Defeasibility in Answer Set Programs via Argumentation Theories

Defeasible reasoning has been studied extensively in the last two decades and many different and dissimilar approaches are currently on the table. This multitude of ideas has made the field hard to navigate and the different techniques hard to compare. Our earlier work on Logic Programming with Defaults and Argumentation Theories (LPDA) introduced a degree of unification into the approaches that rely on the well-founded semantics. The present work takes this idea further and introduces ASPDA—a unifying framework for defeasibility of disjunctive logic programs under the Answer Set Programming (ASP). Since the wellfounded and the answer set semantics underlie almost all existing approaches to defeasible reasoning in Logic Programming, LPDA and ASPDA together capture most of those approaches. In addition to ASPDA, we obtained a number of interesting and non-trivial results. First, we show that ASPDA is reducible to ordinary ASP programs, albeit at the cost of exponential blowup in the number of rules. Second, we study reducibility of ASPDA to the non-disjunctive case and show that head-cycle-free ASPDA programs reduce to the non-disjunctive case—similarly to head-cycle-free ASP programs, but through a more complex transformation. The blowup in the program size is linear in this case.We also shed light on the relationship between ASPDA and some of the earlier theories such as Defeasible Logic and LPDA.