CS 486 Applied Logic Assignment #2
Spring 1997 Due Date: Thurs., 2/6/97

Reading:
Estimated time: less than 5 hours

1. Write up parts of the exercise on Smullyan p.24.
   1. part (3)
   2. part (5)
   3. part (6)
2. Give a tableau proof for Pierce's law from Assignment 1.
3. Solve exercise 3 in Smullyan p.30.
4. A Hilbert-style proof is a sequence of formulas such that each is either an axiom for follows from previous , by a rule of inference.

   Consider a propositional calculus whose formulas include the constant , propositional variables and the compound formulas for formulas.

   Take as axioms these 3 formulas
   Axiom 1
   Axiom 2
   Axiom 3
   As the inference rules take
   Modus Ponens
   Substitution
   We mean by a formula which contains propositional variable and by we mean the formula obtained by replacing each occurrence of in by the formula .

   1. Prove
   2. Try to prove Pierce's law, failing that show some interesting formula you managed to prove in your attempt. (Pierce's law is provable from these axioms.)

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