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 studying because you no longer use Kripke Semantics but instead use something more along the line of Rudolf Carnap's definition for necessitation "□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:
- ◇ = ¬□¬
- □A → A
- A → ◇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!