Tutorial Contents Tutorial Five: Predicate Calculus: Tableaux - The $xj rule - Bad Mistakes and Technical Mistakes - Ticking - Finished Tableaux - Sequents - Soundness and Completeness - Proof of a syntactic sequent: example
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Exercise 5.3

 

1

Can the $xj rule be applied in the following cases? If it can, what would the result be?
  (i)

"x[FxaGx]
$zFz

  (ii)

[$xFx$yGy]

  (iii)

2

Each of the following is a tableau which consists, so far, of just one formula. What rule, if any, can be applied to the formula, and with what result? Note that there is only ever at most one rule which can be applied.
  (i) "x[GxaHxa]
  (ii) [$xGxa"yFy]
  (iii) [$xFxP]
  (iv) $x"y[FxRyax]
  (v) "x"y"z[[RxaRyb]Sxyz]]
  (vi) "x"y"z[[RxyRyz]Sxyz]]

 

 

 

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