- published: 08 Mar 2009
- views: 61657
- author: jmsalsich
Youtube results:
add
Loading...
Branches of Mathematics
Pure mathematics
Applied mathematics
- Dynamical systems and differential equations
- Mathematical physics
- Computing
- Information theory and signal processing
- Probability and statistics
- Game theory
- Operations research
Related Topics
- Electromagnetic Spectrum
- Linear Equations
- Applied Physics
- Nano Technology
- Engineering Sciences
- Mathematical Medicine
- Fluid dynamics
- Computational Mathematics
- Gamma Ray Optics
- Onfrared Optics
- Relative Velocity
- Iciam
- Intelligent Imaging Neuroscience
- Biomedical Engineering
- Neuroscience Research
- Quantum Cosmology
- Brain Research
Open Collage in a new Window
Email the Collage
- Loading...
Loading suggestions ...
- Absolute idealism
- Aesthetics
- Africana philosophy
- Agriculturalism
- Alan Ross Anderson
- Alan Turing
- Alexander Bain
- Alfred Tarski
- Alonzo Church
- Ambiguity
- American philosophy
- Analogy
- Analytic philosophy
- Anarchism
- Ancient philosophy
- Anti-realism
- Antinomy
- Argument
- Argumentation theory
- Aristotelianism
- Aristotle
- Atomism
- Augustus De Morgan
- Averroes
- Averroism
- Avicenna
- Axiology
- Axiom
- Axiomatic system
- Aztec philosophy
- Backward chaining
- Bayes' theorem
- Bayesian inference
- Behaviorism
- Belief
- Bertrand Russell
- Bias
- Boolean function
- Boolean logic
- British philosophy
- Buddhist philosophy
- Business rule
- Business rule engine
- Cantor's theorem
- Cartesianism
- Category Logic
- Category Philosophy
- Certainty
- Chinese philosophy
- Christian philosophy
- Chrysippus
- Church–Turing thesis
- Class (set theory)
- Classical liberalism
- Classical logic
- Cogency
- Cognitive bias
- Cognitive psychology
- Compatibilism
- Completeness
- Computability theory
- Computable function
- Conceptualism
- Confucianism
- Consequentialism
- Consistency
- Countable set
- Credibility
- Critical thinking
- Cynicism
- Cārvāka
- Danish philosophy
- David Hilbert
- David J. C. MacKay
- Decidability (logic)
- Decision problem
- Deconstruction
- Deductive reasoning
- Deductive system
- Definition
- Degree of truth
- Deontic logic
- Deontology
- Description
- Description logic
- Determinism
- Dialetheism
- Domain of a function
- Doxastic logic
- Dualism
- Duns Scotus
- E. T. Jaynes
- Effective method
- Empiricism
- Empty set
- Entailment
- Entscheidungsproblem
- Enumeration
- Epicureanism
- Epiphenomenalism
- Epistemology
- Ernst Schröder
- Ernst Zermelo
- Ethical egoism
- Ethics
- Event (philosophy)
- Evidence
- Existentialism
- Expert system
- Explanation
- Explanatory power
- Extensionality
- Fact
- Fallacy
- Feminist philosophy
- Fictionalism
- Finitary relation
- Finite model theory
- Finite set
- Finitism
- First-order logic
- Formal language
- Formal proof
- Formal system
- Formation rule
- Frankfurt School
- Free will
- French philosophy
- Fuzzy finite element
- Fuzzy logic
- Fuzzy rule
- Fuzzy set
- Fuzzy set operations
- Georg Cantor
- George Boole
- George Boolos
- Gerhard Gentzen
- German philosophy
- Giuseppe Peano
- Gottlob Frege
- Greek philosophy
- Haskell Curry
- Hegelianism
- Henk Tijms
- Hermeneutics
- Heyting arithmetic
- Hilary Putnam
- Hindu philosophy
- History of logic
- Idealism
- Illuminationism
