Parallel Belief Contraction via Order Aggregation
This work addresses a theoretical gap in belief revision for AI and logic, but it appears incremental as it builds on existing serial models and aggregators.
The paper tackles the problem of extending serial belief contraction to handle parallel and iterated removal of multiple information items, proposing a method based on n-ary order aggregators.
The standard ``serial'' (aka ``singleton'') model of belief contraction models the manner in which an agent's corpus of beliefs responds to the removal of a single item of information. One salient extension of this model introduces the idea of ``parallel'' (aka ``package'' or ``multiple'') change, in which an entire set of items of information are simultaneously removed. Existing research on the latter has largely focussed on single-step parallel contraction: understanding the behaviour of beliefs after a single parallel contraction. It has also focussed on generalisations to the parallel case of serial contraction operations whose characteristic properties are extremely weak. Here we consider how to extend serial contraction operations that obey stronger properties. Potentially more importantly, we also consider the iterated case: the behaviour of beliefs after a sequence of parallel contractions. We propose a general method for extending serial iterated belief change operators to handle parallel change based on an n-ary generalisation of Booth & Chandler's TeamQueue binary order aggregators.