Wait until children reach about junior high age to start teaching logic. This is when most children are able to grasp the subject.
Teach logic in a concrete way. Children are not ready to understand abstracts associated with logic because the ability to full understand abstracts is not developed at this young age.
Introduce students to the two types of reasoning in formal logic: deductive and inductive. Deductive reasoning starts with a true statement, and breaks it down to reach a conclusion. For example, all cats are feline. Fluffy is a cat. Therefore, Fluffy is a feline. For inductive reasoning, start with a specific idea and work your way toward a broader statement: All people who have ever lived have a brain. Therefore, all people have brains.
Give the children more examples of logic and see if they can figure out if your examples are using inductive or deductive reasoning. The more examples they see, the easier it will be for them to differentiate the two.
Write out some examples of reasoning and ask the children to finish the logic statements. For example, you might write "Jerry is an Olympic runner. Olympic runners are fast." Then, ask the children to finish the statement starting with the word "Therefore." The answer, of course, is, "Therefore, Jerry is a fast runner."