Semantics for sub-intuitionistic logics
Joost J. Joosten

Abstract:
This paper exposes semantics for various sub-intuitionistic logics. The semantics transparently reflect how assumptions on the epistemic and cognitive abilities of the creative subject influences the underlying logic.  One of these semantics is used to obtain a lower bound on the length of proofs of certain intuitionistic tautologies.

Keywords: Intuitionistic logic;  sub-intuitionistic logics;  lower bounds;  proof complexity;  Kripke semantics