The Logic of Internal Rational Agent

In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent textbf{LRA} cite{LRA}. We call our logic $ bf LIRA$. In contrast to textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic cite{ZS}. This logic may be useful in a situation when according to an agent's point of view her/his reasoning is rational, while from the external one it might be not the case. One may use textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations of textbf{LRA}, two more possibility operators for textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for $bf LIRA$. Finally, we formalize all the truth-functional $ n $-ary extensions of the negation fragment of $bf LIRA$ as well as their basic modal extension via linear-type natural deduction systems.