ABSTRACT. This paper develops a logic programming language, ASP$^\text{EP}$, that extends answer set programming language with a new epistemic operator $\succcurlyeq_x$ where $x\in\{\sharp,\supseteq\}$. The operator are used between two literals in rules bodies, and thus allows for the representation of introspections of preferences in the presence of multiple belief sets: $G\succcurlyeq_\sharp F$ expresses that $G$ is preferred to $F$ by the cardinality of the sets\ignore{ which can be read as \emph{$G$ is more possible than $F$}}, and $G\succcurlyeq_\supseteq F$ expresses $G$ is preferred to $F$ by the set-theoretic inclusion\ignore{ which can be read as \emph{$G$ is true whenever $F$ is true}}. We define the semantics of ASP$^\text{EP}$, explore the relation to the languages of strong introspections, give an algorithm for computing solutions of ASP$^\text{EP}$ programs, and study the applications of ASP$^\text{EP}$ by modeling the Monty Hall problem and the principle of majority.