The Logic Ł3

• A Hollow Logic (with a Gap)
  • Three-valued logic - true (T) and neither (N) and false (F)
  • The designated value is true (T)

• Connectives - classical plus ...

  φ	ψ		¬φ	φ∧ψ	φ∨ψ	φ→ψ	φ↔ψ
  T	N			N	T	N	N
  N	T		N	N	T	T	N
  N	N			N	N	T	T
  N	F			F	N	N	N
  F	N			F	N	T	N

• Interpretation, models, and logical consequence as for classical FOL
  • Some theorems of classical logic are not theorems of Ł3