For questions related to symbolic logic, also known as mathematical logic. Topics might range from philosophical implications of metamathematical results to technical questions.
Questions tagged [symbolic-logic]
315 questions
4
votes
2 answers
What does the colon (:) mean in conjunction with material implication?
Errol E. Harris does an excellent job of explaining dialectical logic in Formal, Transcendental, and Dialectical Thinking, but in the section on formal logic, he assumes a familiarity with symbolic logic that I do not possess. While I have dug up…
Napoletano
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4
votes
2 answers
need some guidance for this easy symbolic logic question
Every dog and cat who is well trained is a good pet.
(F: a is a dog; G: a is a cat; H: a is well trained; I: a is a good pet.)
Here are my options:
a) ∀x((Fx∨Gx)∧Ix→Hx)
b) ∀x((Fx∨Gx)∧Hx→Ix)
c) ∀x((Fx∧Gx)∧Hx→Ix)
d) ∀x∀y(Fx∧Gy∧Hx→Ix)
For a) I…
user125535
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3
votes
1 answer
Help with formalization of argument (ignore premises) in FOL
I am trying to formalize the following argument:
Every Moral theory is equally valid.
There always can get a new moral theory from another one.
For something to be metaphysically real/exists it must be also definable
The definition of morality must…
Rieke
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2
votes
1 answer
In symbolic logic why (p->q) and (p->~q) don't contradict each other?
I am a beginner in symbolic logic and still mostly using intution to solve the problems. After spending some time trying to figure out why (p -> q) is true if p is false I've realized that this also means (p -> q) & ( p -> ~q) is not a…
WVrock
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2
votes
1 answer
What are the legal quantifier negation rules?
Is using Quantifier Negation to flip two quantifiers at once legal in symbolic logic?
Example:
~∀x∀y(Hhx & Hhy)
ƎxƎy~(Hhx & Hhy) 1 QN
Or do I need to do this in 2 steps?
Example:
~∀x∀y(Hhx & Hhy)
Ǝx~∀y(Hhx & Hhy) 1 QN
ƎxƎy~(Hhx & Hhy) 2…
Lily
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2
votes
1 answer
If it is not all wrong, then I have a problem in line 25. Can anybody help, please?
∃x ∃y (Cube(x) ∧ Cube(y) ∧ ¬x = y ∧ ∀z (Cube(z) → (z = x ∨ z = y)))
a∃y (Cube(a) ∧ Cube(y) ∧ ¬a = y ∧ ∀z (Cube(z) → (z = a ∨ z = y)))
bCube(a) ∧ Cube(b) ∧ ¬a = b ∧ ∀z (Cube(z) → (z = a ∨ z = b))
Cube(a) ∧ Cube(b) ∧ ¬a = b ∧ Elim : 3
∀z…
Jens Elsinger
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2
votes
1 answer
How to express possession in predicate calculus
all! I was wondering if I could get help translating this phrase in to first order logic.
I'm trying to say: There exists a u such that u is Russian and there exists a b such that u shot b.
Would it be:
∃u(R(u)) /\ ∃b(Shot(u, b))
Or would it…
London Jennings
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2
votes
1 answer
can you express universal quantification ∀x(Px ≡ Qx) simply as Px ≡ Qx?
Is it permissible and normal to express the prop. ∀x(Px ≡ Qx) simply as Px ≡ Qx? That is, to treat the univ. quantifier as implicit if its scope is all the rest of the prop.?
Toothrot
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1
vote
3 answers
How should I use the propositional logic rules for → and ↔?
My question is how should I use the propositional logic rules for → and ↔ (although other rules may be required) to prove the following:
A → B, B → C ⊢ (AvB) → C
A ↔ B ⊢ ¬A ↔ ¬B
Please use the language of propositional logic.
Kiki
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1
vote
2 answers
Can anyone help me solve this (p → r) → (¬a v b), p → q, b → s, q → r, ¬a → s // (r v s)
I have been working almost three days on this problem and I can't to this answer:
(p → r) → (¬a v b)
p → q
b → s
q → r
¬a → s
// (r v s)
Joseph
- 11
- 1
0
votes
2 answers
What is the 'meaning' of an unassigned formula with free variables?
What does a variable refer to in a formula? If it is a free variable, it has no reference, yet it exists as an element of the formula.
In an unassigned formula, what is the semantic meaning of a variable occurrence? Or simply, do we need to perform…
Confused
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0
votes
3 answers
How to show disjunction can be expressed as a conditional
How to show that formula "A ∨ B" can be constructed from A and B using only the conditional connective (→).
Hu Cares
- 11
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0 answers
How to represent "apart from" formally?
While working on an argument over the last few days, I came to a point where I needed to formally render an "even if" sentence. Here and here, I found some good options, but I'm not sure I get the target conclusion using these translations.
So now I…
Kristian Berry
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0
votes
2 answers
Need help to inconsistency problem
I am using theThe Logic Book)
I need help to find the inconsistencies.
using SD
1.(E V F)=>(G & -I)
2.(G V F)=>I
3 -F=> E
I tried everything to show it
I think showing -I and I might do it
But deriving it has got me stumped
Any help would be…
larry mintz
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0
votes
1 answer
How do you express the following in symbolic logic?
If P is true, then Q is true. P being false or unknown says nothing about Q.
Instead of a truth table like this:
P : Q
0 : 0 = 1
0 : 1 = 1
1 : 0 = 0
1 : 1 = 1
You have a truth table like this:
P : Q
0 : 0 = ?
0 : 1 = ?
1 : 0 = 0
1 : 1 = 1
Or…
Abercrombie Dorfen
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