Subintuitionistic Logics with Kripke Models
Dick de Jongh, Fatemeh Shirmohammadzadeh Maleki

Abstract:
The subintuitionistic logics introduced by Corsi and Restall are developed in a uniform manner. Proof systems are given for derivations without and with assumptions. The results are applied to give conservation theorems for intuitionistic logic IPC over Corsi's system F. For  Visser's basic logic strong completeness is proved and additional conservation results are obtained.

Keywords: intuitionistic logic, subintuitionistic logic, basic logic, modus ponens, completeness, conservativity