Implementing Nonmonotonic Reasoning From Weakly Consistent Conditional Belief Bases

Abstract

In this paper, we develop implementations of nonmonotonic reasoning from conditional belief bases that may
contain both defeasible and undefeasible, strict beliefs. Any belief base containing a strict belief fails to comply with the well-known consistency test by Goldszmidt and Pearl, and can be at most weakly consistent. Although weakly consistent belief bases have more expressive power, they have gained much less attention in research than strongly consistent belief bases. In particular, this observation holds for corresponding implementations. We introduce implementations of established nonmonotonic inference operators that can be applied to weakly consistent belief bases: p-entailment, system Z and thus rational closure, lexicographic inference, and system W. These implementations are integrated into an easy-to-use online reasoning platform. In a system walkthrough, we illustrate the additional functionalities and their effectiveness of the extended platform for dealing with weakly consistent belief bases.