The author email addresses were previously assigned to the incorrect authors in this paper. This error has now been corrected online https://doi.org/10.1093/logcom/exaa067.

Abstract The paper presents semantically complete Hilbert-style systems for some variants of common sense modal predicate logic proposed by van Benthem and further developed by Seligman. The paper also investigates frame definability in the logics and shows what axiom schema is canonical in the logics. In addition to these semantic investigations on the logics, the paper provides the sequent calculi for some of the logics which enjoy cut elimination theorem.