Dialetheic Logic

• Paraconsistency
  • The world is full of contradictions
  • A paraconsistent logic does not derive everything from contradictory axioms.

• A dialetheic logic
  • Three-valued logic - formulae are true (T) xor false (F) xor both (B)
  • Is paraconsistent
  • ⟦φ⟧ = TV means that φ has the truth value TV (T or B or F)

• Examples
  • "This sentence is false"
  • Russell's Paradox
  • A belief system can be a religion and not a religion
  • Actions can be both legal and illegal

• Interpretation
  • Interpretation, models, and logical consequence as for classical FOL
  • The designated values are true (T) and both (B)