A Routley-Meyer semantics for truth-preserving and well-determined Lukasiewicz 3-valued logics

Lukasiewicz 3-valued logic L3 is often understood as the set of all valid formulas according to Lukasiewicz 3-valued matrices ML3. Following Wojcicki, in addition, we shall consider two alternative interpretations of L3: 'truth-preserving' L3a and 'well-determined' L3b defined by two different consequence relations on the 3-valued matrices ML3. The aim of this article is to provide a Routley-Meyer ternary semantics for each one of these three versions of Lukasiewicz 3-valued logic: L3, L3a and L3b.