An inference is an implied, indirect meaning or logic attached to a statement or expression. To infer something in common usage is to suggest. In most cases an inference is considered to be a form of catalytic logic, where the inference leads to a natural assumption. The word is sometimes used as a negative description of a statement, implying that an inference is an insult.
Examples of Inference:
This is a logical sequence of meanings of inference:'I gather you were unavailable all night. I rang eight times, and got no answer.'
'What are you inferring? That I should have been available, so you could get in contact?"