Questions tagged [propositional-logic]
The propositional-logic tag has no usage guidance.
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How can a proof system be unsound?
I have recently started learning propositional logic. I stumbled upon the concepts of soundness and completeness.
According to http://intrologic.stanford.edu/chapters/chapter_04.html, a proof system ...
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1answer
19 views
Is my interpretation of “and” correct in these statements?
Let A mean "Equation A has a solution" and B mean "Equation B has no solution." I am a little confused, so I wrote down some possibilities and I wish to see if my interpretation of ...
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4answers
122 views
Are there multiple definitions of validity?
I have recently started learning the basics of propositional logic. According to http://intrologic.stanford.edu/chapters/chapter_03.html, a sentence is valid if and only if it is satisfied by every ...
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2answers
44 views
Is a vacuously true argument a valid argument? [duplicate]
From what I know, given some argument, the argument is valid when it has true premises that lead to a true conclusion. Now, what if the premises were false? I mean, the conclusion would be vacuously ...
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28 views
Is the truth table method for valuating 0th order sentences not a proof system in its own right?
This might sound a bit opinionated or a bit too pedantic, but in every book (that I've looked at) about propositional logic, usually this chain of events happens:
Discuss the alphabet and grammar of ...
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2answers
80 views
How would I start a formal proof for the conclusion (P → Q) ↔ ¬ (P ∧ ¬ Q) with no premises? [closed]
There are no premises, and I'm doing this in fitch
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2answers
1k views
Is the sentence “all apples are red” an atomic sentence?
In An Introduction to Logic by Patrick Suppes, an atomic sentence is defined as a sentence that contains no sentential connective. However, in a later chapter, a sentence is defined as a formula which ...
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2answers
79 views
If-then statement and time between antecedent and consequent
Suppose the following statement. "If I kick the ball then the ball will hit the wall." Can this sentence have a truth value? I mean the time that I kick the ball, it hasn't reached the wall so the ...
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22 views
Is there a word for instantiating all the things that I suppose in my argument?
Let's say I'm in the propositional logic and I say: "Socrates is a man. All men are mortal. Therefore Socrates is mortal." Sure, it is true that "Socrates is mortal" is the valid conclusion. But it is ...
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6answers
2k views
What is wrong with these two conditionals?
Is it true that these two conditionals if A then B and if not-A then B cannot be both true?
Example :
"If I stay then I will eat fish"
"If I didn't stay then I will eat fish"
The reason I think ...
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1answer
63 views
Proof that if an inference holds in propositional logic, then the inference holds in supervaluationism
I am currently trying to work on problem 8, but I'm not sure exactly how to start it.
I was thinking of starting it by trying to prove that phi is indeed PL valid. I would have to show how that is ...
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1answer
54 views
How to solve: Show that a formula is PL-valid if and only if it is LP-valid [closed]
I don't really understand this problem, but I'm going to spill out what I've taken notes on. I know that in order to solve this we would need to use the contrapositive in each direction.
I'm going ...
3
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1answer
85 views
Classical propositional logic. Are all formulas sentences?
Let L the language of classical (two-valued) propositional logic consisting of a denumerable set of sentential variables as well as the usual operations of negation, disjunction, conjunction, ...
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1answer
115 views
Proving A ⊨ B iff ⊨A → B
Let A and B represent arbitrary formulas.
Also let 1 ≡ True and 0 ≡ False
Prove that A ⊨ B iff ⊨A → B
For my proof, I break down the biconditional into two conditionals and prove each conditional.
...
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0answers
21 views
looking for tool(s) for making diagrams with
I am looking for some tool to create symbolic logic derivation diagrams with horizontal and vertical scope line and sub derivations. Then I want to be able to add them to a word document. Word doesn'...
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1answer
39 views
Is this proof valid (noob)?
I'm trying to prove that from P we can conclude that Q implies (P and Q). I understand how this is true intuitively, but I'm just getting a grasp of how to use propositional logic, its rules, etc. to ...
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1answer
107 views
do 'p & ~p' , '~p & ~~p' equal 'either p or ~p'? [closed]
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 (...
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1answer
47 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
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An ideal citizen would be smart, ethical and politically engaged.
However, what usually happens in reality is this:
If they're smart ...
4
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1answer
106 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 ...
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1answer
83 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 ...
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3answers
190 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 ...
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47 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?
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6answers
189 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 (...
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3answers
3k 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?
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148 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 ...
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175 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.
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2answers
588 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) ...
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1answer
222 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
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1answer
92 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 ...
