Non-prioritized Kernel Revision

Abstract Kernel contraction, introduced by Sven Ove Hansson, is a fundamental method for withdrawing information from belief bases. Through the Levi Identity —which defines revision in terms of contraction— kernel contraction also induces the corresponding revision operator known as kernel revision. Recent work has proposed a non-prioritized variant of kernel contraction which, unlike its classical counterpart, may violate the Success postulate, and thereby permits some non-tautological beliefs to be protected from removal. This article develops a corresponding notion of non-prioritized kernel revision. Building on the machinery of classical kernel revision and non-prioritized kernel contraction, we define a revision mechanism that need not always incorporate incoming evidence. The proposal is given both a constructive formulation, via a generalized Levi Identity, and an axiomatic (postulational) characterization. Finally, we analyse its epistemic impact by showing how non-prioritized kernel revision can weaken or reinforce the degree of firmness of selected beliefs within a belief base, and how these effects can accumulate under iteration, eventually yielding endorsement of the epistemic input and de-endorsement of its negation.