Relationships between Connectives in Three-Valued Logics

In the literature, several 3-valued logics can be found. They differ from a syntactic and proof-theoretic point of view as well as on the interpretation given to the third value, which, nevertheless, often assumes an epistemic flavor. This paper is a preliminary step in the attempt to clarify the situation of three-valued logics from a semantic point of view. Logical operations on three-valued functions are studied and their relationships put forward. They are also linked to existing logics, pointing out their usage and interpretation of the third value. In the long range, the idea is to be able to relate as many three-valued calculi as possible to classes of applications where the third truth-value is naturally interpreted, and the basic connectives make full sense.