  The TMS algorithm and its refinements had a significant impact on AI applications, and this created the need for a logical analysis. (In even fairly simple cases, it can be hard in the absence of analytic tools to see what consequences a TMS should deliver.) This provided a natural and highly specific challenge for those seeking to develop a nonmonotonic logic. The TMS also provided specific intuitions: the idea that the key to nonmonotonicity has to do with inferences based on unprovability was important for the modal approaches to nonmonotonic logic and for default logic. And the TMS’s emphasis on interactions between arguments began a theme in nonmonotonic logic that remains important to this day. (See the discussion of argument-based approaches, in  Section 3.4,  below.)