Cumulativity Tailored for Nonmonotonic Reasoning

• Published in: Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation pp. 96 - 111
• Main Authors: Janhunen, Tomi, Niemelä, Ilkka
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2015
• Series: Lecture Notes in Computer Science
• Subjects: Choice Rule; Default Theory; Integrity Constraint; Logic Program; Stable Model
• ISBN: 9783319147253; 3319147250
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-14726-0_7

In nonmonotonic reasoning, conclusions can be retracted when new pieces of information are incorporated into premises. This contrasts with classical reasoning which is monotonic, i.e., new premises can only increase the set of conclusions that can be drawn. Slightly weaker properties, such as cumulativity and rationality, seem reasonable counterparts of such a monotonicity property for nonmonotonic reasoning but intriguingly it turned out that some major nonmonotonic logics failed to be cumulative. These observations led to the study of variants in hope of restoring cumulativity but not losing other essential properties. In this paper, we take a fresh view on cumulativity by starting from a notion of rule entailment in the context of answer set programs. It turns out that cumulativity can be revived if the expressive precision of rules subject to answer set semantics is fully exploited when new premises are being incorporated. Even stronger properties can be established and we illustrate how the approach can be generalized for major nonmonotonic logics.