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Questions tagged [logic-translation]

For translating between natural language expressions and logic expressions.

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Translating English sentence to First Order Logic sentence

For the following natural language sentence: Hermione is the only Gryffindor student who does not like Flying class. My English to FOL conversion is as follows: ...
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Logic: “the cubic root of a rational number is also a rational number”

I was attempting an online logical and mathematical statements self-test from the University of Toronto and came across the following statement in question 1: The cubic root of a rational number is ...
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Conversion from Propositional Logic to Predicate Logic

I came across a proposition which I'm having a hard time converting into predicate logic. It has been a long while since I have touched the topic. The proposition reads \begin{align} &\text{...
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First order logic: Difference between sentences

My task is to translate the following 2 sentences to first-order logic. I can't figure if my proposed solution is also correct even though it doesn't match the professor's solution. $1$. No student ...
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Formalization / Symbolic representation: Average price for all elements out of set

I'm currently trying to formalize my research requirements for a thesis I'm currently working on. My research Question q1 finds all state-of-the-art products in a specific market. All these products ...
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Translating English to First Order Logic

For the following natural language sentence: No Slytherin students like any student in Gryffindor. How can it be converted to First Order Logic sentence? One possible conversion is: ...
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What is the proper way to read predicate logic?

Basically, in predicate logic, do we read from the inside outwards? In the example question, would 1a) be read as "For all values of y, there exists a value of x which divides y"? I've been told ...
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How would I convert this discrete math statement from logic/equation to English?

Given that $B(x)$ means "$x$ is a bear", $F(x)$ means "$x$ is a fish", and $E(x,y)$ means "$x$ eats $y$", what is the best English translation of $\forall x[F(x)\rightarrow \forall y(E(y,x)\...
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Propositional Logic Translation from sentence

I'm trying to translate below sentences to propositional logic but I don't know if my understanding of the main steps of translation are correct or not. I would like to ask for help to correct me. ...
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How can I convert this sentence to propositional logic (semantic and resolution)?

There were 3 people J, P, A. Only 2 people brought gifts to the party. If J brought a gift to the party, proof that P or A did not brought the gift. What I can think about this sentence is: $ J, P \...
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Propositional logic meets diplomacy at the workplace

This is just a funny little incident that made me think. Please don't take it too seriously or the wrong way. I would still like to hear your opinion on it, though. I wrote an email to a colleague ...
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English to predicate logic help

So essentially I'm given an English sentence and I must list the individuals and domains, the predicates, and the formulas. This first one I think I have correct, but needs checked. ...
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How to prove universally-quantified formula is true by contraposition?

For all natural numbers $x$ and $y$, if $x+y$ is odd, then $x$ is odd or $y$ is odd. How do I prove the following statement is true by contraposition without using a truth table and theorems?
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Express each of these sentences in terms of Q(x, y), quantifiers, and logical connectives [closed]

Let Q(x, y) be the statement “student x has been a contestant on quiz show y.” Express each of these sentences in terms of Q(x, y), quantifiers, and logical connectives, where the domain for x ...
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Does each variable in a premises undergoing Universal Instantiation have to change?

I'm currently working on this problem: “All movies produced by John Sayles are wonderful. John Sayles produced a movie about coal miners. Therefore, there is a wonderful movie about coal miners.” ...
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Translating Sentences into First Order Logic

My professor gave us a study guide a few days ago and the answers to it today. I did the study guide and thought I did it all right, but saw some of my answers were not the same as his. I tried ...
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First-order logic from computational linguistics - implication

I am reading Natural Language Understanding by James Allen. It has the following sentence That John is rich implies that he is happy. And first-order logic ...
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Translate this sentence to predicate logic

The question given asks to translate to predicate logic: Every positive real number has a unique positive real root. My solution to this problem is to separate it into the appropriate quantifiers. ...
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formalize in predicate logic: All students join some course that they don't like.

I came up with two formulas and have no Idea whether their correct. 1. ∀x(S(x)∧¬C(x)) 2. ∀x∃y(S(x)∧C(y)→DoesNotLike(x,y)) And then I have one a bit more complicated, that I can think of multiple ways ...
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∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer

∀x(I(x) → ∃y(I(y) ∧ (x < y))), I(x): x is an integer Is the following a correct translation? For all x, if x is an integer, then there exists an y such that y is an integer and x < y. Is this ...
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States that reach only bad states are bad. Predicate Logic

Consider a system of states with a binary relation R. If R(x,y) holds, we say that state x reaches state y. Further, consider two unary predicates I and B where I(x) means that x is an initial state ...
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Problem in Tranformation translation

The translation $T$ maps $A$ into $B$. Given that $T(P)=Q$ write coordinates of $Q$. How to attempt these type of questions?
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Express Negation in Simple English: There is a student in this class who has chatted with exactly one other student

Am I correct in the following: If the domain is all students, and C(x,y) is the predicate of x having chatted with y. Then the sentence There is a student in this class who has chatted with ...
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Translate a sentence into predicate logic

I want to translate this sentence There exists $a$ such that if for all $b$ different from $a$, $b$ has the propriety $P$ then $a$ has the propriety $Q$ I translated it like this : $\exists a. ...
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In Discrete Mathematics, is there a difference between $(\neg P \wedge \neg Q)$ and $\neg (P \wedge Q)$?

