Full Idea
The Barcan formula corresponds to anti-monotonicity, and the Converse Barcan formula corresponds to monotonicity.
Clarification
If a proof is 'monotonic', nothing new can undermine it
Gist of Idea
The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity
Source
M Fitting/R Mendelsohn (First-Order Modal Logic [1998], 6.3)
Book Reference
Fitting,M/Mendelsohn,R: 'First-Order Modal Logic' [Synthese 1998], p.136
Related Ideas
Idea 13728 The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
Idea 4810 Valid deduction is monotonic - that is, it remains valid if further premises are added [Psillos]
Idea 13525 Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]