System D (Lemmon and Scott)

• [Hughes and Cresswell, 1996]

Disambiguation

This is Lemmon and Scott's D. Zeeman's D = S4.3.1 (Sobociński) [Zeman, 1973, p245]

Notes

Characterized by serial frames. [Hughes and Cresswell, 1996, p45]

D (for Deontic) can be taken as Deontic logic, with Lx taken as "x is required", and Mx as "x is permitted" [Hughes and Cresswell, 1996, p43]

The name "D" is from Lemmon and Scott's 1977 Lemmon Notes. [Hughes and Cresswell, 1996, p50-fn8]

This system is also called KD

This system is also called Kη [Priest, 2001, p39]

Based on

Lemmon and Scott's D (named after "Deontic") is the result of K and the D axiom [Lp>Mp] [Hughes and Cresswell, 1996, p43]

In other words, D is:

• PC
  • Modus Ponens
  • Uniform substitution
• Rules
  • Necessitation
• Axioms
  • K: L(p>q)>(Lp>Lq)
  • D: Lp>Mp

Basis for

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This page was last modified on December 25th, 2006