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Trees

This guide explores the construction of trees in predicate logic using established logical rules. It illustrates various rules such as universal quantifiers, existential quantifiers, and implications, demonstrating how to build trees systematically. By breaking down complex logical expressions into simpler components, readers will gain a deeper understanding of predicate logic. The guide includes examples of tree constructions and proofs that can be applied to solve logical problems effectively. Ideal for students and enthusiasts of logic and reasoning.

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Trees

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  1. Trees Trees for predicate logic can be constructed using the predicate logic rules.

  2. Trees #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx)

  3. Trees 1 #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx) $x(Bx>Vx)

  4. Trees 1 2 #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx) $x(Bx>Vx) Ba&Ma DO #O FIRST!

  5. Trees 1 2 3 4 #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx) $x(Bx>Vx) Ba&Ma Ma>-Va Ba>Va

  6. Trees 1 2 3 4 5 #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx) $x(Bx>Vx) Ba&Ma Ma>-Va Ba>Va Ba Ma

  7. Trees 1 2 3 4 5 6 #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx) $x(Bx>Vx) Ba&Ma Ma>-Va Ba>Va Ba Ma -Ma -Va *

  8. Trees 1 2 3 4 5 6 7 #x(Bx&Mx) $x(Mx>-Vx) -$x(Bx>Vx) #x(Bx&Mx) $x(Mx>-Vx) --$x(Bx>Vx) $x(Bx>Vx) Ba&Ma Ma>-Va Ba>Va Ba Ma -Ma -Va * -Ba Va * *

  9. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A -#x(Sx&Ex) GOAL

  10. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA ?&-? ?,? &I -#x(Sx&Ex) 3-? -I

  11. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA 4) Sa&Ea 3 #O ?&-? ?,? &I -#x(Sx&Ex) 3-? -I DO #O FIRST.

  12. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA 4) Sa&Ea 3 #O 5) Sa>Ia 1 $O 6) Ia>-Ea 2 $O ?&-? ?,? &I -#x(Sx&Ex) 3-? -I

  13. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA 4) Sa&Ea 3 #O 5) Sa>Ia 1 $O 6) Ia>-Ea 2 $O 7) Sa 4 &O 8) Ea 4 &O ?&-? ?,? &I -#x(Sx&Ex) 3-? -I

  14. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA 4) Sa&Ea 3 #O 5) Sa>Ia 1 $O 6) Ia>-Ea 2 $O 7) Sa 4 &O 8) Ea 4 &O 9) Ia 5,7 >O 10) -Ea 6,9 >O ?&-? ?,? &I -#x(Sx&Ex) 3-? -I

  15. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA 4) Sa&Ea 3 #O 5) Sa>Ia 1 $O 6) Ia>-Ea 2 $O 7) Sa 4 &O 8) Ea 4 &O 9) Ia 5,7 >O 10) -Ea 6,9 >O 11) Ea&-Ea 8,10 &I -#x(Sx&Ex) 3-11 -I

  16. Another Proof 1) $x(Sx>Ix) A 2) $x(Ix>-Ex) A 3) #x(Sx&Ex) PA 4) Sa&Ea 3 #O 5) Sa>Ia 1 $O 6) Ia>-Ea 2 $O 7) Sa 4 &O 8) Ea 4 &O 9) Ia 5,7 >O 10) -Ea 6,9 >O 11) Ea&-Ea 8,10 &I -#x(Sx&Ex) 3-11 -I Now try this one with a tree. For more click here

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