What are the steps for using natural deduction in logic?

In summary, the speaker is seeking assistance with a Natural Deduction problem and has already used 'for all' elimination on three premises. They are unsure of the strategy needed to reach the conclusion and are seeking advice on what to manipulate to reach the conclusion. They have reduced the problem to a list of inference rules and are struggling to prove it. The speaker's initial assumption is assuming P(a,b) & P(b,a) and they are looking for help to proceed.
  • #1
Firepanda
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Logic: Natural Deduction

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Can anyone lead me off here? I've broken down the three premises using 'for all' elimination, now I need to start a subderivation with an assumption, but I'm not sure what!

Right now I'm unsure of the strategy I need to use to get to the conclusion, what do I want to be left with to manipulate into the conclusion?

Would be grateful for any help!

A list of the inference rules I have learned so far for Natural deduction can be found HERE
 
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  • #2
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I've reduced the problem to the above, if I can prove the above then I can prove the whole thing! (I think..!)

Any help on this one? Thanks :)
 
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  • #3
Apparantly my above inference isn't valid so I cannot proceed with this method

My initial assumption is assuming P(a,b) & P(b,a)

Really stuck, would appreciate help!

Thanks
 

Related to What are the steps for using natural deduction in logic?

1. What is natural deduction?

Natural deduction is a method of reasoning in logic that uses a set of rules to derive conclusions from given premises. It is based on the idea of breaking down complex arguments into simpler ones and using logical rules to show how the conclusion follows from the premises.

2. What are the benefits of using natural deduction?

One of the main benefits of natural deduction is its intuitive approach to reasoning. It allows for a clear and structured way of thinking about arguments and making logical inferences. Additionally, it is a flexible method that can be applied to a wide range of logical systems.

3. What are the basic components of natural deduction?

The basic components of natural deduction are premises, assumptions, rules of inference, and a conclusion. Premises are statements that are accepted as true, while assumptions are temporary statements used to support the derivation of the conclusion. Rules of inference are logical rules that allow for the manipulation and combination of statements, ultimately leading to the conclusion.

4. How does natural deduction differ from other methods of logical reasoning?

Natural deduction differs from other methods of logical reasoning in its use of rules of inference to derive conclusions. Other methods, such as truth tables, rely on evaluating all possible combinations of truth values to determine the validity of an argument. Natural deduction, on the other hand, focuses on the logical structure of arguments.

5. Can natural deduction be applied to real-world situations?

Yes, natural deduction can be applied to real-world situations. Its use in logic is not limited to theoretical or abstract concepts, but can also be used to analyze and evaluate arguments in everyday life. By breaking down complex arguments and applying logical rules, natural deduction can help us make more informed and rational decisions.

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