The Logic RM3
- A Dialethic Logic of Paradox (but better than LP)
- Three-valued logic -
true (T)
and both (B)
and false (F)
- The designated values are
true (T)
and both (B)
- Connectives - classical plus ...
| φ
| ψ
|
| ¬φ
| φ∧ψ
| φ∨ψ
| φ→ψ
| φ↔ψ
|
|
| T
| B
|
|
| B
| T
| F
| F
|
| B
| T
|
| B
| B
| T
| T
| F
|
| B
| B
|
|
| B
| B
| B
| B
|
| B
| F
|
|
| F
| B
| F
| F
|
| F
| B
|
|
| F
| B
| T
| F
|
- Interpretation, models, and logical consequence as for
classical FOL
- Modus ponens works ... φ, φ → ψ ⊨ ψ ... but ...
Modus tollendo ponens fails ... ¬φ, φ ∨ ψ ⊭ ψ
- Some theorems of classical logic are not theorems of RM3