Weak classical Deontic Logics

Weak classical Deontic Logics

I am writing a paper at the moment and an area of Deontic Logic has
cropped up in it. I know very little about the area and I was wondering if
people could give me opinions on the axiomatic system that I want to use
to for my paper.
I want to keep the system as weak as possible so as to avoid things like
the Good Samaritan paradox or Chisholm's Paradox, so I want to keep my
logic strictly classical, ie. no stronger than the base system $K$. After
doing some searching on the internet, I got the impression that anything
weaker than $K$ isn't really worth stuying because you no longer use
Kripke Semantics but instead use something more along the line of Rudolf
Carnap's definition for necessitation "$\Box P$ is true iff $P$ is true in
all possible worlds". I also got the impression that Carnap's definition
was somewhat flawed but I couldn't find out why. Is this true? I'd be
greatly appreciative if someone could shed light on this and if/why
Carnap's definition is indeed flawed.
The system of axioms that I want to use is:
$\Diamond = \neg \Box \neg$
$\Box A \rightarrow A$
$A \rightarrow \Diamond A$
If anybody knows of any existing material on this system that would be
great. Also, if people have any other comments on the selection of the
above axioms that'd be great too. The axioms are for designing rule
systems so I need the logic to contain rules for "must do then do" and "if
do then it is allowed". Thanks!