  In this paper, by slightly generalizing the notion of 'proposition' in
'Propositional Logic and Modal Logic - A Connection via Relational Semantics'
by Shengyang Zhong, we propose a relational semantics of propositional language
with bottom, conjunction and imlication, which unifies the relational semantics
of intuitionistic logic, Visser's basic propositional logic and orthologic with
strict implication. We study the semantic and syntactic consequence relations
and prove the soundness and completeness theorems for eight propositional
logics.
