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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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