Decrement Operators in Belief Change
This work addresses a specific theoretical gap in belief change for AI and logic researchers, but it appears incremental as it builds on existing concepts like Darwiche and Pearl's iterated revision.
The paper tackles the problem of iterated contraction in belief change by introducing weak decrement operators as a non-prioritized generalization, and it presents postulates and representation theorems for these operators in the framework of total preorders.
While research on iterated revision is predominant in the field of iterated belief change, the class of iterated contraction operators received more attention in recent years. In this article, we examine a non-prioritized generalisation of iterated contraction. In particular, the class of weak decrement operators is introduced, which are operators that by multiple steps achieve the same as a contraction. Inspired by Darwiche and Pearl's work on iterated revision the subclass of decrement operators is defined. For both, decrement and weak decrement operators, postulates are presented and for each of them a representation theorem in the framework of total preorders is given. Furthermore, we present two sub-types of decrement operators.