Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE).
A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
Statistical inference uses quantitative or qualitative (categorical) data which may be subject to random variations.
The process by which a conclusion is inferred from multiple observations is called inductive reasoning.
That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference.
To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.
The small city was remote and historically had never distinguished itself; its soccer season was typically short because of the weather.
Large cities might field good teams due to the greater availability of high quality players; and teams that can practice longer (possibly due to sunnier weather and better facilities) can reasonably be expected to be better.
More recent work on automated theorem proving has had a stronger basis in formal logic.
Additionally, the term 'inference' has also been applied to the process of generating predictions from trained neural networks.
This type of inference is widely used in applications ranging from image recognition to natural language processing.
Its main job is to check whether a certain proposition can be inferred from a KB (knowledge base) using an algorithm called backward chaining.
Recently automatic reasoners found in semantic web a new field of application.
Philosophers and scientists who follow the Bayesian framework for inference use the mathematical rules of probability to find this best explanation.
By contrast, everyday reasoning is mostly non-monotonic because it involves risk: we jump to conclusions from deductively insufficient premises.
More recently logicians have begun to approach the phenomenon from a formal point of view.
The result is a large body of theories at the interface of philosophy, logic and artificial intelligence.