All Questions
Tagged with symbolic-logic propositional-logic
17
questions
0
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39
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What is a definition, written in symbolic logic, for a person living nearby?
Students often need some axioms and/or definitions to play with in order to learn formal logic.
What is a definition of a neighbor written in the style of symbolic logic?
By neighbor, we mean a person ...
4
votes
1
answer
61
views
Can assumption in Hilbert style proof system be contradictory?
⊢（¬A→A）→A
I don't know how to solve this proof with the Axiom, Theorem and Inference rule in Hilbert-style proof system so I ask my classmate and he show me his answer. After viewing his proof, I was ...
- 41
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
5
votes
3
answers
2k
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What's the difference between "iff" and "=df"?
Just a quick question I stumbled upon from my readings.
When some philosophers write A ↔ B and others write A =df B, is there supposed to be a difference?
- 764
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2
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108
views
First use of exportation/importation in formal logic?
Who is the logician who first used exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r))?
Gödel used it in his 1939 Logic lecture, but it doesn’t seem to have been known from the Aristotelian ...
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-1
votes
2
answers
328
views
Is there a proof of exportation/importation from more obviously true implications such as Modus ponens?
Is there a proof of exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r)), from more obviously true implications such as the Modus ponens, Transposition, de Morgan etc.
I don’t believe that ...
- 8,363
3
votes
3
answers
290
views
How do you prove that a logic system is sound?
I am aware of the fact that a logic system must be sound, in order to be useful. However, I am not sure, about how, after setting up or coming up with the basic logic axioms that make up my system, I ...
2
votes
1
answer
73
views
Sentential Interpretation in P. Suppes (1957)
Patrick Suppes gives a working definition of sentential interpretation, based on a sentence maintaining its form. By working definition, I mean an incomplete definition that is needed for someone to ...
-4
votes
1
answer
154
views
Hi! I'm 99% sure my formal argument is valid, but can you check? [closed]
I wrote this argument, and while i'm sure it is valid, it has been awhile since I've done basic logic.Thanks!
- 46
0
votes
1
answer
66
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Semantic consequence and Sound Argument
Is that correct to say that semantic consequence is equivalent to the concept of sound argument in classical propositional logic?
If it is the case, arguments or theories with contradictory premises ...
-1
votes
3
answers
1k
views
Proof for "⊢ (A → ¬¬A)"
I've spent 4.5 hours on this, with no exaggeration. I clearly have no idea what I'm doing here, and it's become a serious time sink. If any of you could help in proving this, I would be eternally ...
- 15
-1
votes
1
answer
111
views
Help with proving: P, ¬(Q ∧ P) ⊢ ¬Q
Here's the issue, there's no usage of derived rules allowed. So no DeMorgan's Law. All that's allowed is the basic TFL elimination/introduction rules, IP, (e)X(plosion), and ⊥. I'm absolutely lost on ...
- 15
2
votes
0
answers
86
views
What is 'expendable' in logic and how to explain 'tautology' given this image?
This image is from http://www.nfillion.com/index.php/teaching/9-logic-112. According to this, a proposition can have 4 basic properties: (1) necessarily, (2) not possibly, (3) missing, and (4) ...
0
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2
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256
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Is the material implication the correct model of conditional reasoning in mathematics?
Question:
Do you believe that the material implication correctly models the kind of conditional reasoning necessary in mathematics to prove a theorem?
Example:
If x > y and y > 0, then x > ...
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0
votes
2
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67
views
Is there a symbol for what a logic gate yields?
Is there a logic symbol for what output a logic gate yields?
For instance, for an AND gate:
A
B
A ^ B
T
T
T
T
F
F
F
T
F
F
F
F
I want to propagate A ^ B into output C, but I wouldn't want to use ...
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