Correcting my first order logic translations

In summary, the problem is to translate sentences into first-order logic. The first sentence states that no barber shaves a person who is shaving themselves. The second sentence states that any barber shaves all persons who are not shaving themselves. The third sentence states that white birds are capable of flying. The last sentence states that a bird is happy if all its children can fly. Corrections and suggestions are welcome and the person apologizes for any mistakes in their English.
  • #1
toshiba_me
1
0

Homework Statement



Well the problem is: translate the following sentences in first order logic. I cannot verify whether they are correct or not. Maybe someone can point out my mistakes.

1. No barber shaves persons shaving themselves.
[tex](\neg \exists x)(Barber(x) \wedge (\forall y)(Shaves(y,y) \Leftrightarrow Shaves(x,y)))[/tex]

2. Any Barber shaves all the persons not shaving themselves.
[tex](\forall x)(Barber(x) \wedge (\forall y) (\neg \Shaves(y,y) \Leftrightarrow Shaves(x,y)))[/tex]

3. White birds can fly.
[tex](\forall x)(Bird(x) \wedge White(x) \rightarrow Fly(x))[/tex]

4. A bird is happy if all its children can fly.
[tex](\forall x,y)(ChildOf(x, y) \wedge Fly(x) \rightarrow Bird(y) \wedge Happy(y))[/tex]

Thanks for your help.

Please make corrections and suggestions whenever you do see fit. Excuse me for my english.
 
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  • #2
Homework Equations The Attempt at a Solution 1. No barber shaves persons shaving themselves.(\neg \exists x)(Barber(x) \wedge (\forall y)(Shaves(y,y) \Leftrightarrow Shaves(x,y)))2. Any Barber shaves all the persons not shaving themselves.(\forall x)(Barber(x) \wedge (\forall y) (\neg Shaves(y,y) \Leftrightarrow Shaves(x,y)))3. White birds can fly.(\forall x)(Bird(x) \wedge White(x) \rightarrow Fly(x))4. A bird is happy if all its children can fly.(\forall x,y)(ChildOf(x, y) \wedge Fly(x) \rightarrow Bird(y) \wedge Happy(y))
 

Related to Correcting my first order logic translations

1. How do I know if my first order logic translation is correct?

To determine the correctness of your first order logic translation, you can use a truth table or model to check if the logical equivalence holds. You can also consult with a fellow scientist or an expert in first order logic for feedback and verification.

2. What are some common mistakes to avoid when correcting first order logic translations?

Some common mistakes to avoid when correcting first order logic translations include incorrect quantifier scope, incorrect use of parentheses, missing or incorrect variables, and incorrect translation of complex sentences. It is important to carefully check each step of the translation process and to use proper notation and symbols.

3. Is there a specific method or approach to correcting first order logic translations?

There are several methods and approaches that can be used to correct first order logic translations. Some common methods include using proof rules, using truth tables or models, and consulting with experts. It is important to choose a method that works best for you and to carefully review and analyze each step of the translation process.

4. How can I improve my skills in translating and correcting first order logic statements?

One of the best ways to improve your skills in translating and correcting first order logic statements is through practice. You can also study and review examples and exercises, attend workshops or seminars, and collaborate with other scientists to exchange ideas and feedback. Additionally, reading and studying textbooks and articles on first order logic can also help improve your skills.

5. Are there any online resources or tools available to assist with correcting first order logic translations?

Yes, there are several online resources and tools available to assist with correcting first order logic translations. These include proof assistants, automated theorem provers, and online forums or communities where you can ask for help and feedback from other experts. However, it is important to use these resources as a supplement and not solely rely on them for correcting your translations.

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