Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [predicate-logic]

Questions concerning predicate calculus, i.e. the logic of quantifiers.

Some well-known formal systems covered by this term are

  • first-order logic, containing the quantifiers $\forall$ and $\exists$
  • second-order logic
  • many-sorted logic
  • infinitary logic
4144 questions
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Is this predicate logic semantic tree open or closed?

I have this formula: $\forall y\neg A(y)\land\exists x A(x)$ . Is a semantic tree for this formula closed or open?
TKN
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MUST an I and O proposition simultaneously be be true?

In the Square of Opposition, MUST I and O proposition "simultaneously be be true" ? The webpage is silent on it. I think it "COULD be true" as in the square but not a "MUST be true". Can someone show me both a Venn diagram and predicate languages…
New Student
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Predicate Logic with Nobody

Nobody is a college student and not smart. How does this translate into predicate logic? I am stuck between two: ¬∃x[person’(x) ∧ student’(x) ∧ ¬smart’(x)] ¬∃x[[person’(x) ∧ student’(x)] → ¬smart’(x)] Thanks!
joseyjones
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Translation to language P (Predicate Logic)

I am taking an intro class in philosophy and I have having trouble with some assignment questions. I need to translate into the language P. Here's the translation keys: Fx: x is a firefighter Dx: x is a doctor Nx: x is an nurse Gx: x plays…
GarlicSTAT
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Doubt on mathematical Logic

Consider the following first order logic statement $I)\forall x\forall yP\left ( x,y \right )$ $II)\forall x\exists yP\left ( x,y \right )$ $III)\exists x\exists yP\left ( x,y \right )$ $III)\exists x\forall yP\left ( x,y \right )$ Which one of the…
Srestha
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Need help with converting sentence to predicate logic

I'm trying to write a predicate logic for this statement but I'm not sure if I'm writing this correctly. Can anyone validate and let me know if this is correct and if not, help to come up with the correct syntax, please. Thanks in advance. ∀x (P(x)…
Kifayat
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Predicate Logic, and Predicate Form.

I am currently researching mathematics, and I am currently stumped on Predicate Logic. I was just wondering how to put this statement into predicate form. "Each Student must play at least 2 sports" thank you in advance.
newbieMaths
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Predicate Logic - Prove or disprove

I have a phrase in English, and I need to determine if it is true or false. If it is true, I need to prove it, and if it is false, I need to disprove it. The phrase is based on the famous phrase "every pot has a lid", and it goes like this: "If…
user3275222
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semantically equivalent

question about: $((\forall x A)\lor B)$ is semantically equivalent to $(\forall x(A\lor B))$ with the condition that $x$ is not free in $B$. I have thought about structure, $U = \{ k , h \}$ ... where $k$ and $h$ are names of humans $A:= \{ x$ eats…
hany.mha.ibrahim
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Transcribing a piece of English into set-theoretic notation

Suppose I've got the following model M = where D is a non-empty set {John, Jane, Jonathan, Julia}, S = {L, a, b, c, d} where L is a binary relation symbol, read as 'loves', a-d are nullary function constant symbols, and finally, i, the…
Kas
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$\{(\forall(x))P(x) \implies(\forall(x))Q(x)\} \implies (\forall(x))(P(x) \implies Q(x))$

$(\forall(x))(P(x) \implies Q(x)) \implies \{(\forall(x))P(x) \implies (\forall(x))Q(x) \}$ why this is not valid and how the converse of this is valid?
user249855
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Help with English to Predicate Logic

Alex likes anything that contains chocolate. a - Alex L(x,y) - x likes y C(x) - x contains chocolate $1. \forall x \space (C(x) \implies L(a,x)) $ $2. \forall x \space (C(x) \space \text{^} \space L(a,x)) $ Is there a difference between 1 and 2?…
Zee
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Formal logic statements symbolic representation.

If the horse is fresh, then the knight will win. $H -> K$ A fresh horse is a necessary condition for the knight to win. $K -> H$ I think the first sentence should have same notation. I don't understand why are different.
Mike90s
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Given that $\forall xQ(x)$ is true, is $\exists xQ(x)$ also true?

Given that $\forall xQ(x)$ is true, is $\exists xQ(x)$ also true? Thanks in advance.
gachaSalt
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