Convert sentences into First Order Logic

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Homework Help Overview

The discussion revolves around converting natural language sentences into First Order Logic (FOL). The subject area includes logic, mathematical reasoning, and formal language representation.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to translate sentences into FOL and are discussing the placement of parentheses to clarify quantifier scope. There are questions about the correctness of the initial translations and suggestions for improving clarity.

Discussion Status

Some participants have provided feedback on the translations, suggesting improvements and clarifications. There is an ongoing exploration of how to properly structure the logical statements, with no explicit consensus reached yet.

Contextual Notes

Participants are considering the implications of variable binding and the importance of parentheses in logical expressions. There is an acknowledgment of potential ambiguities in the original translations.

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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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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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)
 
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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