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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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English statement to logic

If anyone cheats, everyone suffers. $S1:\forall x(cheat(x) \rightarrow \forall y\, suffer(y))$ $S2:\forall x \forall y(cheat(x) \rightarrow suffer(y))$ I thought Both S1 and S2 are wrong because they imply that if everyone cheats then everyone…
user3767495
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How would one prove $\forall x \in \mathbb{R}$, $\exists y \in \mathbb{R}$, $(x^2-y < 100)$ in predicate logic.

$\forall \ x \in \mathbb{R}$, $\exists \ y \in \mathbb{R}$, $(x^2-y < 100)$ How would one go about proving this? Should one use a direct proof or proof by contraposition? How can one prove this for every x?
user59177
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Syntax for complex restrictions on domains of quantifiers

In restricting the domains of the universal and existential quantifiers, all of the examples that I've seen take the form: $\forall x \in X[P(x)]$. But what is the correct syntax for more complicated domain restrictions such as $x \in \mathbb{R}$…
Geoff
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How can I justify this existential quantifier transformation in predicate logic?

I'm doing the following transformations over a statement with an existential quantifier that I believe is valid, but I don't know how to justify it in my chain of equivalences: $$ \begin{align} \exists y \in Y \{ y \in B \land &\exists x \in X \{ x…
jviotti
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Translating from English to a proposition using predicate calculus

The following sentence needs to be translated from english to a proposition using universal and existential quantifiers. Everyone in this class knows exactly one person that goes to university. I have been using the following predicates: let U =…
Jessica Tiberio
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Predicate logic - are these two formulas equivalent?

Are these two logical formulas logically equivalent or not? What I am asking is whether these two formulas mean the same thing or not. (1) ∃x ∀y ((A(x) ∧ B(y)) → ¬C(x, y) ) (2) ∃x (A(x) ∧ ∀y (B(y) → ¬C(x, y) )) Many thanks in advance
daveid
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Predicate to prove a set is countably infinite

Hi I have this question and have been struggling to find an answer. Prove that the set of numbers which are powers of 2 (i.e. $\{1, 2, 4, 8, 16, 32, \ldots\}$) is a countably infinite set. Not sure if I've been over thinking it but I've been…
mrtoeknee
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Having trouble proving an L-sentence is not logically valid

I'm having trouble with an assignment in Predicate Calculus specifically related to an L-sentence. I need to prove that $((\forall x (Px \Rightarrow Qx)) \lor(\forall x(Px \Rightarrow \lnot Qx)))$ is not logically valid. I understand L-structures…
vfantina
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Question with transcribing English to Predicate Logic & find assertion which is logically equivalent.

Anyone knows how to solve the question 10(especially 10(b)) & 11? I actually have the standard/model answers, but I don't really know how they understand the question and solve it step by step. Anyone can explain it and help me out....I am in…
Joseph Tam
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Natural Language to Formal Propositional Logic, "get neither"

I've been working through a few translations and I found one I am not too sure as to the formatting of. I believe the first part is right but in the second part where it says he will get neither, I am unsure if the correct format is to negate both…
Reggie Snow
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Predicate Formulae: Bound and Free

(P(x, y) ∨ (∀x (∃y (Q(x) → R(x, y,z))))) I know that for P(x,y), x and y are free because there are no quantifiers. But for (∀x (∃y (Q(x) → R(x, y,z)))), x and y are are bounded, and z is free. In this case, which occurrences of each variable in the…
JiHua
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What is the difference in the proof by resolution procedures in the following scenarios?

I am unsure what the difference in proof by resolution is in the following two scenarios, one being an implies, the other being an entails: $(\exists y\forall x P(x, y)) \to (\forall x\exists y P(x, y))$ $(\exists y\forall x P(x, y)) \vdash (\forall…
Jack Williamson
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monadic predicate logic

This is my first post, so if I am doing anything wrong, please notify me. In predicate logic, can one produce a truth-functional extension of a sentence containing 3 constants for a set containing two constants? For example, is it possible to…
Thrasymaque
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Ambiguous Quantifiers

i wondered what kind of quantifiers do not involves ambiguous reading ?
Lisa
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I think this question about predicate calculus logic I got in a test was impossible to solve, please tell me if I'm missing something...

The question reads: The following describes a world of discourse of flowers: Colored flowers are always scented. I dislike flowers that are not grown in the open air. No flowers grown in the open air, are colorless. The following fact is…
user2942952
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