Ernst Mally's Deontik (Deontic) Logic System.

[Hilpinen, 1981, pages 1-6]

Notes

This system was published by Ernst Mally in 1926 in his Monograph "Grundgesetze des Sollens: Elemente der Logik des Willens". It has the distinction of being the first formal axiomatic Deontic logic I can find.

It also has the unfortunate characteristic of being wrong. It is wrong in the sense that it (unknown to him) reduces to the Trivial Modal Logic where Lp==p and Mp==p. [Hilpinen, 1981, page 5]

This system uses a modality "O", where Op is taken as meaning p is something that Ought to be done.

Based on

• PC
  • Modus Ponens
  • Uniform substitution
• Constants
  • u: Unconditionally obligatory
  • n: A state of affairs incompatible with u
  • w: That which is the case.
  • m: That which is not the case
• Axioms
  • A1: [ (p > Oq) & (q > r) ] > (p > Or)
  • A2: [ (p > Oq) & (p > Or) ] > (p > O (q & r) )
  • A3: [ (p > Oq) == O(p > q)
  • A4: exists (u, Ou)
  • A5: ~(u > On), Hilpinen gives this as ~(u > O~u)

Basis for

Nothing... It has serious problems as a Deontic logic.

Compare with

• Deontic ("Standard")
• Deontic (von Wright, 1951)
• Deontic (von Wright, 1956)
• Deontic (von Wright, 1965)

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