To determine the correct statement about a deductive argument, it is important to understand what a deductive argument is. In logic, a deductive argument is one where the conclusion is necessarily true if the premises are true. This is because the conclusion follows with logical necessity from the premises.

Now, let us evaluate each of the given options based on this definition:

1. Option 1: "The relation between premises and conclusion is one of matter of fact"
   • A "matter of fact" suggests an empirical observation, which is not inherent in deductive reasoning.
   • Deductive arguments rely on logical structure rather than empirical observations.
   • This option does not accurately describe the deductive process, and thus, it is incorrect.
2. Option 2: "The relation between premises and conclusion is one of logical necessity"
   • In deductive arguments, if the premises are true, the conclusion must also be true due to logical necessity.
   • This accurately describes the nature of deductive reasoning, aligning with its characteristics.
   • Therefore, this option is correct.
3. Option 3: "The relation between premises and conclusion is that of empirical necessity"
   • Empirical necessity refers to conclusions based on observed or experimental evidence.
   • Deductive arguments are not based on empirical evidence but on logical consistency.
   • Hence, this option does not fit the deductive context and is incorrect.
4. Option 4: "The relation between premises and conclusion is a matter of ascertainment of probability"
   • Probability pertains to inductive reasoning where conclusions are likely or probable, not certain.
   • Deductive reasoning provides certainty given true premises, not mere probability.
   • Thus, this option is inappropriate for deductive reasoning and is incorrect.

Conclusion: Based on the evaluation above, the correct statement about a deductive argument is that "The relation between premises and conclusion is one of logical necessity."