Relative Contingency and Bimodality

In §2 and §3 it is proved that there exists a one-one mapping between a minimal contingential logic extended with a suitable axiom for a propositional constant τ , namedK∆τw, and a logic of necessityKjτw whose language contains j and τ . The form of the proposed translation aims at giving a solution to a problem which was left open in a preceding paper. It §4 it is shown that the presence of τ in the language of K∆τw allows for the definition, in terms of the non-contingency operator ∆, not only of j but of a second necessity operator O. It is observed that this fact opens the road to an investigation of the τ -free multimodal fragments of K∆τw. Mathematics Subject Classification (2010). 03B45.