# Questions tagged [propositional-logic]

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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 ...
55 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 ...
38 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 ...
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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 ...
84 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 ...
528 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 ...
50 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 ...
50 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 ...
43 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. ...
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 ...
53 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 ...
47 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) ...
199 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 > ...
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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 ...
65 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 &...
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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) ...
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 ...
66 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 ...
241 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 ...
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### 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 ...
154 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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### 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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### 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 ...
109 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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### 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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### 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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### 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 ...
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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### 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 ...
84 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 ...
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### 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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### 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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### 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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### 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 ...
219 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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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### 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) ...