Layered irredundant covering

Abduction is generally defined as inference to the best explanation. Many approaches to abductive problem solving involve covering or accounting for what needs to be explained using a parsimonious set of explanation elements. Various criteria of parsimony, including irredundancy have been studied in diagnostic problem solving. We studied irredundancy further, in the context of other abductive problems such as natural language processing and Boolean function minimization, where the nature of the underlying knowledge is somewhat different. Despite differences, all the task domains involve layers of covering, e.g., to capture causal chaining in diagnosis, various subcubes in Boolean minimization, or to parse layer by layer in language processing. In all these three domains, irredundant covering has been noted to be transitive in a certain sense, making it possible to focus on a pair of consecutive layers at any time. These observations raise the question as to whether this kind of transitivity is inherent to irredundancy. We examine this question and some associated computational problems