CS486 Spring 1997

Lecture 6 Thursday, Feb. 6, 1997

• Reading: Smullyan Chapter IV for Thurs., February 13, 1997
• Summary of deductive systems: BDD, Tableau, Refinement, Gentzen, Hilbert (later we'll see Natural Deduction and Algebraic proofs)
• Tableau Gentzen Refinement Logic (RL)
  • Presentation varies (top_downvs. bottom_up)
  • Different specific systems
    
    single-goal vs. multiple goals
    cut vs. cut_free
    sets vs. sequences
• Theorem: Single-conclusion with Magic and Cut Tableau
  • Specify the task: to convert to
  • Idea for solution: simulate the multiple goal sequent proof
  • Sample cases:
    
    
  • Need for
  • Need for Cut: e.g. using the fact
• Deduction Theorem for Hilbert systems and Generalized Deduction Theorem
  • Define
  • Deduction Theorem
  • Generalization

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