Reflexive-insensitive modal logics (Q2804478)

This is a very interesting paper. It proposes a semantical method to turn modal logics insensitive to reflexivity. The idea originated in the works of \textit{J. Marcos} [Bull. Sect. Log., Univ. Łódź, Dep. Log. 34, No. 1, 43--56 (2005; Zbl 1117.03305)] and \textit{C. Steinsvold} [Notre Dame J. Formal Logic 49, No. 4, 385--392 (2008; Zbl 1180.03017)], but the current paper seems to provide a more structural analysis of the subject.NEWLINENEWLINEThe semantic trick is based on an additional modal operator, which is rather intuitive and natural. Then, the authors show the completeness of this new modal logic with the new modality using the standard techniques (maximal consistent sets).NEWLINENEWLINEWhat I think the most important contribution of the paper is its study of the translation from normal modal logics to the reflexivity-insensitive logics. The reason why I found that part interesting is that it has potential to relate to many other many-valued logics by way of a syntactic translation.NEWLINENEWLINEFinally, it seems that there is an intrinsic relation between reflexivity-insensitivity and (a global interpretation of) negation, which still remains to be explored more in detail.