Subintuitionistic logics and the implications they prove

This is an investigation of the implications of IPC which remain provable when one weakens intuitionistic logic in various ways. The research is concerned with logics with Kripke models as introduced by G. Corsi in 1987, and others like G. Restall, Došen, Visser. This leads to conservativity results for IPC with regard to classes of implications in some of these logics. Moreover, similar results are reached for some weaker subintuitionistic systems with neighborhood models introduced by the authors in 2016. In addition, the relationship between two types of neighborhood models introduced in that work is clarified. This clarification leads also to modal companions for weaker logics.