Logic, as the trivium will treat it, is the art of ordering discourse toward truth. It presupposes significant speech: terms that mean, statements that can be true or false, questions and commands that are not statements, paragraphs that convince the audience of something true. You cannot follow an argument or an attempt to persuade without that argument or persuasive effort being put into language.
What about images? Sometimes we speak of images as having a rhetoric or a discourse or being able to persuade people of something. This is true, of course, but only figuratively speaking: an image cannot persuade you of anything; it is what the image seems to imply that may persuade you when you understand it in the right context. Imagine a candid image of a famous politician caught on camera doing something terrible and the politician had seen the camera right before the picture was taken and he is reaching toward the camera to block it. The image itself is damning, but only because we understand the context and know the politician and that the activities he was caught doing are wrong.
It is words that communicate, speak truth, and persuade.
Most readers here will begin with grammar. The reason is just that we must first be able to speak and hear correctly and to know what is meant with our words, before we can ask in detail whether what the words say is true or not.
If you wanted to begin with inference and logic, that's good. Nothing in these foundations will ask you to become less strict. They will ask you to become more strict about speech, since speech is where inference and discourse are always found. Ars Syllogistica will train you in inference. But you do well not to neglect the preliminary study, even if it is not a difficult one.
Next, we begin from ordinary experiences of being misunderstood, of teaching a name, of arguing, of reading a law. The art of inference belongs after that, true, but it does not replace grammar.
Continue to Why we begin with words.