All Questions
Tagged with symbolic-logic predicate-logic
10
questions
1
vote
1
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59
views
Did Russell had something like the notion of domain in the sense defined now by mathematics textbooks?
The expression ∀x(ϕx → ψx) is supposed to mean that, in Russell's parlance, ϕx → ψx is true "for all values of x". However, what are those values that Russell is referring to?
At some point ...
- 8,363
2
votes
0
answers
139
views
Why not just give up on the idea of truth-functionality?
I understand that today only a minority of academics who are specialised in formal logic accept the horseshoe (aka "Classical Logic" or "First-Order Logic") as an accurate, or even ...
- 8,363
1
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0
answers
130
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Nested Quantifiers Proof - Logic
When I prove this: -∃x.P(x) ⊢ ∀x.-P(x) [True]
I did it like that:
∀x.-P(x) ⊢ ∀x.-P(x) because (negative ∃) -∃x.P(x) becomes ∀x.-P(x) so that we can say that it's true.
However, I didn't ...
- 11
0
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1
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64
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Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)
Does ∃x(Nx & ~Nx) contradiction itself?
Is there an error in my proof?
Thank you
- 3
-1
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2
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122
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3
votes
3
answers
288
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Is ¬(a = b) the same as (a ≠ b) in logic
Are these the same in predicate logic with identity:
¬ (a = b)
a ≠ b
I'm not quite sure whether they can be used interchangeably in proofs.
Any help would be great!
- 31
0
votes
1
answer
316
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Question about v-variants of variable assignments
In Full Predicate Calculus, some variable assignment q satisfies a disjunction under interpretation U if q satisfies one or both disjuncts under U, it satisfies a conjunction under interpretation U if ...
2
votes
2
answers
152
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Truth Value of Definite Descriptions
I'm currently studying definite descriptions in logic. My textbook postulates Bertrand Russell's view of definite descriptions, but I'm curious about other views as well (in the context of classical 2-...
- 317
0
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2
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208
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How does one tell if logical expressions are equivalent?
How do I check if these expressions are equivalent?
∀a,b [P(a) ∧ ¬R(a) ∧ S(b)] → G(a,b)
∀a [(P(a) ∧ ¬R(a)) → (∀b [S(b) → G(a,b)])]
- 11
5
votes
2
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609
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Is it possible to construct infinitely many non-equivalent formulas in predicate logic?
In the language of predicate logic with only identity and no predicates, function
symbols, or constants, is it possible to construct infinitely many non-equivalent
formulas?
