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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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How does a model of set of predicate logic formulas change when the domain of discourse is finite and infinite

I found this problem in an old logic textbook in the library but it unfortunately did not have any answers is my understanding/attempt correct? Can it be improved? Consider the set Φ consisting of the following five predicate logic formulas. $∀x…
Jerry Springer
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Position of quantifiers in predicate logic

I have attempted to translate the English sentence "the very best candy is chocolate" into predicate logic as follows: $$\lnot \exists x \exists y[(C_x \land \lnot C_y)\to B_{yx} ]$$ where $x$ and $y$ are candies, $C_x:x$ contains chocolate, and…
Jack
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Problem translating an argument into predicate logic.

The (clearly flawed) argument I am attempting to translate is this: "All my dreams are in black and white. Old TV shows are in black and white. Therefore, some of my dreams are old TV shows". This is my attempt: $$\forall x (D_x \to B_x)$$ $$O_x \to…
Jack
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Quantifying a variable without using it in the quantified statement

Suppose I write something like: $\forall x \exists y P(x)$ or even $\forall x \forall y P(x)$ In either case, the variable $y$ is quantified but does not appear in my predicate statement. Is this syntactically valid, and if so, how should $\exists…
alexw
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Can someone help me understand predicate logic by explaining 2 statements?

∀n : ((0≤n<19) →(A(n) < A(19)) I want to know what this statement means. I'm new to Logic and I'm starting to understand parts of it (mainly the basics) however I've come up stuck when it comes to this statement. A relates to an array but i can't…
Peter
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Predicate logic: role of the free variables in the satisfaction of a formula

I'm learning predicate logic and in the textbook I'm using it's written that "whether or not an assignment σ satisfies a formula α solely depends on the values that σ assigns to the free variables in α". I can't understand precisely why this is so.…
user405159
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Predicate Logic (∃y∀x)

I'm having some issues understanding predicate logic. For example, given the proposition: These propositions are based on a set of numbers. $$\forall x \exists y (x \cdot y = x)$$ This means for every $x$ there exists a $y$ that when you multiply…
denn1s
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Confusion between existential and universal quantifier

"Everyone is loved by someone or other" I'm not sure how to translate this into predicate logic. At first, I said $\forall x\exists y,Lyx$ where $Lxy$ is x loves y. However, it is not true that there is someone who loves everyone. The sentence says…
JC1
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Discrete Math and about domain of discourse

Determine the truth value and give the reason. Domain of discourse is $\mathbb R$ $$\forall x,\exists y, xy\ge0$$ Is the answer true?
ack17
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Subformula determining using two definitions

In Angelo Margaris's First Order Mathematical Logic a subformula is defined as follows, A subformula of the forumla $P$ is a consecutive part of $P$ that is itself a formula. Whereas in S. M. Srivatava's Course on Mathematical Logic it is defined…
user170039
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Logic: Who doesn't eat meat, is vegetarian

How to translate "Who doesn't eat meat, is vegetarian" into a formula with predicate letters Lx meaning x is meat, Exy meaning x eats y, and Vx meaning x is vegetarian? I tried, "for every x and for every y, if y is meat and x doesn't eat y, then x…
Godfried
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in finite structure formula true

P is a two digits relation-symbol and $\phi$ the formula: $(\forall x Pxx \wedge \forall x \forall y \forall z(Pxy \wedge P yz \rightarrow P xz) \wedge \forall x \forall y (Pxy \vee Pyx) \rightarrow \exists x \forall y Pxy) $ Proof that, if a…
Lauren Veganer
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Validity of three quantifier sentences using truth tree

I am having a lot of trouble figuring out how to close the paths of the Truth tree for the following argument: ∀x∀y∀z(Axy->Azx) Conclusion: (∃x∃yAxy ->∀x∀yAxy) My attempt is as follows: (1) ∀x∀y∀z(Axy->Azx) (2) -(∃x∃yAxy ->∀x∀yAxy) (3) ∃x∃yAxy (from…
SeesSound
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Prenex form of an expression: Cannot understand example

My new course in this semester starts of with predicate-logic and on the way touches prenex form, quantifiers, skolemization and unification - all topics quite new for me. I do not start completely from scratch but with little previous…
Ralf
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Deciding if a statement is true or false for given sets

Given the sets: $A = \{a,b,c\},\enspace B = \{a,b,A,C\},\enspace C = \{a,c\},\enspace D = \{A,B,C\},\enspace and\enspace G = \{A,B,C,D\}$ How can I determine if the following statement is true or false: $∃x ∈ D : ∃y ∈ x : y ∉ B ∪ x$ First…
stillenat
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