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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
4144 questions
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How to use uniqueness existential quantifier for more than one

$P(x,y)$ is a predicate function meaning that person $x$ has read person $y$'s book. Now I want to say there exists only 3 people having read person $t$'s book . How can I state it with quantifiers? Is this ok? : $\exists! x\exists! y\exists!…
fmatt
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Show that one cannot infer from the formula ∃xR0(x,c) the formula ∃xR0(c,x)

"Show that one cannot infer from the formula ∃xR0(x,c) the formula ∃xR0(c,x)". I'm looking for help understanding the difference between the formulas
user63764
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Doubt in the answer for a Predicate logic question for the zoo example

Form a sentence using the variables p, q, and r to denote that ”I will go to the zoo if it is sunny and I wear sunglasses”. Let p be ”It is sunny”. Let q be ”I wear sunglasses”. Let r be ”I will go to the zoo”. Is the solution to…
JBlack
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Completeness theorem for Predicate logic with uncountable sentences?

I know the proof of completeness theorem for Predicate derivateion. And it's used that sentences of PLE(Predicate logic with identity) is countable for proving that for any consistent set A in PLE, there is a maximally consistent set of PLE that…
정재우
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What is the correct formalization of the following mathematical statement about prime numbers in a predicate logic notation?

I have to formalize the following mathematical statement in a predicate logic in a language L = {+, *, 0, 1, <} : "There are infinitely many prime numbers" I have found the following formalization but it is not clear to me why there is a necesity…
TKN
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Is it true that exists a natural number (zero excluded) that is divisible by every natural number?

I have the following formula: $(\exists x)(\forall y) r(x,y)$ Is this formula true in a model where r(x,y) is a binary predicate interpreted as "x is divisible by y" and the universe is all natural numbers except for zero? Why?
TKN
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Predicate logic - Which of these formulas is equivalent to the first?

Working on basic first-order logic for uni, I have been given the answers to an assignment which I don't agree with. Question: Which of these formulas is equivalent to ∀x∃y(Bx → Cy)? a) ∃xBx → ∃yCy b) ∀xBx → ∃yCy I say a), the answer sheet says…
user2891462
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How to write this natural language sentence as a predicate logic formula?

I should write the following sentence as a predicate logic formula: "It is not true that all soccer players are fearless and it is not true that some sailors aren't fearless." I would write it like this, but I'm not sure if it is correct:…
TKN
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Operator precedence - Discrete Math (Predicate logic)

Can someone please give me a hint as to how these two statements are different? Thank you! ∀x ∈ S, ∃y ∈ T, P(x, y) ⇒ Q(x) (Statement 1) ∀x ∈ S, (∃y ∈ T, P(x, y)) ⇒ Q(x) (Statement 2)
ComputerScience523
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What will "He always wears a suit to work. " be in predicate language?

Please check my answer: $\forall x[H_x \supset W_x ]$ which translates as "For all x, if x is he (goes to work) then he wears suit to work" (Bold ones are the symbols I pickedup) Venn would a diagram for an A proposition shown as:
New Student
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Is existential import only about implications on subject or other nouns/objects too?

Question 1 This mentions "...belief in the existence of members of the subject class". Is this necessarily true ? Consider "Some pizza has pepperoni on it". You get the following. Which is one is an existential import ? Pizza exists Non-pizza…
New Student
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How do I conclude that this predicate logic formula is valid or not valid when I do not really understand it to begin with?

Have a hard time to conclude when a given predicate logic formula is invalid/valid. For example, this is one that I have spent a lot of time on $$\vdash \exists x P(x) \wedge \exists x (P(x) \rightarrow Q(x)) \rightarrow \exists x Q(x)$$ To start…
Salviati
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Quantifier scope

I'm having trouble understanding predicate logic. I get very confused in interpreting the parentheses, to be able to correctly demarcate the scope of quantifiers, particularly in the following (from our unit book): (x)(Bx → (Cx & ~Dx)) & ((∃y)(Ey &…
explorer
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(∃a)(∀b)(∃c)(∀d)(a · c = d · b) as 2 equal formulas using only one type of quantifier

How to do 2 equal formulas using only one type of quantifier (∃a)(∀b)(∃c)(∀d)(a · c = d · b) I have to use only ∀ in the first formula and only ∃ in the second formula.
lasto
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Given the predicate Q(x,y):xy =1 where x ∈ Z and y ∈ Z..Determine the true values of the following statements. Explain each of your answer

Given the predicate Q(x,y):xy = 1 where x ∈ Z and y ∈ Z. Determine the true values of the following statements. Explain each of your answer 1)∃x Q(1,y) 2)∀x∃y Q(x,y) 3)∃x∀y Q(x,y) My self-do answer is 1)Yes. For some x as 1, there is a y for x so…
Hanyi Koh
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