**A Brief Overview**

Deontic logic is the study of the logical relationships among
propositions that assert that certain actions or states of affairs are
morally obligatory, morally permissible, morally right or morally
wrong. Mally developed the first such deontic logic. In his
monograph, *Grundgesetze des Sollens: Elemente der Logik des
Willens* (Graz: Leuschner & Lubensky, 1926), he presented
axioms for the notion ‘*p* ought to be the case’,
using the formal notation ‘!*p*’ to represent this
claim.

Unfortunately, one can derive from Mally's axioms the claim that
*p* ought to be if and only if *p* obtains (formally:
!*p* ≡ *p*). But, there are lots of
counterexamples to this result, for there are states of affairs that
obtain but which ought not to be, and there are states of affairs
which ought to be but which don't obtain.

For a more complete description of Mally's deontic logic, and some suggestions for how to repair it, see Gert-Jan Lokhorst's entry in the Stanford Encyclopedia of Philosophy:

Mally's Deontic LogicFor a complete introduction to deontic logic, see Paul McNamara's entry in the Stanford Encyclopedia of Philosophy:

Deontic LogicSee also D. Follesdal and R. Hilpinen's article, "Deontic Logic: An Introduction" (in