  Answer set programming (ASP) is an efficient problem-solving approach, which
has been strongly supported both scientifically and technologically by several
solvers, ongoing active research, and implementations in many different fields.
However, although researchers acknowledged long ago the necessity of epistemic
operators in the language of ASP for better introspective reasoning, this
research venue did not attract much attention until recently. Moreover, the
existing epistemic extensions of ASP in the literature are not widely approved
either, due to the fact that some propose unintended results even for some
simple acyclic epistemic programs, new unexpected results may possibly be
found, and more importantly, researchers have different reasonings for some
critical programs. To that end, Cabalar et al. have recently identified some
structural properties of epistemic programs to formally support a possible
semantics proposal of such programs and standardise their results. Nonetheless,
the soundness of these properties is still under debate, and they are not
widely accepted either by the ASP community. Thus, it seems that there is still
time to really understand the paradigm, have a mature formalism, and determine
the principles providing formal justification of their understandable models.
In this paper, we mainly focus on the existing semantics approaches, the
criteria that a satisfactory semantics is supposed to satisfy, and the ways to
improve them. We also extend some well-known propositions of here-and-there
logic (HT) into epistemic HT so as to reveal the real behaviour of programs.
Finally, we propose a slightly novel semantics for epistemic ASP, which can be
considered as a reflexive extension of Cabalar et al.'s recent formalism called
autoepistemic ASP.
