In formal logic, both semantic entailment and the conditional connective are used to formalize the intuitive notion of implication. The former is defined in the meta-language of the logic, and the latter in the language of the logic. Their interaction determines to what extent the conditional connective relates to entailment as an implication should. This paper addresses this question for a number of related three-valued logics based on Kleene's strong truth tables, and defines a suitable implication for Partial Logic