Title: Where relevance meets many-valued logic: six interesting systems and their  semantics.

Abstract:

In my doctoral dissertation, six new 4-valued logics of interest within the context of non-classical logics and in particular, logics in the family of relevance logic, were developed and studied in depth by means of different kinds of semantics. These logics are built upon implicative variants of Brady’s 4-valued matrix MBN4 which verify Routley and Meyer’s basic logic B.

On the one hand, Routley and Meyer’s logic B is an essential system among weak relevance logics due to the fact that it has traditionally served as a starting point to develop one of their most characteristic semantics: Routley-Meyer ternary relational semantics. On the other hand, Brady developed a central system among many-valued and relevance logics: the logic determined by the 4-valued matrix MBN4. This logic has been considered as the most suitable for relevant contexts involving inconsistent and incomplete information. As a matter of fact, Brady chose the label BN4 for his system because it contains Routley and Meyer’s basic logic B and has neither as one of its four characteristic truth-values.

The aim of this talk is twofold: (1) show the main properties of the six aforementioned systems and (2) explain the main features of the different semantics which they were endowed with.