The "Standard" System of Deontic Logic

• [Hilpinen, 1981, pages 13-15]

Notes

Hilpinen alleges that most formal Deontic sytems include this system. This gives it some claim to being the "Standard" system.

This system uses a modality "O" where Op is taken as meaning p is Obligitory

Based on

• PC
  • Modus Ponens for >
  • Uniform substitution
• Axioms (Following the numbering of Halpinen):
  • D1: Op > ~O~p
  • D2: O(p&q) == (Op & Oq)
  • D3: O(p+~p)

D2 can be replaced by O(p>q) > (Op>Oq) [This axiom is really modal logics Axiom K, with O standing in for L], and one gets the same system.

Basis for

Many systems that I don't know enough to categorize yet.

Compare with

• Deontic (von Wright, 1951)
• Deontic (von Wright, 1956)
• Deontic (von Wright, 1965)
• Deontik (Mally)

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This page was last modified on January 24th, 2007