System S7⁰

[Hughes and Cresswell, 1996]

Notes

Based on

The system S7⁰ is S3⁰ plus the axiom MMp

The system S7⁰ is therefore:

• Definitions
  • ?
• Rules
  • Uniform substitution (US)
  • Strict detachment (MP=>)
  • Adjunction (given a, b, return a&b) (AD)
  • substitution of strict equivalents. (EQS)
• Axioms
  • M1: (p&q)=>(q&p)
  • M2: (p&q)=>p
  • M3: ((p&q)&r)=>(p&(q&r))
  • M4: p=>(p&p)
  • M5: ((p=>q)&(q=>r))=>(p=>r)
  • M8: (p=>q)=>(Mp=>Mq)
  • S: MMp

[Hughes and Cresswell, 1996, p354]

Basis for

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This page was last modified on January 24th, 2007