An Assumption-based Framework for Non-monotonic Reasoning
A. G. Bondarenko, Francesca Toni, Robert Kowalski · Logic Programming and Non-Monotonic Reasoning · 1993
The notion of assumption-based framework generalises and refines 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 first 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 first introduced for logic programming and used to give a unified 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 general...