I am wondering, in discrete mathematics, whether there is a difference between $(\neg P \wedge \neg Q)$ and $\neg (P \wedge Q)$. My query comes from a practice problem in a book: Either John and ...
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Language, Proof & Logic (LPL) Exercise 11.21 - Sentences 7, 9

I'm working on LPL's Exercise 11.21, which asks to provide translations of the English language sentences into First Order Logic sentences. Unlike the majority of exercises in the book, as I ...
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Propositional Logic Translation

I am trying to convert the following into propositional logic in order to construct a semantic tableaux: If Mark goes to the party, then so does Pat. John or Pat will go to the party. John will not ...
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Predicate Logic Natural Number Problems

I am trying to translate the following statements into predicate logic using the following predicates: $E(x) = x$ is even, $P(x) = x$ is prime, $L(x,y) = x < y$ (i): Some Primes are Odd. (ii): ...
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Universal Quantified Statement being equivalent when variables are swapped

I was given this statement and asked to express this with universal quantifiers. Likes(x,y) is a Binary Relation that means that person x likes person y. The statement given was: "Everybody is ...
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How to write “There is at least 2 Cars are not the same Colour” in logic

I would like to know how to write “At least 2 Cars are not the same Colour” in logic. I know that "at least two cars" can be defined as ∃x(C(x)∧∃y(C(x)∧y≠x)). is ...
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Predicate Calculus and Statement

I'm having a hard time to understand predicate Calculus, Statement and Prolog programming. Let $male$ be a unary predicate symbol with the indicated meaning. Let $parent$, $son$, $sibling$, and $...
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Rewriting a logical statement

Only lakers are irrational people. I believe it technically should be translated as: All irrational people are lakers. Is there is any way at all to rewrite the above statement to mean the ...
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Rewriting predicate sentences to logically equivalent statements that doesn't use the negation operator

a) $\sim\! \exists x \in \mathbb{H}_{\sqrt{2}}, \forall n \in N, \sim\! \exists z \in \mathbb{R}, (x^n > z) \land \sim\! (z < n)$ b) $\exists x \in D, \sim\! \forall y \in C, \sim\! \exists n \...
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how to convert sentence that contains “no more than 3” into predicate logic sentence?

How to convert sentence that contains “no more than 3” into predicate logic sentence? For example: "No more than three $x$ satisfy $R(x)$" using predicate logic. This is what I have for "exactly ...
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Translating predicate logic statements to english [duplicate]

Consider the following predicates over the domains $B$ of all bunny rabbits, $M$ of all magicians, and $J$ of all jazz musicians. $F(x; y)$: person $x$ sent a friend request to person $y$. $D(x; y): ...
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Translating predicate logic statements

Consider the following predicates over the domains $B$ of all bunny rabbits, $M$ of all magicians, and $J$ of all jazz musicians. $F(x; y)$: person $x$ sent a friend request to person $y$. $D(x; y): ...
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Why is my translation of $\exists{x}\,(C(x) \rightarrow F(x))$ into an English sentence wrong?

Let $\text{C(x): x is a comedian}$ and $\text{F(x): x is funny}$ Let $$\alpha:\quad\exists{x}\,(C(x) \rightarrow F(x))$$ and the domain consists of all people. I needed to translate $\alpha$ into ...
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Logic Translation

"a and e are both larger than c, but neither is large" I thought the translation $$\large (\text{Larger}(a, c)\land \text{Larger}(e, c))\land\lnot(\text{Large}(a)\land \text{Large}(e))$$ would be ...
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First Order Predicate Logic

I would like some help to check my solution for the translation of a sentence into predicate logic. The sentence is given as: ...
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Translating Predicate Logic to English

$E(x,y)$: $x$ can eat $y$ $L(x,y)$: $x$ loves eating $y$ $D$ is the domain of all dogs $S$ is the domain of all snakes Predicate Logic to English:             &...
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Translating english sentences to predicate logic

Trying to practice translating english sentences into predicate logic and vice versa. $E(x,y)$: $x$ can eat $y$ $L(x,y)$: $x$ loves eating $y$ $D$ is the domain of all dogs $S$ is the domain of all ...
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Translating into Logical Statements

I was giving the following sentence to translate into a logical statement. “Everyone has exactly one best friend" The way I set it up is by letting ...
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is this predicate logic statement correct for this indirect proof?

Just for context, my goal is to prove the square root of 2 is an irrational number. I already did this using proof by contradiction both algebraically and geometrically, however, I want to begin the ...
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“Although it is necessary for $n$ to be prime in order for $R_n$ to be prime” as logic statement

This is a statement about Repunits from this paper. How can I write this as an if/then statement? Knowledge about Repunits isn't required. The question is basically: what does "although it is ...
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Confusion in determining an argument's validity?

I understand that an argument is basically an implication in the sense that: $$premise1 \land premise2 \land premise3.... \to conclusion$$ And an argument would be considered valid when such an ...
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logical equivalence in predicate logic

I was studying discrete mathematics, one of the basic subjects in cs department. In particular, studying the chapter "Logics", I came to have some trouble. While solving problem saying " Let $S(x)$ ...
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Negating first order logic

I am struggling to understand how to really negate in first order logic. Take the following examples: "Somebody loves everybody" Negating this would be: "It is not the case that somebody loves ...
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Rewrite each of the following sentences using logical connectives

Rewrite each of the following sentences using logical connectives. Assume that each symbol $f, x_0, n, x, S, B$ represents some fixed object. (a) If $f$ has a relative minimum at $x_0$ and if $f$ ...
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Predicate Is Before The Subject Is This The Correct Translation?

I'm trying to figure out what the proper translation in predicate logic would be for the example below, I'm confused because the predicate comes before the subject. So i'm wondering if I need to ...
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“Except” in predicate logic

I have a phrase that I am trying to translate into predicate logic. The phrase is as follows: All lions except old ones roar So far I have written down that: $∀x((L(x) \land \lnot O(x)) \to R(x))$...