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According to Wikipedia:

In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system

  • How can something be a semantic version of another thing? What does that even mean(hehe)?

  • I'm also having a hard time grasping how a concept that is about the form of something be a concern of semantics instead of syntax.

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  • The point is precisely that logical form maps form (syntax) to meaning (semantics). A statement is a syntactic entity; the LF provides its semantics.
    – lemontree
    Apr 20 at 16:22
  • @lemontree Thanks. So are you saying in a formal system, a statement is just a WFF devoid of meaning?
    – csp
    Apr 20 at 16:49
  • Think of logical form as a template ("form") with fillable spots that gets semantically interpreted by substituting objects from models into them. It is a semantic version of the formal sentence with non-logical (interpretable) symbols, but different formal sentences can represent the same form (be semantically equivalent).
    – Conifold
    Apr 20 at 18:03
  • @Conifold Thanks. But what role does semantics play in transforming(hehe) formal sentences into a logical form? I don't see the difference between how logical forms are being described and just saying logical forms have certain syntactical rules, and we use semantics only on those forms. So I can't make sense of saying logical forms ARE semantic versions of sentences, nor how anything can be a semantic version of anything.
    – csp
    Apr 20 at 18:41
  • Different sentences can have the same semantic form, i.e. it can be expressed by different formulas. For example, A and ~~A express the same form. So semantic form is not something you transform into, it is not uniquely represented by a formula, it is the logical meaning that the formula has. Hence "semantic", just like ordinary meanings are semantic versions of ordinary words.
    – Conifold
    Apr 20 at 19:53
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Below is from reference here:

To demonstrate the important notion of the form of an argument, substitute letters for similar items throughout the sentences in the original argument. Original argument:

All humans are mortal. Socrates is human. Therefore, Socrates is mortal.

Argument form:

All H are M. S is H. Therefore, S is M.

All that has been done in the argument form is to put H for human and humans, M for mortal, and S for Socrates. What results is the form of the original argument. Moreover, each individual sentence of the argument form is the sentence form of its respective sentence in the original argument.

Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.

So clearly logical forms are not unique and can be expressed in different ways such as propositional or more formal predicative first order fashions, but the key thing is it has to preserve its original semantic meaning from natural language. The idea is that once you arrive at a correct formal logical form, it should be fairly easy and nearly automatic to determine its formal validity (such as using proof checker programs). You may regard its corresponding formal system's inference rules as the more syntactic part to complete the above evaluation.

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It literally boils down to perspective. If you say something with a specific intent and it is understood under a different context, it becomes a matter of semantics. Often times, this is brought up in argumentative scenarios because the digestion of said statement will support one side of the argument more than the other. When, at the end of the day? It can be construed or misconstrued however people decide to take it. But the intent can only be that...

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