional graphs with message- passing channels added, allowing related terms to commu- nicate about the results of inference, or to control inference. IGs implement L A , a Logic of Arbitrary and Indefinite Ob- jects (Shapiro, 2004), which uses structured quantified terms. One type of FR using IGs was briefly proposed in (Schlegel & Shapiro, 2013b), but unimplemented. Here we discuss the issue in detail, including two other types of FR, in an imple- mented system. While our primary interest is in building a mind, any large knowledge base (KB) which allows for interleaved assertions and queries may benefit from FR. For example, 1 web services which perform frequent queries for users, such as eBay’s saved searches (eBay, Inc., 2013) which email new match- ing items to users daily, could use FR to send updates as soon as they are available, avoiding batch processing. Diagnostic tasks may also benefit: one may start with a problem they wish to solve, and then do diagnostic tests. The results could be added to the KB, where they are automatically applied to only the focused problem, without deriving other, unrelated, conclusions. Another application might be within event- 1 We have not done significant study on these applications yet. Focused Reasoning Humans often consider problems they may not yet have an- swers for, and push those problems to the “back of their mind. ” In this state, a human is still looking for a solution to a problem, but is doing so somewhat passively – allowing the environment and new information to influence the prob- lem solving process, and hopefully eventually reaching some conclusion. That is, the examination of the problem persists beyond the time when it is actively being worked on. 3 We wish to add a similar capability to a reasoning system. There are three types of FR possible within a reasoning system: forward FR, where all possible derivations are per- formed only from some specific new piece of knowledge, and continued upon the addition of relevant rules to the KB; forward-in-backward FR, in which backward inference oc- curs to try to answer a query, and as new facts or rules rel- evant to the query are added to the KB, they are used in at- tempting to answer the query; and backward-in-forward FR, which combines the previous two FR mechanisms. Forward FR can be thought of as a kind of full-forward reasoning carried out only for a single asserted term. Full- forward reasoning is used most notably in production sys- tems, and especially RETE networks (Forgy, 1979, 1982). In a RETE net, all new information is filtered through a graph generated from a set of production rules. Nodes in the graph perform comparisons against accepted values, and combine pieces of compatible information together. When a piece of information reaches some leaf node in the graph, the rule that leaf node represents is said to have matched. Full-forward inference produces the logical closure of a KB, but this is horribly wasteful in both time and space, so we favor doing 2 Portions of the material in Sections 2 and 3 are adapted from (Schlegel & Shapiro, 2013a, 2014). 3 Understanding this type of problem solving in humans is still active research, what has been discussed is only an intuitive expla- nation. It is distinct from the “Eureka effect” (Auble, Franks, & Soraci, 1979) which deals with insight, and limitations of memory recall in humans.