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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
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predicate logic negation laws, two quantifiers

Is $\lnot\, \forall\ x\exists\, y \lnot\ P(x,y)$ equivalent to $\exists\, x \exists yP(x,y)$ ? I understand the negation rule, I just need to make sure i got it right. help please
Mahmoud Mahmoud
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Proving whether a statement is true or false; regards predicate logic.

(1) ∀x ∀y (P(x, x, y)∧ ∼≈ (x, 0) → L(0, x)), (2) ∀x ∀y (P(x, x, y)∧ ∼≈ (x, 0) → L(0, y)), where P(x, y, z)is meant to be x · y = z; L(x, y) is interpreted as x < y; and ≈ (x, y) is interpreted as x = y I'm trying to figure out whether the statements…
Helpsun
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Reexpressing a quantification as a conjunction, disjunction and negation

Suppose that the domain of the propositional function $P(x)$ consists of $-5,-3,-1,1,3,5$. Express $\forall x((x\ne1\rightarrow P(x))$ without using quantifiers, instead using only negations, disjunctions, or conjunctions. Select the choice or…
yroc
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Stating whether the stament that uses predicate logic is true in certain domains?

Let Z = {...,−2,−1,0,1,2,...} be the domain of integers and N the naturals (i.e. non-negative integers). The predicate symbol S(x, y, z) is interpreted as x + y = z; P (x, y, z) is meant to be x.y = z; L(x,y) is interpreted as x < y; and ≈ (x,y) is…
Desperate
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A number that is even and prime.

So I have the following sentence : There exists a unique prime number that is even. I have the following predicates : Prim(x) : x is a prime number. Even(x) : x is an even number. My answer : Prim(Even(x)) I don't know, but I think that this would…
user108343
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Predicate that indicates if a number is even or not.

So I'm kinda new to predicates and there was something that I was wondering. If I have the following predicate: $\text{even}(x) : x$ is an even number. And let's say I want to test if a number is odd, does the negation of $\text{even}(x)$ achieve…
user108343
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If a variable does not exist is it bound?

I've been doing Logic equivalences questions and I've been taught that a variable $x$ is bound if it is under any quantifier such as $ \exists $ or $ \forall$ however I've come across a question where in the answer it states that a variable is bound…
Nubcake
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A question on terminology

I started reading a Mathematical logic book.I wondered what is a definition by abstraction as well axiom schemata.
Bill
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predicate logic conversion

I am a novice in learning the conversion of english sentences to predicate logic.I can not convert these sentences into predicate logic. 1.Sue eats everything Bill eats. 2.Nazrul is a national poet. 3.CUET is an engineering university. Can anyone…
Shahed al mamun
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Free and bound variables in quantificational logic

I'm solving exercise 3 in page 63 of the book "How to prove it" by Daniel J. Velleman. I don't know if my solutions are correct so I post those solutions here and want you to tell me if I'm correct, and a form of reasoning that allows me to solve…
freinn
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Proof of equivalent formulas

I've been working on proving equivalent formulas using equivalences in predicate logic however I'm stuck trying to prove that these two formulas are equivalent: $ \forall x (A(x) \Rightarrow \exists y B(x,y)) $ $ \forall x \exists y (A(x)…
Nubcake
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Determining a suitable universe of discourse

The question is this: Question: Identify a suitable universe of discourse such that the predicate z2 + 4 = 0 has existential import. Now if you try to factor this equation, you will see that it is not possible. If you try to solve for z, what you…
Deathslice
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$(\forall x)(Ax \Rightarrow Bx) \Rightarrow [(\forall x)Ax \Rightarrow (\forall x)Bx]$?

$(\forall x)(Ax \Rightarrow Bx)$ is same as $(\forall x)[(Ax \land Bx) \lor (\lnot Ax)]$ if for every $x$, $Ax \land Bx$ is true then we get $(\forall x)(Ax)$ true and $(\forall x)(Bx)$ true. We get $(\forall x)(Ax) \Rightarrow (\forall x)(Bx)$ is…
Arjun
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Predicate logic of sorting algorithm

I'm confusing with this question. How can we tranlate a sorting algorithm for a list of N numbers to predicate logic, especially for insertion sort? Thank you very much!
Peter Nguyen
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Predicative logic implication, is it true?

I'm struggling to find a counterexample for this expression... $\left(\forall x P(x) \longrightarrow \forall x Q(X)\right) \overset{is\ this \ true??}{\longrightarrow} \forall x (P(x) \longrightarrow Q(x)) $
Werner Germán Busch
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