First order logic : definitions

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The discussion centers on clarifying the differences between terms and atoms in first-order logic (FOL), with participants noting the inconsistent definitions found in various sources. There is confusion regarding the use of these terms, especially in examples where they seem interchangeable. Additionally, the term "monadic" is questioned, particularly in relation to its application in FOL. The current Wikipedia article on first-order logic lacks a clear definition of "atom," despite mentioning "atomic formulas." Participants encourage sharing specific sources to facilitate better understanding of these concepts.
Saduina
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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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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.
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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