Semantical analysis of weak Kleene logics

ABSTRACT This paper presents a semantical analysis of the Weak Kleene Logics and from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical consequence in – that is, we individuate necessary and sufficient conditions for a set Δ of formulas to follow from a set Γ in – and a characterisation result for logical consequence in . The paper also investigates two subsystems of and and discusses the relevance of the results against existing background. Finally, the paper discusses some issues related to Weak Kleene Logics – in particular, their philosophical interpretation and the reading of conjunction and disjunction – and points at some open issues.