Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

intro to logic > fol (first order logic) > Flashcards

fol (first order logic) Flashcards

1
Q

fol terms

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

examples of names in fol

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

what is an atomic sentence?

A

predicate + right number of names

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

variables of FOL

A

x,y,z,u,v,w

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

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

A

only cat

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

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

A

open formula. Dog(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

what is a sentence with no free variable?

A

closed formula. AxDog(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

what is a well formed formula (WFF)?

A

open and closed formulas

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

null quantification

A

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))

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

true or false: the universal quantifier distributes over &

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

true or false: the existential distibutes over &

A

false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

true or false: the existential distributes over the v

A

true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

true or false: the universal distributes over the v

A

false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

all quantifiers are widest scope

A

prenex normal form (PNF)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

what is DeMorgan’s for Quantifiers?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

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

A

true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

what is the abominable form?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

how do you say “All Ps are Q”?

A

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

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

how do you say “some Ps are Q”?

A

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

20
Q

how do you say “no Ps are Q”?

A

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

21
Q

how do you say “some Ps are not Q”?

A

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

22
Q

what is a vacuously true conditonal?

A

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

23
Q

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

A

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

24
Q

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

A

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

25
Q

what is a tautological equivalence?

A

equivalence that depends just on the truth-function connectives

26
Q

what does is mean for something to be “null”?

A

a quantifier that doesn’t bind any variables

27
Q

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

A

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

28
Q

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

A

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

29
Q

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

A

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

30
Q

translate the sentence into Aristotelian form: “some dogs don’t go to heaven”

A

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

31
Q

how do you translate a sentence into truth functional form?

A
  1. underline full scopes of quantifiers and atomic sentences
  2. replace identical underline strings of symbols w the same sentence letters
32
Q

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

A

~~P->P

33
Q

how do you place sentences using the delete rows method?

A
  1. make truth table
  2. FOL: delete what is impossible
  3. Logical: delete what is impossible
34
Q

what is an FO validity?

A

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

35
Q

what is a FO falsity?

A

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)

36
Q

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

A

fo falsity

37
Q

what guarantees a sentence is necessarily true?

A

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

38
Q

place the sentence in FOL: (a<b)->~(b<a)

A

logical truth

39
Q

how do you say “there are 2 distinct dogs”?

A

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

40
Q

what does it mean when “X is stronger than Y”?

A

X entails Y, but Y doesn’t entail X

41
Q

which is stronger: ExAy or AyEx?

A

ExAy is always stronger

42
Q

how do you say “at least n…”

A

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

43
Q

how do you say “at most n…”

A

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

44
Q

how do you say “exactly…” in the long way?

A

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

45
Q

how do you say “exactly” in the short way?

A

n existentials and 1 universal

46
Q
A

intro to logic (6 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions