Belnap's First Degree Entailment (FDE) Logic

• A hollow dialetheic logic
  • Four-valued logic - true (T) and both (B) and neither (N) and false (F)
  • The designated values are true (T) and both (B)

• (Only 3) Connectives - classical plus ...

  φ ψ ¬φ φ∧ψ φ∨ψ B T B B T B B B B B N F T B F F B

  φ ψ ¬φ φ∧ψ φ∨ψ N T N N T N B F T N N N N N F F N

• Interpretation, models, and logical consequence as for classical FOL

• No conditional connective (→)
  • Only first-degree entailment between formulae
  • Cannot say a formulae follows from others
  • Not very useful! (to the undead in logic)