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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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Limit size of a collection.

I am trying to express the constraints of a database domain. A database domain can be limits the values that can be stored in a single cell of a table. The restriction I am trying to describe is the following: All elements of the collection must be…
SomeDutchGuy
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Comma notation in universal qunatification

Is the expression $\forall a,b,c \in M : \varphi(a,b,c)$ equivalent to $\forall a \forall b \forall c : (a \in M \land b \in M \land c \in M) \rightarrow \varphi(a,b,c)$ ?
ikkowy
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Kenneth Rosen-Propositional Logic-Exercise 1.4

There is a student in your class who has sent everyone else in your class an e- mail message. M(x,y)=x has sent an e-mail message to y Domain-All students of your class My solution: (there exists x)(for all y)((x!=y)<->M(x,y)) The…
Diya
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How to formulate that there is no politician who is not ambitious in predicate logic?

I want to go back to the logic of predicates. I tried to translate the following hrase: There is no politician who is not ambitious : $p\wedge \not a $, where $p$ is politician. Is that correct ? Or should I write $\not\exists p,p\wedge \not a $,…
Revolucion for Monica
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Converting to Prenex Normal Form.

I need convert $ \forall x \forall y(P(x,y) \sim Q(x,y)) \vee \exists x \exists y(P(x,y) \sim Q(y))$ into Prenex Normal Form. Can I use this formula: $(\exists x\phi )\lor \psi $ is equivalent to $\exists x(\phi \lor \psi )$ like $$ \forall x…
aid78
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Help with Relational Predication Logic

Translate into predicate form. (Relational predication is required.) Every animal lives somewhere. Mars lives nowhere. So, Mars is not animal. [A = “is a animal”, L = “lives”, P = “is a place”, M = m “Mars” N = nowhere] ∀x(Ax⟶∃y(Py & Lxy), ∃x(Lx…
Kris Letang
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how do express “multiple” in predicate logic?

I hope you can give me some tips on how to translate part of the following sentence into predicate logic: “No woman loves a man that loves multiple women”. Which quantifier would you use to express the part “multiple”? It of course means “more than…
user637252
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Distinguish 'the only f are g' from 'only f are g' in predicate logic

I'm trying to teach myself some predicate logic by reading Howard Pospesel's Predicate Logic and doing the exercises. In chapter 2, exercise 7 contains some optional, challenging exercises, and one of them has me a bit stumped. In its entirety, the…
Mark Seemann
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Find Interpretation for predicate logical formula

I Have to find a Interpretation so that $\Im (\alpha)$ is true. But how can i do that? $$ \alpha1 = \forall x \exists y \exists z (S(x,b) \to Q(x,y,z) \land \forall v (R(v,y) \to T(v,y))), \omega = \mathbb N $$ for $\alpha1$ as a hint is give: "Each…
Ambriador
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Expressing statements in terms of predicates and quantifiers

Given two sets: A={ Me, Ve, Ea, Ma, Jup, Sat, Ura, Nep} ; B={Eu, Io, Dei, Fo}. I need to express the following statements in terms of predicates and quantifiers: (a) There is a planet that does not orbit the sun; (b) All planets and their moons…
Yuri Adamov
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Convert to predicate logic: the relation $R$ on the set $X$ is antisymmetric

How would I cast the following to logical symbols The relation $R$ on the set $X$ is antisymmetric.
Vise
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Converting a sentence to Predicate Logic

Need help translating this sentence to predicate logic. If a student brings a candy bar for him or herself, then that student brings a candy bar for everyone. Use $C(w)$ as the one-place predicate "$w$ is a candy bar" Use $B(x, y, z)$ as the…
Vise
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Is my Skolem normal form of $(\forall x \exists y\exists zT(x,y)\land S(y,z))\land(\lnot\forall yP(y))$ correct?

Is my skolem normal form of $(\forall x \exists y \exists z T(x,y)\land S(y,z))\land (\lnot \forall yP(y))$ correct? $$ \begin{array}{|c|c|} \hline ( \forall x \exists y \exists z \; T(x,y) \land S(y,z) ) \land (\neg \forall y \;…
user3352632
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How to express the ellipsis in predicate logic?

Consider a statement like: the graph G has an infinite path. I'm trying to translate that into predicate logic. I keep finding myself relying on the crutch of the ellipsis, e.g. expressing a path as $a_1, a_2 ... a_k$, but the ellipsis is not…
user485260
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Does ∧ still mean intersection when using predicate logic?

Does ∧ still mean intersection when using predicate logic? This is one of the questions asked in class. Is the sentence valid? (∃xQ(x) ∧ ∃xR(x)) → ∃x(Q(x) ∧ R(x)) If it is, explain why. If it isn’t, give an interpretation under which it is…
Handsome Woman
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