What is the meaning of the word "assertion"? I often see the word "assertion" in logic books. They may list a sentence like :
Snow is white.
Then somewhere in the context, they may write "assertion of that sentence". I'm confused about the meaning of the word "assertion". In the following sentences, which is equivalent to which?

*

*Snow is white.

*"Snow is white" is true.

*assert snow is white

*assert "Snow is white" is true

*think/believe snow is white

*think/believe "Snow is white" is true

*say/write/utter "Snow is white"

 A: You are looking for the meaning of ASSERTION in *isolation & hence you are getting into the listed variations to figure out some meaning, where variations 1,2,3,4 are all Equivalent.
[[ "Believe , think" are generally not used in Logic , might be used in Decision Support Systems or Belief Networks or Probability or Fuzzy Logic or Such ]]
The right way (in my View Point) is not by considering variations , but by comparing with other Concepts.
The CORE Issue is that DENIAL & ASSERTION & NEGATION go together in Logic.
ASSERTION is when we say that some thing is true.
"P" or "P is true" or "It is true that P"
NEGATION is when we say that the opposite is true.
"$Q == \lnot P$"
DENIAL is when we want to state something is not true , which is a nuanced or stronger way than NEGATION.
"Q ~~ It is not true that P"
There are some Logicians who state that "NEGATION == DENIAL" while some other Logicians state that "DENIAL of P" is DISTINCT from "$\lnot P$". Luckily I am not a Logician , hence I am not able to make out much between these two Cases !!
In such Discussions among Logicians , ASSERTION & DENIAL & NEGATION are the necessary terminology.
Eg : "Snow is White" :  We can either ASSERT it [ "Snow is White" / "It is true that Snow is White" / "Yes , Snow is White" ] or we can DENY it [ "It is not true that Snow is White" ] or we can NEGATE it (ASSERT the NEGATION) [ "Snow is not White" ]
Eg : "1+2=12" : We can either ASSERT it [ "1+1=12" / "It is true that 1+1=12" / "Yes , 1+12 is 12" ] or we can DENY it "It is not true that 1+2=12" or we can NEGATE it (ASSERT the NEGATION) [ "1+2 is not 12" ]
Here are a few references :
 Oxford  : Negation and Denial [ Stephen Mumford ] :
"It is assumed that we can Assert that something is not the case. A simple alternative would be to deny that thing instead. .... Assertion requires a truthmaker and is relatively determinate. .... The account tells us that, rather than Assert not-P, we are better simply denying P."
 Science Direct  : Assertion and Denial: A contribution from logical notations [ Ahti-Veikko Pietarinen Francesco Bellucci ] :
"This paper presents two major aspects of Frege's and Peirce's views on Assertion and Denial .... choices concerning the representation of Assertion and Denial .... We show that while Frege's notation has an ad hoc sign of assertion and an ad hoc sign of negation, Peirce has a sign of assertion which is also a sign of logical conjunction, and a sign of scope which is also a sign of negation."
 Cambridge  : Negation and Denial [ Stephen Mumford ] :
"How do Negation and Denial relate? Is one of them prior to or more basic than the other? .... There is at least a Prima facie connection between them, since one way in which we can deny something is to say that it is not the case. .... Even if Negation and Denial belong to different categories, however, it is plausible that some relation holds between them."
