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| + | [[Image:lighterstill.jpg]][[Image:Face_off_2small.jpg|right|frame]] |
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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. |
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| * [[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. |
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| ==The accuracy of inductive and deductive inferences== | | ==The accuracy of inductive and deductive inferences== |
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− | mortal(X) :- man(X). | + | mortal(X) :- man(X). |
− | man(socrates). </code> | + | man(socrates). |
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| 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. |
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| ==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. |
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| See [[Bayesian inference]] for examples. | | See [[Bayesian inference]] for examples. |
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− | ===Frequentist statistical inference===
| + | ==Frequentist statistical inference== |
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− | ===Fuzzy logic=== (to be written)
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| === Nonmonotonic logic === | | === Nonmonotonic logic === |
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| * 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]. |