First order logic : definitions

In summary, the conversation discusses the difference between terms and atoms in FOL logic. The terminology is not standardized and the Wikipedia article on first order logic does not define "atom." However, the adjective "atomic" is used in terms such as "atomic formulas."
  • #1
Saduina
1
0
Hi all,
Just a few question about FOL logic.

What is the difference between terms and atoms, I read lot's of differents definitions, then when I think that I've understood, I find an exemple where both are used without any difference (for ordering by instance).

An another question is :
What does monadic mean ? Monadic terms, litterals, ...

Thank you
 
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  • #2
Saduina said:
What is the difference between terms and atoms, I read lot's of differents definitions, then when I think that I've understood, I find an exemple where both are used without any difference (for ordering by instance).

I'm not a logician, so I'm unsure of how standardized such terminology is.

I'll give your thread a bump by noting that the current Wikipedia article on first order logic does not define the term "atom". It does define terms where the adjective "atomic" appears, such as "atomic formulas". The fact the adjective "atomic" appears in terminology doesn't require that the definition of the noun "atom" must be established.

Perhaps if you quote or cite some of the material that confuses you, another forum member can sort it out.
 

1. What is first order logic?

First order logic is a formal system used in mathematical and computer science to represent knowledge and make logical deductions. It is also known as first order predicate calculus or first order logic with identity.

2. What are the basic components of first order logic?

The basic components of first order logic include variables, quantifiers, logical connectives, and atomic formulas. Variables represent objects, quantifiers specify the scope of variables, logical connectives connect formulas, and atomic formulas are statements about objects.

3. How is first order logic different from propositional logic?

First order logic is more expressive and allows for the representation of complex relationships between objects, whereas propositional logic only deals with the truth values of simple statements. Additionally, first order logic uses quantifiers to specify the scope of variables, while propositional logic does not have this feature.

4. What is the importance of first order logic in artificial intelligence?

First order logic is a fundamental tool in artificial intelligence as it allows for the representation of knowledge and reasoning about objects and their relationships. It is used in various AI applications such as natural language processing, automated reasoning, and expert systems.

5. What are the limitations of first order logic?

First order logic has limitations in dealing with uncertainty, vagueness, and incomplete information. It also struggles with handling non-monotonic reasoning, which involves changing conclusions based on new information. These limitations have led to the development of other logic systems such as fuzzy logic and modal logic.

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