System E2⁰

[Hughes and Cresswell, 1996]

Based on

[Hughes and Cresswell, 1996, p363] Say E2 can be axiomitized by PC, T, K, US, MP, and R* They also say (P 364) that E2-0 is E2 - T. *SO*

The system E2⁰ (E2 superscript 0) is

• Rules
  • Uniform Substitution
  • Modus Ponens
  • R* Given A>B, Produce LA>LB
• Axioms
  • PC
  • K: L(p>q)>(Lp>Lq)

Basis for

E2⁰ + Lp>p [Axiom T] is E2 [Hughes and Cresswell, 1996, p364]

E2⁰ + E3 [L(p>q)>L(Lp>Lq)] is E3⁰ [Hughes and Cresswell, 1996, p364]

E2⁰ + MMp [Axiom S] is E6⁰ [Hughes and Cresswell, 1996, p364]

E2⁰ + Mp is E+ [Hughes and Cresswell, 1996, p364]

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This page was last modified on October 6th, 2005