more from M Fitting/R Mendelsohn

### Single Idea 13729

#### [catalogued under 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula]

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]**