Semi-contraction is a withdrawal operation defined by Fermé in "On the logic of theory change: Contraction without recovery." In this paper we propose: (1) an axiomatic characterization of semi-contraction; (2) an alternative construction for semi-contraction based on semi-saturatable sets, inspired by Levi's saturatable sets; (3) a special kind of semi-contraction that satisfies the Lindström and Rabinowicz interpolation thesis.
"Semi-Contraction: Axioms and Construction." Notre Dame J. Formal Logic 39 (3) 332 - 345, Summer 1998. https://doi.org/10.1305/ndjfl/1039182250