Syntax Splitting for Iterated Contractions

Parikh developed the notion of syntax splitting to describe belief sets with independent parts. He also formulated a postulate demanding that belief revisions respect syntax splittings in belief sets. The concept of syntax splitting was later transferred to epistemic states with total preorders and ranking functions by Kern-Isberner and Brewka along with corresponding postulates for belief revisions. Besides revision, contraction is also a central operation in the field of general belief change. In this paper, we analyse belief contractions with respect to syntax splitting. Based on the work on syntax splitting for revision, we develop syntax splitting postulates for contractions on ranking functions, on epistemic states with total preorder, and on belief sets. Finally, we evaluate different contractions from the literature, namely moderate contraction, natural contraction, lexicographic contraction, and c-contractions with respect to the newly developed contraction postulates.