Questions tagged [propositional-logic]
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13
questions
-3
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1answer
71 views
do 'p & ~p' , '~p & ~~p' equal 'either p or ~p'?
In classical logic,
(1) p & ~p is equivalent to (2) ~p & ~~p;
if we read 'p & ~p' as p, ~p are both true/the case, and if we read '~p & ~~p' as p, ~p are both false/not the case (...
2
votes
1answer
42 views
A set of three statements, of which only two at a time can be true: is there a specific term for this type of combination game?
Here's two examples of what I'm talking about
1
An ideal citizen would be smart, ethical and politically engaged.
However, what usually happens in reality is this:
If they're smart ...
4
votes
1answer
87 views
Did William of Soissons prove the law of explosion in the 12th century?
In the 12th century, William of Soissons attempted to prove that any proposition can be inferred from a contradiction. I've adapted his proof into a logical system I'm more familiar with:
Let E ...
-1
votes
1answer
63 views
How to derive P > (Q > R) from (P > Q) > R in Fitch?
I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof.
Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
4
votes
3answers
137 views
Why is it argued that an argument has one and only one conclusion?
Why can't an argument have more than just one conclusion? If we assume some premises and we assume them to be true, then by some inference rules we are sometimes able to deduce more than just one true ...
0
votes
2answers
45 views
What are some key differences between an argument in logic and a theory in mathematics?
Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
2
votes
6answers
128 views
Is it true in some sense that the only “truth” people are capable of knowing is the “truth” that they assume to be true?
What are some viewpoints on the following assertion in philosophy and logic?
Anything people argue to be true is only their assertion based on some axioms or premises which they assume to be true (...
3
votes
3answers
975 views
What is the difference between a premise and an assumption in logic?
It seems to me that an assumption is an untold premise in my argument. Is it right?
2
votes
1answer
70 views
Is there a reference list of classic tautologies that are not intuitionistic tautologies for propositional logic?
An example of a classic tautology would be ¬¬A ↔ A. Since double negative elimination is not intuitionistically valid, this classic tautology would not be an intuitionisitic tautology since ¬¬A → A is ...
1
vote
2answers
161 views
Confused about the answers to two logic problems
True or False? If monkeys can fly, then 1 + 1 = 3.
What is logically equivalent to all x (p(x) + ~q(x))?
For the first one I think it is False.
4
votes
2answers
564 views
What are the conditions for RAA?
My textbook states that:
In this case, however, what about situations where we can get Q ^ ~Q (sorry, unfamiliar with this formatting) without depending on P? For instance, the proof of EFQ:
1 (1) ...
0
votes
1answer
198 views
Using predicate logic, how to solve symmetric and anti reflexive
The networks is: A->B->C->D
The channels used by the network are: lo, med, hi
h-hi, l-lo, m-med
i) A network uses one, and only one channel.
ii) Networks within close proximity cannot both use the ...
3
votes
1answer
90 views
Is b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C possible?
Are there any cases where b and C are real world statements where b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C where b and C are not tautologies? It may seem like a silly question, but after searching hard and deep, I couldn't ...
