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Inference

Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.

For the 1992 album by pianist Marilyn Crispell and saxophonist Tim Berne, see Inference (album). For the process in statistics and machine learning, see Statistical inference.

Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and 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 variations.

Examples[edit]

Example for definition #1[edit]

Ancient Greek philosophers defined a number of syllogisms, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with a famous example:

Incorrect inference[edit]

An incorrect inference is known as a fallacy. Philosophers who study informal logic have compiled large lists of them, and cognitive psychologists have documented many biases in human reasoning that favor incorrect reasoning.

 – Two types of knowledge, justification, or argument

A priori and a posteriori

 – Inference seeking the simplest and most likely explanation

Abductive reasoning

 – Form of reasoning

Deductive reasoning

 – Method of logical reasoning

Inductive reasoning

 – Relationship between statements that hold true when one logically follows from another

Entailment

Epilogism

 – Cognitive process of transferring information or meaning from a particular subject to another

Analogy

Axiom system

Axiom

 – Logical inference from a single statement

Immediate inference

Inferential programming

 – Any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem

Inquiry

 – Study of correct reasoning

Logic

Logic of information

 – Statement in a metalanguage

Logical assertion

 – Type of diagrammatic or visual notation for logical expressions

Logical graph

 – Systematic logical process capable of deriving a conclusion from hypotheses

Rule of inference

List of rules of inference

 – In mathematics, a statement that has been proved

Theorem

 – Type of statistical inference

Transduction (machine learning)

Carnap, Rudolf; Jeffrey, Richard C., eds. (1971). Studies in Inductive Logic and Probability. Vol. 1. The University of California Press.

Jeffrey, Richard C., ed. (1980). . Vol. 2. The University of California Press. ISBN 9780520038264.

Studies in Inductive Logic and Probability

Angluin, Dana (1976). An Application of the Theory of Computational Complexity to the Study of Inductive Inference (Ph.D.). University of California at Berkeley.

Angluin, Dana (1980). (PDF). Information and Control. 45 (2): 117–135. doi:10.1016/s0019-9958(80)90285-5.

"Inductive Inference of Formal Languages from Positive Data"

Angluin, Dana; Smith, Carl H. (Sep 1983). (PDF). Computing Surveys. 15 (3): 237–269. doi:10.1145/356914.356918. S2CID 3209224.

"Inductive Inference: Theory and Methods"

Gabbay, Dov M.; Hartmann, Stephan; Woods, John, eds. (2009). Inductive Logic. Handbook of the History of Logic. Vol. 10. Elsevier.  978-0-444-52936-7.

ISBN

Goodman, Nelson (1983). . Harvard University Press. ISBN 9780674290716.

Fact, Fiction, and Forecast

Inductive inference:


Abductive inference:


Psychological investigations about human reasoning:

at PhilPapers

Inference

Inference example and definition