Questions tagged [propositional-logic]
The propositional-logic tag has no usage guidance.
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What is the relationship between possible worlds and a valuations?
A propositional formula is something like this, A&~B, which uses letters to represent propositions. The letters are called propositional variables.
Compare the following two sets of terminologies ...
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How does "if p, then q" compare to "p only if q"?
How do the statements if p then q and p only if q compare
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What is the difference between a tautological corresponding conditional and (P v ~P)?
The Wikipedia article on the corresponding conditional contains the following sentence:
An argument is valid if and only if its corresponding conditional is a logical truth.
Some sources use "...
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How to show DeMorgan Law in intuitionistic logic using weak excluded middle?
I am trying to show in intuitionistic logic that ~(A & B) > (~A v ~B) using the deduction theorem and weak excluded middle (~A v ~~A). I already proved (~~A & ~~B) > ~~(A&B) and ~(A &...
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Help reconstructing argument
I saw the following argument in Paul Guyer's text "Kant" (Routledge). I am trying to reconstruct it, yet am not sure the of the form of the argument. Can anyone provide help?
If whenever ...
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Justification of the material conditional truth function in Introduction to Formal Logic
Pages 150-151 of §18.3 of Introduction to Formal Logic by Peter Smith provide two justifications for the truth table of the material conditional.
In the first justification (paragraph (a) - (c) on pg. ...
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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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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 ...
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Truth-functional vs non-truth functional conditionals
I'm struggling to understand truth functionality.
I know that a connective is truth-functional if the truth value of a compound statement formed with that connective is completely determined by the ...
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Translating English statements to logical expressions
this is my first questions so I apologize for any formatting mistakes.
Given the following propositions:
c: I will return to college.
j: I will get a job.
and given the sentence:
"There is no ...
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Intersection of the Gettier problem and knowing-what or knowing-how
From what I can tell, it seems like the Gettier problem comes down to Smith not knowing that the man who has ten coins in his pocket is going to get the job. What about Smith knowing what the ...
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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 ...
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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 ...
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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!
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How understand abstraction when some cases can’t be abstracted?
Like the liar sentence “this sentence is false” is said not to be a proposition.
So not all sentences can be abstracted into props. Can infinite sentences be abstracted into propositions. Can infinite ...
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Philosophy book written using logic statements
I would like to translate a philosophy text into logic axioms and propositions. Then, I would like to use prolog to check if the text is logically consistent.
However, I find it difficult to translate ...
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Translation of Arguments from Propositional Logic to Predicate Logic
How exactly does this work? What can we assume stays the same, what changes?
Take for an example this (valid) argument:
A & ~C
~C > ~D
~D > B
∴ B
Now let us take rewrite it according to ...
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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 ...
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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 ...
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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 ...
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What does it mean, intuitively and then also precisely, that a particular English word is not truth functional?
What does it mean, intuitively and then also precisely, when we say that a particular English word is not truth functional? Let me present some examples.
Example 1
As far as I can tell from a book I ...
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Proofs of propositional logic truth tree rules in natural deduction?
It is a great irony of natural deduction that some of the most seemingly obvious inferences are also some of the trickiest to prove! So far, I haven't been able to prove the following, and I'd greatly ...
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How to interpret "P ⟺ Q is true if and only if the first-order logic sentence P ↔ Q is logically necessary"?
I'm learning about the two truth-functional connectives "material conditional" and "material biconditional".
I came across this particular snippet in a book:
An important fact ...
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Prove that if S tautological consequence of P, S tautological consequence of Q, then S tautological consequence of P | Q
Consider the following argument:
S is a tautological consequence of P.
S is a tautological consequence of Q.
Therefore, S is a tautological consequence of P | Q.
I wish to give an informal proof of ...
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Why is any sentence a logical consequence of a set of inconsistent premises?
If a set of premises is inconsistent, there is no situation that makes all the premises true simultaneously.
Given a sentence S, there is no situation in which a conjunction of a set of inconsistent ...
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How to understand a proof by contradiction in minute detail?
I am following the course "Language, Proof, and Logic" from Stanford on EdX. I am trying to understand proof by contradiction specifically. I understand the gist of this type of proof, and I ...
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If A entails C, and B entails C, why doesn’t (A and B) necessarily entail C?
