Quick Definition: Using facts to reach logical conclusions
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.
Alternatively, inference may be defined as the non-logical, but rational means, through observation of patterns of facts, to indirectly see new meanings and contexts for understanding. Of particular use to this application of inference are anomalies and symbols. Inference, in this sense, does not draw conclusions but opens new paths for inquiry. (See second set of Examples.) In this definition of inference, there are two types of inference: inductive inference and deductive inference. Unlike the definition of inference in the first paragraph above, meaning of word meanings are not tested but meaningful relationships are articulated.
Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference.
Statistical inference uses mathematics to draw conclusions in the presence of uncertainty. This generalizes deterministic reasoning, with the absence of uncertainty as a special case. Statistical inference uses quantitative or qualitative (categorical) data which may be subject to random variation.