An Assumption-Based Framework for Non-Monotonic Reasoning

The notion of assumption-based framework generalises and reenes the use of abduction to give a formalisation of non-monotonic reasoning. In this framework, a sentence is a non-monotonic consequence of a theory if it can be derived monotonically from a theory extended by means of acceptable assumptions. The notion of acceptability for such assumptions is formulated in terms of their ability successfully to \counterattack" any \attacking" set of assumptions. One set of assumptions is said to \attack" another if the rst set monotonically implies a consequence which is inconsistent with an assumption in the second set. This argumentation-theoretic criterion of acceptability is based on notions rst introduced for logic programming and used to give a uniied account of such diverse semantics for logic programming as stable models, partial stable models, preferred extensions, stable theories, well-founded semantics, and stationary semantics. The new framework makes it possible to generalise various improvements rst introduced for the semantics of logic programming and to apply these improvements to other formalisms for non-monotonic reasoning. The paper investigates applications of the framework to logic programming , abductive logic programming, logic programs extended with \classi-cal" negation, default logic, autoepistemic logic, and non-monotonic modal logic.