Convert sentences into First Order Logic

So I'd write:(1) ∀x [(thin(x) ∧ tall(x) ∧ energetic(x)) → good_basketball_player(x)](2) ∃x [(tall(x) ∧ ¬ good_basketball_player(x))](3) ∀x [(do_exercise(x) ∨ eating_healthy_food(x)) → energetic(x)](4) thin(saman) ∧ tall(saman) ∧ do_exercise(saman)
  • #1
Upeksha
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(1) Anyone who is thin, tall and energetic will be good basketball player.
(2) Some people are tall but not good basketball players.
(3) Anyone who do exercise or eating healthy food will be energetic.
(4) Saman is thin and tall person who do exercises.

Write the above sentences in First Order Logic.

I have tried like this:

(1) ∀x thin(x) ∧ tall(x) ∧ energetic(x) → good_basketball_player(x)
(2) ∃x tall(x) ¬ good_basketball_player(x)
(3) ∀x do_exercise(x) ∨ eating_healthy_food(x) → energetic(x)
(4) thin(saman) ∧ tall(saman) ∧ do_exercise(saman)
 
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  • #2
Some parentheses in the first three sentences would help to make it clear which part the quantifiers apply to. You're also missing a ∧ in #2.
 
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  • #3
Thank you. Is it correct now?

(1) ∀x [thin(x) ∧ tall(x) ∧ energetic(x)] → good_basketball_player(x)
(2) ∃x [tall(x) ∧ ¬ good_basketball_player(x)]
(3) ∀x [do_exercise(x) ∨ eating_healthy_food(x)] → energetic(x)
(4) thin(saman) ∧ tall(saman) ∧ do_exercise(saman)
 
  • #4
I'd probably put parentheses around the whole statement for 1 and 3. Otherwise you've got a situation where x is both a free and a bound variable.
 
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FAQ: Convert sentences into First Order Logic

1. What is First Order Logic?

First Order Logic (FOL) is a formal language used in mathematics and computer science to represent statements or sentences in a structured and unambiguous way. It is also known as Predicate Logic or First Order Predicate Calculus.

2. How do you convert sentences into First Order Logic?

To convert a sentence into First Order Logic, you need to first identify the objects, properties, and relationships mentioned in the sentence. Then, you can use quantifiers (such as "for all" and "there exists") and logical connectives (such as "and", "or", and "not") to represent the sentence in a symbolic form.

3. What are the benefits of using First Order Logic?

First Order Logic allows for the expression of complex statements in a precise and concise manner. It also enables the use of mathematical tools for reasoning and analyzing the statements. Additionally, FOL is the basis for many automated reasoning systems and is widely used in artificial intelligence and knowledge representation.

4. Are there any limitations to First Order Logic?

One limitation of First Order Logic is that it cannot handle uncertainty or incomplete information. It also does not have the ability to express time or change, which can be important in certain contexts. Additionally, FOL can become complex and difficult to interpret when dealing with large or highly nested sentences.

5. How is First Order Logic used in science?

First Order Logic is used in science to formalize and represent scientific theories, hypotheses, and laws. It allows scientists to express and analyze statements about the world in a precise and logical manner. FOL is also used in the development of computational models and simulations in various scientific fields.

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