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Rules for Predicate Logic

Rules for Predicate Logic

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Rules for Predicate Logic

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  1. Rules for Predicate Logic The system for predicate logic in this course is quite simple. We will learn 3 rules which can be used for proofs and also with trees.

  2. Rules for Predicate Logic The system for predicate logic in this course is quite simple. We will learn 3 rules which can be used for proofs and also with trees. $O Universal Out #O Existential Out QE Quantifier Exchange There are no quantifier In rules.

  3. Taking an Instance $x(Px>Qx)

  4. Taking an Instance $x(Px>Qx) Pa>Qa

  5. Taking an Instance $x(Px>Qx) Pa>Qa To take an instance: 1. Remove the quantifier. Px>Qx 2. Substitute the same name (a-w) for each occurrence of the variable. Pa>Qa

  6. Taking an Instance $x(Px>Qx) Pa>Qa To take an instance: 1. Remove the quantifier. Px>Qx 2. Substitute the same name (a-w) for each occurrence of the variable. Pa>Qa Pa>Qx WRONG Pa>Qb WRONG Pb>Qb RIGHT

  7. Taking an Instance $x(Px>Qx) Pa>Qa To take an instance: 1. Remove the quantifier. Px>Qx 2. Substitute the same name (a-w) for each occurrence of the variable. Pa>Qa This should be familiar from algebra. x+7=7+x 3+7=7+3 RIGHT 3+7=7+4 WRONG

  8. Universal Out 1) Ba A 2) Da A -$x(Dx>-Bx) GOAL

  9. Universal Out 1) Ba A 2) Da A 3) $x(Dx>-Bx) PA ?&-? ?,? &I -$x(Dx>-Bx) 3-? -I

  10. Universal Out 1) Ba A 2) Da A 3) $x(Dx>-Bx) PA 4) Da>-Ba 3 $O ?&-? ?,? &I -$x(Dx>-Bx) 3-? -I

  11. Universal Out 1) Ba A 2) Da A 3) $x(Dx>-Bx) PA 4) Da>-Ba 3 $O ?&-? ?,? &I -$x(Dx>-Bx) 3-? -I $O Rule $xAx An

  12. Universal Out 1) Ba A 2) Da A 3) $x(Dx>-Bx) PA 4) Da>-Ba 3 $O 5) -Ba 4,2 >O ?&-? ?,? &I -$x(Dx>-Bx) 3-? -I

  13. Universal Out 1) Ba A 2) Da A 3) $x(Dx>-Bx) PA 4) Da>-Ba 3 $O 5) -Ba 4,2 >O 6) Ba&-Ba 1,5 &I 7) -$x(Dx>-Bx) 3-6 -I

  14. Universal Out 1) Gj A 2) $x(Gx>Rx) A 3) $x(Rx>Ux) A Uj GOAL

  15. Universal Out 1) Gj A 2) $x(Gx>Rx) A 3) $x(Rx>Ux) A 4) Gj>Rj 2 $O Uj GOAL

  16. Universal Out 1) Gj A 2) $x(Gx>Rx) A 3) $x(Rx>Ux) A 4) Gj>Rj 2 $O 5) Rj>Uj 3 $O Uj GOAL

  17. Universal Out 1) Gj A 2) $x(Gx>Rx) A 3) $x(Rx>Ux) A 4) Gj>Rj 2 $O 5) Rj>Uj 3 $O 6) Rj 4,1 >O Uj GOAL

  18. Universal Out 1) Gj A 2) $x(Gx>Rx) A 3) $x(Rx>Ux) A 4) Gj>Rj 2 $O 5) Rj>Uj 3 $O 6) Rj 4,1 >O 7) Uj 5,6 >O For more click here