出版社：Philosophy Department, University of Melbourne
摘要：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 LRA [16]. We call our logic LIRA (Logic of Internal Rational Agency). In contrast to LRA, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramnko's bi- facial truth logic 42]. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use 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 LRA definable by . Means of four valued Kripke -style semantics and show that, due to two negations (as well as their combination) of LRA, two more possibility operators for LRA can be defined. Then we slightly modify all these modalities to be appropriate for LIRA. Finally, we formalize all the truth- functional n-ary extensions of the negation fragment of LIRA (including LIRA itself) as well as their basic modal extension via linear type natural deduction systems.
其他摘要：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 extbf{LRA} te{LRA}. We call our logic $ f LIRA$ (Logic of Internal Rational Agency). In contrast to extbf{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 te{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use extbf{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 extbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of extbf{LRA}, two more possibility operators for extbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for $ f LIRA$. Finally, we formalize all the truth-functional $ n $-ary extensions of the negation fragment of $ f LIRA$ (including $ f LIRA$ itself) as well as their basic modal extension via linear-type natural deduction systems.
关键词：Logic of rational agent; logic of internal rational agency; four-valued logic; logic of generalized truth values; modal logic; natural deduction; correspondence analysis.
