To be clear, a is the acceleration of the object, F is the net force on the object, and m is the mass of the object.
Can we use commas for connecting independent clauses as a list? Is the above sentence grammatically correct, or is there a comma splice?
I think we can use semicolons instead of commas, but then there would be a lot of semicolons, which is, as I've learned, something to avoid if possible.
'To be clear' is a pragmatic marker (in this case one indicating clarifying specification in the matrix sentence), syntactically apart from the matrix sentence, and this setting off needs some separator. Introductory pragmatic markers (and there are many types), whether single- or multi-word, are usually set off by commas.
While semicolons could be used to separate main clauses (and are really needed in many cases – see 'comma splices' in other threads here), they are usually too heavy-duty between listed main clauses, as here. Also, more than one semicolon in a sentence is not normal, and a semicolon before 'and' is unusual.
However, the different roles of the first (parenthetical offsetting) comma and the other commas here clashes somewhat. I'd use:
I have seen such sentences many times in scientific articles. They used commas. This is correct.
For example, look at the following text in page 4 from the following paper:
Text: "where the ai.s are taken to normalize over all the {vj}, Q(.) is a smooth function, and U is the weight matrix to be learned."
Paper: Quanzeng You, Liangliang Cao, Hailin Jin, Jiebo Luo, "Robust Visual-Textual Sentiment Analysis: When Attention meets Tree-structured Recursive Neural Networks", MM’16, October 15-19, 2016, Amsterdam, Netherlands.
