Logics of Non­actual Possible Worlds

Studies in Logic, Vol. 16, No. 6 (2023): 17–38                      PII: 1674­3202(2023)­06­0017­22

Jie Fan

Abstract. In Jia Chen (2020), a logic of strong possibility and weak necessity, which we call ‘logic of non­actual possible worlds’ here, is proposed and axiomatized over various frames. However, the completeness proof therein is quite complicated, which involves the use of copies of maximal consistent sets in the construction of the canonical model, among other considerations. In this paper, we demonstrate that the completeness of some systems thereof can be reduced to those of the familiar systems in the literature via translations, which builds a bridge among these systems. We also explore the frame definability of such a logic.