Many researchers believe that certain aspects of natural language processing, such as word sense disambiguation and plan recognition in stories, constitute abductive inferences. We have been working with a specific model of abduction, called parsimonious covering, applied in diagnostic problem solving, word sense disambiguation and logical form generation in some restricted settings. Diagnostic parsimonious covering has been extended into a dual-route model to account for syntactic and semantic aspects of natural language. The two routes of covering are integrated by defining “open class” linguistic concepts, aiding each other. The diagnostic model has dealt with sets, while the extended version, where syntactic considerations dictate word order, deals with sequences of linguistic concepts. Here we briefly describe the original model and the extended version, and briefly characterize the notions of covering and different criteria of parsimony. Finally we examine the question of whether parsimonious covering can serve as a general framework for parsing.