Cumulativity without closure of the domain under finite unions

TL;DR

This paper explores how the rule of Cumulativity in nonmonotonic logics behaves differently when the domain isn't closed under finite unions, revealing an infinite variety of conditions.

Contribution

It demonstrates that Cumulativity splits into infinitely many conditions without domain closure under finite unions, highlighting nuanced logical behaviors.

Findings

Cumulativity varies infinitely without finite union closure

Different conditions emerge for nonmonotonic logics

Domain closure impacts logical properties significantly

Abstract

For nonmonotonic logics, Cumulativity is an important rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.