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'''Inference''' is the act or process of deriving a [[conclusion]] based solely on what one already knows.
'''Inference''' is the act or process of deriving a [[conclusion]] based solely on what one already knows.
* [[Statistics|Statisticians]] have developed formal rules for inference from quantitative data.
* [[Statistics|Statisticians]] have developed formal rules for inference from quantitative data.
* [[Artificial intelligence]] researchers develop automated inference systems.
* [[Artificial intelligence]] researchers develop automated inference systems.
==The accuracy of inductive and deductive inferences==
==The accuracy of inductive and deductive inferences==
mortal(X) :- man(X).
mortal(X) :- man(X).
man(socrates). </code>
man(socrates).
This states that all men are mortal and that Socrates is a man. Now we can ask [[Prolog]] about Socrates.
This states that all men are mortal and that Socrates is a man. Now we can ask [[Prolog]] about Socrates.
==Inference and uncertainty==
==Inference and uncertainty==
[[Image:Inference_model.jpg|right|frame]]
Traditional logic is only concerned with [[certainty]] - one progresses from certain [[Premise_%28argument%29|premises]] to certain conclusions. There are several motivations for extending logic to deal with uncertain propositions and weaker modes of reasoning.
Traditional logic is only concerned with [[certainty]] - one progresses from certain [[Premise_%28argument%29|premises]] to certain conclusions. There are several motivations for extending logic to deal with uncertain propositions and weaker modes of reasoning.
See [[Bayesian inference]] for examples.
See [[Bayesian inference]] for examples.
==Frequentist statistical inference==
=== Nonmonotonic logic ===
=== Nonmonotonic logic ===
* Ian Hacking. ''An Introduction to Probability and Inductive Logic''. Cambridge University Press, (2000).
* Ian Hacking. ''An Introduction to Probability and Inductive Logic''. Cambridge University Press, (2000).
* Edwin Thompson Jaynes. [http://titles.cambridge.org/catalogue.asp?isbn=0521592712 ''Probability Theory: The Logic of Science''.] Cambridge University Press, (2003). ISBN 0-521-59271-2.
* Edwin Thompson Jaynes. [https://titles.cambridge.org/catalogue.asp?isbn=0521592712 ''Probability Theory: The Logic of Science''.] Cambridge University Press, (2003). ISBN 0-521-59271-2.
* David J.C. McKay. ''Information Theory, Inference, and Learning Algorithms''. Cambridge University Press, (2003).
* David J.C. McKay. ''Information Theory, Inference, and Learning Algorithms''. Cambridge University Press, (2003).
* Stuart Russell, Peter Norvig. ''Artificial Intelligence: A Modern Approach''. Prentice Hall, (2002).
* Stuart Russell, Peter Norvig. ''Artificial Intelligence: A Modern Approach''. Prentice Hall, (2002).
* Henk Tijms. ''Understanding Probability''. Cambridge University Press, (2004).
* Henk Tijms. ''Understanding Probability''. Cambridge University Press, (2004).
* André Fuhrmann: [http://www.uni-konstanz.de/FuF/Philo/Philosophie/Fuhrmann/papers/nomoLog.pdf Nonmonotonic Logic].
* André Fuhrmann: [https://www.uni-konstanz.de/FuF/Philo/Philosophie/Fuhrmann/papers/nomoLog.pdf Nonmonotonic Logic].
