Kernel Contraction and the Order of Relevance

The postulate of relevance provides a suitable and general notion of minimal change for belief contraction. Relevance is tightly connected to smooth kernel contractions when an agent's epistemic state is represented as a logically closed set of formulae. This connection, however, breaks down when an agent's epistemic state is represented as a set of formulae not necessarily logically closed. We investigate the cause behind this schism, and we reconnect relevance with smooth kernel contractions by constraining the behaviour of their choice mechanisms and epistemic preference relations. Our first representation theorem connects smooth kernel contractions with a novel class of epistemic preference relations. For our second representation theorem, we introduce the principle of symmetry of removal that relates relevance to epistemic choices. For the last theorem, we devise a novel class of smooth kernel contractions, that satisfy relevance, which are based on epistemic preference relations that capture the principle of symmetry of removal.