1 / 18

Rules for Predicate Logic

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. Rules for Predicate Logic. The system for predicate logic in this course is quite simple.

salazarcurtis
Download Presentation

Rules for Predicate Logic

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related