Questions tagged [propositional-logic]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
0 answers
37 views

Hi! I'm 99% sure my formal argument is valid, but can you check?

I wrote this argument, and while i'm sure it is valid, it has been awhile since I've done basic logic.Thanks!
user avatar
0 votes
1 answer
33 views

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 ...
user avatar
  • 1,324
2 votes
3 answers
120 views

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 ...
user avatar
-1 votes
3 answers
97 views

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 ...
user avatar
0 votes
1 answer
45 views

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 ...
user avatar
0 votes
3 answers
123 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 that just isn't worth struggling over. If any of you could help in ...
user avatar
-1 votes
1 answer
99 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 ...
user avatar
0 votes
0 answers
35 views

Language, Proof, Logic - Problem 7.32 solution verification: exclusive disjunction introduction and elimination formal rules [duplicate]

In the book "Language, Proof, and Logic" there is the following problem 7.32 that doesn't have an available solution that I can check. Later on in the book, there is the following comment: ...
user avatar
0 votes
1 answer
71 views

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 ...
user avatar
-2 votes
1 answer
58 views

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 ...
user avatar
0 votes
1 answer
62 views

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 ...
user avatar
1 vote
1 answer
39 views

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 ...
user avatar
3 votes
3 answers
141 views

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 ...
user avatar
1 vote
2 answers
124 views

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 ...
user avatar
0 votes
1 answer
136 views

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 ...
user avatar
1 vote
2 answers
99 views

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 ...
user avatar
  • 311
1 vote
1 answer
60 views

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 ...
user avatar
1 vote
1 answer
91 views

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 ...
user avatar
1 vote
0 answers
95 views

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 ...
user avatar
  • 19
0 votes
0 answers
64 views

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 ...
user avatar
0 votes
0 answers
42 views

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 ...
user avatar
0 votes
0 answers
108 views

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 ...
user avatar
-1 votes
1 answer
110 views

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 ...
user avatar
  • 169
2 votes
3 answers
573 views

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 ...
user avatar
2 votes
1 answer
72 views

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 ...
user avatar
  • 385
-2 votes
1 answer
77 views

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 ...
user avatar
  • 164
0 votes
1 answer
65 views

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. ...
user avatar
  • 164
0 votes
0 answers
27 views

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 ...
user avatar
0 votes
1 answer
54 views

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 ...
user avatar
2 votes
0 answers
63 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) ...
user avatar
  • 187
0 votes
2 answers
210 views

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 > ...
user avatar
  • 3,531
0 votes
2 answers
60 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 ...
user avatar
  • 187
2 votes
1 answer
85 views

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 ...
user avatar
  • 23
0 votes
1 answer
73 views

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 &...
user avatar
  • 385
-2 votes
1 answer
38 views

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) ...
user avatar
  • 9
0 votes
0 answers
15 views

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 ...
user avatar
  • 101
2 votes
1 answer
80 views

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 ...
user avatar
2 votes
1 answer
421 views

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 ...
user avatar
  • 45
0 votes
1 answer
31 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 ...
user avatar
  • 304
2 votes
3 answers
162 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 ...
user avatar
  • 45
0 votes
2 answers
139 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 ...
user avatar
  • 304
0 votes
0 answers
31 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 ...
user avatar
-2 votes
2 answers
124 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
user avatar
  • 9
4 votes
2 answers
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 ...
user avatar
1 vote
4 answers
273 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 ...
user avatar
  • 711
0 votes
0 answers
23 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 ...
user avatar
  • 355
5 votes
6 answers
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 ...
user avatar
  • 2,349
-2 votes
1 answer
67 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 ...
user avatar
0 votes
1 answer
106 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 ...
user avatar
3 votes
1 answer
104 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, ...
user avatar
  • 279