What does this negation on both sides of K mean: A = ¬ K ¬

Question

What does this negation on both sides of K mean: (A = ¬K¬) ?

I'm not sure if it's a typo, as there are some errors in this paper (Hong et al.).

Hong, Zhi Ling, and Mei Hong Wu. "Constrained Epistemic Extension on Agent Knowledge Acquisition." Advanced Materials Research 651 (2013): 943-948.

The paper is on constrained default logic. Here's the excerpt:

Definition 2. A constrained epistemic default logic theory (C-EDL) is a triple $<D,W,C>$ , where $W$ is a set of consistent formulas of first-order logic (the facts) which has the form $K\alpha$, $D$ is a set of $\alpha$ default rules to make $W$ complete and $C$ called constrained sets. A default is a rule of the form $K\alpha: A\beta,\ldots, A\beta\; /\; B\omega \;(n\ge 1)$, where $K$, $B$ are modality word, $A = \lnot K \lnot$ , and $\alpha, \beta, \omega$ are formulas of propositional logic $L$, $\alpha$ is the prerequisite of the default $D$, $\beta$ is the justification of the default $D$ and $\omega$ is the consequent of the default $D$.

Answer 1

See Epistemic Logic.

If your $K$ correspond to the epistemic operator $K_c$ such that :

$K_c \alpha$ reads "Agent $c$ knows $\alpha$"

then $\lnot K_c \lnot$ is simply : "Agent $c$ does not know not-$\alpha$".

Thus, $A := \lnot K \lnot$ is only an abbreviation.

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Note

Like in "standard" Modal Logic, where possibility can be defined in terms as necessity :

$◊A = \lnot □ \lnot A$.