rules for predicate logic
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Rules for Predicate Logic
The system for predicate logic in this courseis quite simple.
We will learn 3 rules which can be used for proofsand also with trees.
Rules for Predicate Logic
The system for predicate logic in this courseis quite simple.
We will learn 3 rules which can be used for proofsand also with trees.
$O Universal Out#O Existential Out
QE Quantifier Exchange
There are no quantifier In rules.
Taking an Instance
$x(Px>Qx)
Taking an Instance
$x(Px>Qx)
Pa>Qa
Taking an Instance
$x(Px>Qx)
Pa>Qa
To take an instance:1. Remove the quantifier.
Px>Qx2. Substitute the same name (a-w) for each occurrence of the variable.
Pa>Qa
Taking an Instance
$x(Px>Qx)
Pa>Qa
To take an instance:1. Remove the quantifier.
Px>Qx2. Substitute the same name (a-w) for each occurrence of the variable.
Pa>Qa
Pa>Qx WRONGPa>Qb WRONGPb>Qb RIGHT
Taking an Instance
$x(Px>Qx)
Pa>Qa
To take an instance:1. Remove the quantifier.
Px>Qx2. Substitute the same name (a-w) for each occurrence of the variable.
Pa>QaThis should be familiar from algebra. x+7=7+x
3+7=7+3 RIGHT3+7=7+4 WRONG
Universal Out
1) Ba A2) Da A
-$x(Dx>-Bx) GOAL
Universal Out
1) Ba A2) Da A3) $x(Dx>-Bx) PA
?&-? ?,? &I -$x(Dx>-Bx) 3-? -I
Universal Out
1) Ba A2) Da A3) $x(Dx>-Bx) PA4) Da>-Ba 3 $O
?&-? ?,? &I -$x(Dx>-Bx) 3-? -I
Universal Out
1) Ba A2) Da A3) $x(Dx>-Bx) PA4) Da>-Ba 3 $O
?&-? ?,? &I -$x(Dx>-Bx) 3-? -I
$O Rule
$xAxAn
Universal Out
1) Ba A2) Da A3) $x(Dx>-Bx) PA4) Da>-Ba 3 $O5) -Ba 4,2 >O ?&-? ?,? &I -$x(Dx>-Bx) 3-? -I
Universal Out
1) Ba A2) Da A3) $x(Dx>-Bx) PA4) Da>-Ba 3 $O5) -Ba 4,2 >O6) Ba&-Ba 1,5 &I7) -$x(Dx>-Bx) 3-6 -I
Universal Out
1) Gj A2) $x(Gx>Rx) A3) $x(Rx>Ux) A
Uj GOAL
Universal Out
1) Gj A2) $x(Gx>Rx) A3) $x(Rx>Ux) A4) Gj>Rj 2 $O
Uj GOAL
Universal Out
1) Gj A2) $x(Gx>Rx) A3) $x(Rx>Ux) A4) Gj>Rj 2 $O5) Rj>Uj 3 $O
Uj GOAL
Universal Out
1) Gj A2) $x(Gx>Rx) A3) $x(Rx>Ux) A4) Gj>Rj 2 $O5) Rj>Uj 3 $O6) Rj 4,1 >O Uj GOAL
Universal Out
1) Gj A2) $x(Gx>Rx) A3) $x(Rx>Ux) A4) Gj>Rj 2 $O5) Rj>Uj 3 $O6) Rj 4,1 >O7) Uj 5,6 >O
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