Partial Information Ionic Logic Programming

Abstract

Let us reconsider the Tweety example: Tweety is a bird. Birds typically fly. In this example, query: Does Tweety fly? should fail, because it asks whether some kernel knowledge is present, and that knowledge is simply not there. However, a weaker question may be asked: Is there any justification such that Tweety flies under that justification? This weaker query will succeed, and compute the corresponding justification (Tweety flies). Thus, since we shall need to use justifications as objects of computation, one needs to have a way of referring to these objects. In other words, one needs justification variables. Also, from a practical point of view, it is annoying to have to specify from the very start the number of justification variables to be used in a given computation. It is more convenient to be able to ask: Are there any justifications such that under those justifications, Tweety flies ? Whence the slightly modified infinitary version of the language of PIL used in this chapter.