What motivations might one have for choosing a Strong-K3 interpretation in sentential logic (over other three-valued logics).
I'm looking at the functional outputs of each of the connectives on L3, K3 and B3. I know that L3 and K3 are both normal and uniform. So, in each case they uphold our intuitions about classical logic in a fortunate way, so I am wondering what other factors might be crucial in the decision making process given that the two are equivalent in this regard. I know that L3 is only slightly variant from K3 given in terms of the outputs of its connectives (I'm thinking specifically of the conditional), and that the nature of the conditional on L3 is favourable to L3, so why might someone go for K3?
As far as I know, the greatest advantage of K3 is that it preserves the classical definition of the material conditional in classical two-valued logic; (P $\supset $ Q) $\equiv$ (~P $\lor $ Q).
However, I don't see any real benefit here. I believe that the apparent identity of (P $\supset $ Q) and (~P $\lor $ Q) is a coincidence, an artifact of the limited set of 2-valued logical connectives. It does not convey any useful insight into the nature of logical implication in the three valued case and may actually be misleading.