The Class of all 3-valued Implicative Expansions of Kleene?s Strong Logic Containing Anderson and Belnap's First Degree Entailment Logic.

We define all 3-valued implicative expansions of Kleene’s strong 3-valued matrix (with both only one and two designated values) verifying Anderson and Belnap’s First degree entailment logic, FDE. Then, the logics determined by each one of these implicative expansions are axiomatized by using a Belnap- Dunn ‘two-valued’ semantics. This semantics is ‘overdetermined’ in the case of two designated values and ‘underdetermined’ when there is only one.

Authors

• Gemma Robles

Keywords

• 3-valued logic
• Kleene’s strong 3-valued logic
• Belnap-Dunn ‘twovalued’ semantics
• First degree entailment logic FDE
• implicative logic