This essay shows that some recent work by George Weaver can be reformulated in an especially perspicuous way within the theory of closure systems. Closure theoretic generalizations of some theorems of Robert Goldblatt are presented. And, more generally, the relation between closure systems and the deducibility relations of Goldblatt is explored.
Norman M. Martin. Stephen Pollard. "Contractions of Closure Systems." Notre Dame J. Formal Logic 35 (1) 108 - 115, Winter 1994. https://doi.org/10.1305/ndjfl/1040609298