Are our ways of conceptual construction the same or not in the scholarship of teaching and learning logic even if we use the same formal language to represent the world?

This question points out differences between many logica docens. For example, comparing the most commonly used textbooks Artificial Intelligence: A Modern Approach (Stuart Russell and Peter Norvig) with one of the most commonly used formal logic textbooks Logic and Philosophy: A Modern Introduction (Tidman, Hausman, and Kahane) in Taiwan, the logic (first-order logic), delivered in the former one, is obviously a kind of representation. Other ways for representations include semantic webs and frames. In this way, logic is a kind of descriptive formal language. The elementary logic, delivered in the latter one, is often taught in the philosophy department. Although propositional logic and predicate logic are also logical systems obtained by using formal languages, the two crucial notions: logical consequence and logical truth actually play the most important role in this subject; the validity and soundness are two important logical properties that we are concerned in such a course.

The unit Logic in the course Introduction to Artificial Intelligence is a kind of application of logic (applied logic) in a specific sense, and the elementary logic is a theoretic subject, which lies in the intersections of formal logic and philosophy. In general education at university level in Taiwan, where a literacy-based curriculum (information literacy) course design could possibly be a continuation of the 12-year Base Education Curricula in Taiwan, do we still have to focus on the latter? Besides, in both cases, there seems to be no need to teach natural deduction. In short, do we still need to teach any natural deduction system?