The original question is in Greek letters Γ and Δ, each representing a set of sentences, and φ representing an individual sentence (atomic proposition). The question is from Introduction to Logic by ...
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Is Propositional Logic (or Zeroth-order logic) the most basic form of logic?
Could all systems of logic (not only classical logic 1, but also non-classical logics like intuitionistic logic 2, quantum logic 3, many-valued logic 4, modal logic 5, paraconsistent logic 6...etc) be ...
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Is "Not all S are P", ambiguous?
I read Kelley's book (the art of reasoning: An Introduction to Logic and Critical Thinking 4th edition). On page 150, I found this statement:
"A special problem arises with statements that have ...
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Am I correct that tautologies and contradictions are NOT truth-functional?
We call a statement truth functional if its truth value depends on truth value of its parts. Like A⊃B can be true or false, depending on truth values of A and B.
But, it's not the case with ...
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How to define ‘impossible’ using propositional modal logic?
I am trying to define impossibility using the symbols we have in propositional modal logic. I got ‘negation diamond alpha’ in mind as equivalent to ‘it is impossible that alpha’. It that correct and ...
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Understanding David Deutsch's assertion about the laws of physics as emerging from those of biology
In the Chapter 1 of the Fabric of Reality, David Deutsch says the following:
There is no reason to regard high-level theories as in any way 'second-class citizens'.
Each of them has implications for ...
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so im arranging these arguments from strongest to weakest, and am confused?
Either reublocrats are uninformed, or democrans or independents are uninformed
it is not true that republocrats are uninformed
someone is uninformed
either republocrats are informed or they are not ...
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Issue with the interpretation of Propositional Logic
I’m having an issue with the terminology and perception authors use. Some authors perceive PL as a branch of logic “with subsets” with classical or truth-functional PL as these subsets. Other perceive ...
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i don't understand modus ponens
I'm learning about modus ponens in propositional logic but it doesn't makes sense to me
I can think of an examples where a true premises leads to a false
conclusion:
p -> q
p
Therefore q
If the kid ...
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Structure of "affirming the consequent fallacy"
The formal structure of affirming the consequent fallacy is,
P1 - If A is true, then B is true
P2 - B is true
---------------------------------
C - Therefore, A is true
Now if I give another similar ...
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Propositions as set of possible worlds in FOL
In possible world semantics for propositional calculus, possible worlds are usually taken to be models for propositional formulas (the set of valuations in which a certain formula is true)
In first ...
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Show the following is valid in SD+: How to solve this derivation
This is not Homework.l do this for fun and expand my learning.
I am obviously having difficulties with SD+,thus l post many problems.
I am using the Logic Book
Problem has be done in SD+
Using goal ...
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I am stuck on SD+ style proof and need to know how to do it
I am using SD+. Most of the derivation has to
be done using it
I am finding this one tricky
I request help or hints to solve it
Derive L => H
1.~L v (~Z v ~U). Assume
2.(U & G) v H Assume
3.Z. ...
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How to apply Transdisciplinarity Logic to Truth Tables?
I've been having trouble trying to figure out Transdisciplinarity Logic. I have had little success while trying to research on my own, finding sources that are either too difficult to understand or ...
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Understanding Damore's statement about decreasing the false negative rate
At page 6 of his well-known memo, James Damore talks about the harm of Google's biases:
Hiring practices which can effectively lower the bar for "diversity" candidates by decreasing the ...
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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) ...
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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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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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Soundness and Completeness of Tableaux
Tableaux to my knowledge are both sound and complete.
The statement:
"If P is valid then tableau for -P eventually closes".
Does this statement prove that tableau is sound and complete or ...
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Equivalence of truth conditions
Truth conditions, roughly, are the way things should be in order for a sentence to be true.
For instance, the condition for the sentence "Paul is a cat" is that the individual denoted by &...
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How to prove: 1. (A^B)v(A^C) 2. (AvD) -> E //E
This proof has stumped me. It seems that getting (AvD) alone then using Modens ponens to therefore prove E would be the correct way of going about things but I cannot seem to find a way to get (AvD) ...
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Tautology of p implies q and not p or q [duplicate]
I'm learning about tautologies right now. I see that a tautology is when two propositional statements have the same truth values. But I'm struggle with the truth table my professor provided about the ...
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What are some of the struggles that come with teaching formal logic? [closed]
I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
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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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