existential out the existential out rule is dangerous

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Existential Out The Existential Out rule is DANGEROUS.

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Page 1: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

Page 2: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

#x(Bx&Mx) Some BUNNIES are MARRIED. Ba&Ma Anne is a married bunny.

INVALID!

Page 3: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

#x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny.

BARELY OKProvided that n

is a brand new name.

Page 4: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

#x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny.

BARELY OKn is like a new

social security number.

Page 5: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

#x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny.

BARELY OKn is like a new

social security number.

Page 6: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

#x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny.

WATCH OUT!There are extra deductionsfor violating the restriction

on the EO rule.

Page 7: Existential Out The Existential Out rule is DANGEROUS

Existential Out

The Existential Out rule is DANGEROUS.

#x(Bx&Mx) Some BUNNIES are MARRIED. Bn&Mn n is a married bunny.

WATCH OUT!There are extra deductionsfor violating the restriction

on the EO rule.

The EO Restriction:The letter chosen for the instance must

be new to the proof.

Page 8: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A

-$x(Bx>Vx) GOAL

Page 9: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 10: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 11: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 12: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O6) Ba>Va 3 $O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 13: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O6) Ba>Va 3 $O7) Ba 4 &O8) Ma 4 &O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 14: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O6) Ba>Va 3 $O7) Ba 4 &O8) Ma 4 &O9) Va 6,7 >O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 15: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O6) Ba>Va 3 $O7) Ba 4 &O8) Ma 4 &O9) Va 6,7 >O10) -Va 5,8 >O ?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 16: Existential Out The Existential Out rule is DANGEROUS

Sample Proof

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O6) Ba>Va 3 $O7) Ba 4 &O8) Ma 4 &O9) Va 6,7 >O10) -Va 5,8 >O11) Va&-Va 9,10 &I -$x(Bx>Vx) 3-11 -I

Page 17: Existential Out The Existential Out rule is DANGEROUS

EO Strategy

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 18: Existential Out The Existential Out rule is DANGEROUS

EO Strategy

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba>Va 3 $O5) Ma>-Va 2 $O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 19: Existential Out The Existential Out rule is DANGEROUS

EO Strategy

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba>Va 3 $O5) Ma>-Va 2 $O6) Ba&Ma 1 #O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

Page 20: Existential Out The Existential Out rule is DANGEROUS

EO Strategy

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba>Va 3 $O5) Ma>-Va 2 $O6) Ba&Ma 1 #O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

#O Restriction VIOLATED!

Page 21: Existential Out The Existential Out rule is DANGEROUS

EO Strategy

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba>Va 3 $O5) Ma>-Va 2 $O6) Ba&Ma 1 #O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

#O Restriction VIOLATED!ADVICE: DO #O FIRST!

Page 22: Existential Out The Existential Out rule is DANGEROUS

EO Strategy

1) #x(Bx&Mx) A2) $x(Mx>-Vx) A3) $x(Bx>Vx) PA4) Ba&Ma 1 #O5) Ma>-Va 2 $O6) Ba>Va 3 $O

?&-? ?,? &I -$x(Bx>Vx) 3-? -I

#O Restriction VIOLATED!ADVICE: DO #O FIRST!

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