1. There are at least 2 senses for the term 'argument':
2. SENSE 1: The broad sense of a dispute or disagreement (often heated or angry) between individuals
3. SENSE 2: The narrow sense of mere logical entailment
4. 
   
5. In accordance with SENSE 2, an argument is a connected series of statements
6. The 1^st half of this series is an n-member premise set (P1, P2, …,Pn)
7. The 2^nd half of this series is an n-member conclusion set (C1, C2, …,Cn)
8. 
   
9. 
   
10. In what follows, we shall be concerned with SENSE 2 rather than SENSE 1

1. We could have any of the following:
1. A single-member premise set and a single-member conclusion set;
2. A multiple-member premise set and a single-member conclusion set;
3. A single-member premise set and a multiple-member conclusion set; or
4. A multiple-member premise set and a multiple-member conclusion set.
2. 
   
3. Here is an EXAMPLE of an argument:
1. P1: All men are mortal.
2. P2: All that are identical to Socrates are men.
3. C: ∴ All that are identical to Socrates are mortal.
4. 
   
5. In the 'Socrates is mortal' argumentative EXAMPLE:
1. There is a 2-member premise set (viz. P1 and P2)
2. There is a single-member conclusion set (viz. C)

φ ⊦_L ψ

1. φ denotes the premise set
2. ψ denotes the conclusion set
3. ⊦ denotes a logical entailment relation between ϕ (the premise set) and ψ (the conclusion set)
4. L denotes the formal system under which the logical entailment relation holds
5. 
   
6. Q: What would a formal system L look like?