fol (first order logic)

Question 1

fol terms

Answer 1

all objects: constants and variables and names. lowercase. (pia, p, 1, x)

Question 2

examples of names in fol

Answer 2

pia, p, quinn
no numbers and no uppercase and no variables

Question 3

what is an atomic sentence?

Answer 3

predicate + right number of names

Question 4

variables of FOL

Answer 4

x,y,z,u,v,w

Question 5

what does Ex bound in this sentence: ExCat(X)Dog(x)

Answer 5

only cat

Question 6

what is it called when there is a free variable in the formula?

Answer 6

open formula. Dog(x)

Question 7

what is a sentence with no free variable?

Answer 7

closed formula. AxDog(x)

Question 8

what is a well formed formula (WFF)?

Answer 8

open and closed formulas

Question 9

null quantification

Answer 9

if there are no variables in the formula that the quantifier binds, then the quantifier can be put wide scope around formula
P&AxQ(x) ==> Ax(P&Q(x))

Question 10

true or false: the universal quantifier distributes over &

Answer 10

true
Ax(P(x)&Q(x)) ==> AxP(x)&AxQ(x)

Question 11

true or false: the existential distibutes over &

Answer 11

false

Question 12

true or false: the existential distributes over the v

Answer 12

true

Question 13

true or false: the universal distributes over the v

Answer 13

false

Question 14

all quantifiers are widest scope

Answer 14

prenex normal form (PNF)

Question 15

what is DeMorgan’s for Quantifiers?

Answer 15

~AxP(x) ==> Ex~P(x)
~ExP(x) ==> Ax~P(x)

Question 16

true or false: a quantifier can apply to an object with no name

Answer 16

true

Question 17

what is the abominable form?

Answer 17

Ex around conditional
Ex(P(x)->Q(x))

Question 18

how do you say “All Ps are Q”?

Answer 18

Ax(P(x)->Q(x))

Question 19

how do you say “some Ps are Q”?

Answer 19

Ex(P(x)&Q(x))

Question 20

how do you say “no Ps are Q”?

Answer 20

Ax(P(x)->~Q(x))

Question 21

how do you say “some Ps are not Q”?

Answer 21

Ex(P(x)&~Q(x))

Question 22

what is a vacuously true conditonal?

Answer 22

always true when the antecedent is false
- all unicorns are magical: true because there are no unicorns

Question 23

how do you translate this sentence? Ax(P(x)->Q(X))

Answer 23

~Ex(P(x)&~Q(x))

Question 24

how do you translate this sentence? ~Ax(P(x)->Q(x))

Answer 24

Ex(P(x)&~Q(x))

Question 25

what is a tautological equivalence?

Answer 25

equivalence that depends just on the truth-function connectives

Question 26

what does is mean for something to be "null"?

Answer 26

a quantifier that doesn't bind any variables

Question 27

translate the sentence into Aristotelian form: "all dogs go to heaven"

Answer 27

Ax(D(x)->H(x))

Question 28

translate the sentence into Aristotelian form: "some dogs go to heaven"

Answer 28

Ex(D(x)&H(x))

Question 29

translate the sentence into Aristotelian form: "no dogs go to heaven"

Answer 29

Ax(D(x)->~H(x))

Question 30

translate the sentence into Aristotelian form: "some dogs don't go to heaven"

Answer 30

Ex(D(x)&~H(x))

Question 31

how do you translate a sentence into truth functional form?

Answer 31

1. underline full scopes of quantifiers and atomic sentences 2. replace identical underline strings of symbols w the same sentence letters

Question 32

translate the sentence into TFF: ~~ExP(x)->ExP(x)

Answer 32

~~P->P

Question 33

how do you place sentences using the delete rows method?

Answer 33

1. make truth table 2. FOL: delete what is impossible 3. Logical: delete what is impossible

Question 34

what is an FO validity?

Answer 34

necessary truths of FOL - a=a - any logical truth that depends on =, A, E - any equivalence of FOL w biconditional between them

Question 35

what is a FO falsity?

Answer 35

necessary false in FOL - if the symbols A, E, or = ensure sentence is always false, then it is an FO falsity, not a taut-falsity - ~(p=p)

Question 36

place the sentence in FOL: ~(p=p)

Answer 36

fo falsity

Question 37

what guarantees a sentence is necessarily true?

Answer 37

truth functional form algorithm. tells what is doing the work in a sentence; the connectives or the quantifiers

Question 38

place the sentence in FOL: (a~(b

Answer 38

logical truth

Question 39

how do you say "there are 2 distinct dogs"?

Answer 39

ExEy(D(x)&D(y)&~(x=y))

Question 40

what does it mean when "X is stronger than Y"?

Answer 40

X entails Y, but Y doesn't entail X

Question 41

which is stronger: ExAy or AyEx?

Answer 41

ExAy is always stronger

Question 42

how do you say "at least n..."

Answer 42

n existential quantifiers (Ex) and enough distinctive clauses (~(x=y))

Question 43

how do you say "at most n..."

Answer 43

takes n+1 universal quantifiers (Ax) AxAyAz((D(x)&D(y)&D(z))->(x=y v x=z v y=z))

Question 44

how do you say "exactly..." in the long way?

Answer 44

combine "at most" and "At least" -n Es and n+1 As

Question 45

how do you say "exactly" in the short way?

Answer 45

n existentials and 1 universal