Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [logic-translation]

For translating between natural language expressions and logic expressions.

0
votes
0answers
20 views

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. ...
0
votes
2answers
43 views

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 \...
-3
votes
0answers
26 views

Answer depending on whether the exponent is odd or even?

Can the the answer be true for every even $x$ and false for every odd $x$? 4 $\exists x\in\mathbb N^*$ s.t. $y^x\ge0\ \forall x\in\mathbb R$ Translate. There is at one $x$ in $\mathbb N^*$, s.t. ...
1
vote
2answers
49 views

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 ...
-1
votes
0answers
29 views

English to predicate logic assistance

So I need to translate to predicate logic, I have to list the individuals/domains, the predicates, and lastly the formula. I have completed this one: ...
0
votes
0answers
68 views

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. ...
2
votes
1answer
45 views

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?
0
votes
1answer
27 views

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 ...
0
votes
1answer
25 views

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.” ...
0
votes
1answer
23 views

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 ...
1
vote
1answer
22 views

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 ...
1
vote
2answers
90 views

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. ...
0
votes
1answer
41 views

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 ...
0
votes
2answers
28 views

∀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 ...
0
votes
2answers
38 views

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 ...
0
votes
0answers
4 views

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?
3
votes
2answers
71 views

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 ...
0
votes
2answers
34 views

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. ...
0
votes
3answers
58 views

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 ...
2
votes
1answer
48 views

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 ...
0
votes
1answer
27 views

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 ...
0
votes
1answer
43 views

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): ...
0
votes
1answer
33 views

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 ...
0
votes
1answer
65 views

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 ...
0
votes
1answer
36 views

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 $...
1
vote
3answers
39 views

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 ...
2
votes
1answer
60 views

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 \...
0
votes
2answers
113 views

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 ...
0
votes
0answers
38 views

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): ...
4
votes
1answer
47 views

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): ...
4
votes
2answers
56 views

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 ...
0
votes
1answer
30 views

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 ...
1
vote
1answer
51 views

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: ...
1
vote
2answers
62 views

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:             &...
0
votes
1answer
57 views

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 ...
0
votes
1answer
20 views

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 ...
0
votes
1answer
25 views

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 ...
1
vote
2answers
74 views

“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 ...
2
votes
1answer
43 views

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 ...
0
votes
1answer
36 views

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 $S(x)$ ...
1
vote
2answers
86 views

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 ...
2
votes
1answer
128 views

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 $f$ ...
3
votes
2answers
41 views

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 ...
2
votes
2answers
352 views

“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: $∀x((L(x) \land \lnot O(x)) \to R(x))$...
0
votes
6answers
402 views

Is the negation of “p iff q”, “(not p) iff q”?

My logic teacher says that the negation of $p \!\!\iff\!\! q$ is $(\lnot p) \!\!\iff\!\! q$. This seems wrong to me, because I feel like $(\lnot p) \!\iff\! q$ is a too strong statement to be the ...
3
votes
4answers
112 views

truth value of “if…then…”

From the truth table, when both $p$ and $q$ are true, then "if $p$ then $q$" is true. However, this is a little weird as "if $p$ then $q$" is used to show the relationship between $p$ and $q$. If $q$ ...
1
vote
2answers
151 views

Predicate Statements— Every person loves at most only one reindeer

I was given a question by my professor during lecture today, to translate into predicate logic statements, "Every human loves a reindeer, but every human loves at most only 1 reindeer", without ...
0
votes
2answers
68 views

Confused with regard to converting English sentences to If-Then Conditional Logic

Whenever I come across questions, where they ask me to translate English sentences to propositional logic, I often have trouble figuring out which is the if and which part of the sentence is the Then....
-2
votes
1answer
44 views

“Many” quantifier in first order logic [closed]

Suppose I want to express this sentence in first-order logic: "Many printers are broken" If $p(x)$ is true if the term $x$ is a printer and $b(x)$ is true if $x$...
1
vote
1answer
33 views

Properly Translate Propositional Statement to Discrete Math

What is the proper way to write this statement mathematically? "All people are smokers or non-smokers but not both." $ H = humans, S = smoker, NS = non-smoker $ My first attempt was: $$\forall x \...