Which field of science wasn't included to the trivium, the lower division of the seven liberal arts?

The trivium is the lower division of the seven liberal arts and comprises grammar, logic, and rhetoric.

Grammar, logic, and rhetoric were essential to a classical education, as explained in Plato's dialogues. The three subjects together were denoted by the word trivium during the Middle Ages, but the tradition of first learning those three subjects was established in ancient Greece. Contemporary iterations have taken various forms, including those found in certain British and American universities (some being part of the Classical education movement) and at the independent Oundle School in the United Kingdom.

Grammar teaches the mechanics of language to the student. This is the step where the student "comes to terms," defining the objects and information perceived by the five senses. Hence, the Law of Identity: a tree is a tree, and not a cat.

Logic (also dialectic) is the "mechanics" of thought and of analysis, the process of composing sound arguments and identifying fallacious arguments and statements and so systematically removing contradictions, thereby producing factual knowledge that can be trusted.

Rhetoric is the application of language in order to instruct and to persuade the listener and the reader. It is the knowledge (grammar) now understood (logic) and being transmitted outwards as wisdom (rhetoric).