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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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Please explain, "Asymmetric is stronger than simply not symmetric".

In some textbook I found a statement like, "Asymmetric is stronger than simply not symmetric". But as I try to perceive this statement, both appear to be same to me. For example, parentof is an asymmetric relation. If $A$ is a parentof $B$, $B$ can…
Masroor
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Difference between terms and atomic formula

What is the difference between terms and atomic formulae? I get contradicting advice from everywhere. On one hand I have got written if $t_1,\ldots,t_n$ are terms and if $F$ is a function symbol with arity $n$ then $F(t_1,\ldots,t_n)$ is a…
user204450
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3 answers

Why is predicate logic semidecidable?

Could someone explain clearly why predicate logic is said to be "semidecidable"? I know that the set of invalid formulas of a predicate language is not effectively numerable, which implies that predicate logic is not decidable (a set of expressions…
user405159
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Is "you know everything" the (using sentential logic) logical negation of "you know nothing"?

My friend and I are trying to settle a debate here. Someone joked that they're "not Jon Snow" when debating a yes/no question, and I retorted that the logical negation of "you know nothing, Jon Snow" is not "you know everything, Jon Snow", but my…
Vatsal Manot
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Is my attempt with predicate-logical symbols correct?

I have this statement (it's translated from a different language): "if x divides y and y divides x, then x = y" I want to write that statement predicate-logical symbols. I'm new to this so my question is if my attempt is correct. If not please…
Bioelli
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Can finite theory have only infinite models?

I always thought, that when creating a theory (set of formulas of predicate logic of first order in some language) and when you want to have only infinite models, you must use infinite number of axioms. That's how Peano arithmetic or ZF are…
Ivan Kuckir
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What would happen in predicate logic if the domain of discourse was allowed to be empty?

I was thinking about this and I believe that some of the popular equivalences, like this one: $\neg \forall x P(x) \equiv \exists x \neg P(x)$ won't hold up anymore. Is this correct? But equivalences like that are very useful, what else would we…
zlaaemi
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A valid argument resulting from the distribution of the universal quantifier over a conditional.

$\forall x \bigl( P(x) \Rightarrow Q(x) \bigr)$ $\forall x \bigl( P(x) \bigr) \Rightarrow \forall x \bigl( Q(x) \bigr)$ In a world where statement 1 is true, statement 2 must be true through natural deduction. Let us assume that P stands for the…
أحمد الدسوقي
  • 111
4
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3 answers

What's the difference between ∀x(P(x)) and ∀xP(x)?

Edit: Changed logically equivalent to logically implies! Sorry. Also realized removing the context when trying to understand something is a bad idea. Just started learning predicate logic. What I'm trying to prove is that ∀x∃y( P(x)->Q(y) ) is…
user2719875
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True or false: The negation of $∃x : P(x)$ is $∃x, \neg P(x)$

I am trying to understand the negation of propositional logic with regards to universal and existential quantifiers. I want to know if the negation of $∃x, P(x)$ is $∃x, \neg P(x)$ is true or false. I believe that this is true. I know that the…
User
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Predicate logic, Every boy who loves a girl is also loved by a girl

I'm doing some selfstudying and I'm lacking the anwsers to check if I'm correct. So this is why I'm on here so frequently, as I really want to understand the matter. So here is the sentence I'm trying to convert to predicate logic: Every boy who…
Byebye
  • 277
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2 answers

Translating Nested Quantifiers to English sentences

For this entire question, please use the following propositional function: $P(x,y)$: $x$ has sent a postcard to $y$. Translate the following quantified propositions to English sentences. Try to use sentences as natural as possible. (a) $\forall…
harsefhf
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Relationship between universal quantifier and existential quantification. Is it always equivalent by just moving the negation symbol?

Say C: set of courses P(x,y): 'x is a prerequisite for course y' Statement: No course is a prerequisite for itself. is same as: For all x in C, ¬P(x,x) But is this correct? There doesn't exist x in C, P(x,x) And if this is correct, is it true for…
merlin
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The instantiation of the statement ∀x(P(x))⇒∀x(Q(x)) and its contrapositive.

∀x(P(x)⇒Q(x)) ∀x(P(x))⇒∀x(Q(x)) Let P stands for the category of breathing people and let Q stands for the category of alive people. In a world where statements 1 and 2 are both true, there's a difference in the information we can deduce using…
أحمد الدسوقي
  • 111
3
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5 answers

Negation of there exists quantifier?

The problem states to find the negation of the following statement: There exists a number which is equal to its square. Original Answer: There does not exist a number which is equal to its square. My answer: There exists a number which is not…
Aura
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