- Immediate inference
- Index of philosophy
- Indian philosophy
- Inductive reasoning
- Inference
- Inference engine
- Informal logic
- Inquiry
- Intuitionism
- Intuitionistic logic
- Iranian philosophy
- Islamic philosophy
- Italian philosophy
- Jain philosophy
- Japanese philosophy
- Jewish philosophy
- Jon Barwise
- Jurisprudence
- Kalam
- Kantianism
- Kokugaku
- Korean Confucianism
- Korean philosophy
- Kurt Gödel
- Kyoto school
- Legal positivism
- Leopold Löwenheim
- Linear logic
- List of fallacies
- List of logicians
- List of paradoxes
- List of philosophers
- List of philosophies
- Logic
- Logic of information
- Logical assertion
- Logical atomism
- Logical connective
- Logical form
- Logical graph
- Logical positivism
- Logical truth
- Logicism
- Ludwig Wittgenstein
- Marxist philosophy
- Materialism
- Mathematical logic
- Mathematics
- Mazdak
- Medieval philosophy
- Metalogic
- Metamathematics
- Metaphilosophy
- Metaphysics
- Metatheorem
- Modal logic
- Modal operator
- Model theory
- Modern philosophy
- Modernism
- Mohism
- Monism
- Moral absolutism
- Moral particularism
- Moral universalism
- Name
- Natural deduction
- Neo-Confucianism
- Neo-Kantianism
- Neo-Thomism
- Neoplatonism
- Neotaoism
- New Confucianism
- Nihilism
- Nominalism
- Non-classical logic
- Non-standard model
- Nonmonotonic logic
- Norm (philosophy)
- Ontology
- Ontology language
- Opinion
- Ordered pair
- Outline of logic
- Pain (philosophy)
- Paraconsistent logic
- Paradox
- Parsimony
- Paul Bernays
- Peripatetic school
- Peter Geach
- Peter Norvig
- Philosophical logic
- Philosophy
- Philosophy of design
- Philosophy of film
- Philosophy of logic
- Philosophy of mind
- Philosophy of music
- Philosophy of sex
- Philosophy of war
- Plato
- Platonic realism
- Platonism
- Polish philosophy
- Political philosophy
- Portal Logic
- Portal Philosophy
- Portal Thinking
- Possible world
- Post-structuralism
- Power set
- Pragmatism
- Predicate calculus
- Predicate logic
- Premise
- Presupposition
- Probability
- Process philosophy
- Programming language
- Prolog
- Proof theory
- Propaganda
- Proposition
- Prudence
- Pythagoreanism
- Quantification
- Range (mathematics)
- Rationalism
- Raymond Smullyan
- Reality
- Reason
- Reasoning
- Reasoning System
- Recursion
- Recursive set
- Reference
- Relativism
- Relevance
- Relevance logic
- Renaissance humanism
- Rhetoric
- Rigour
- Romanian philosophy
- Rudolf Carnap
- Rule of inference
- Russian philosophy
- Satisfiability
- Saul Kripke
- Scholasticism
- School of Names
- Second-order logic
- Semantic web
- Semantics
- Set (mathematics)
- Set theory
- Sherlock Holmes
- Socrates
- Solipsism
- Sophism
- Soundness
- Square of opposition
- Statement (logic)
- Stephen Cole Kleene
- Stoicism
- Strict implication
- Structural rule
- Structuralism
- Stuart J. Russell
- Subset
- Substitution (logic)
- Substructural logic
- Sufi philosophy
- Syllogism
- Symbol (formal)
- Symbology
- Syntax (logic)
- Taoism
- Template Logic
- Template talk Logic
- Temporal logic
- Term logic
- Theorem
- Theories of humor
- Thomism
- Thoralf Skolem
- Transcendentalism
- Truth
- Truth table
- Truth value
- Type theory
- Uncountable set
- Utilitarianism
- Vagueness
- Validity
- Venn diagram
- Vienna Circle
- Virtue Ethics
- Well-formed formula
- Western philosophy
- Wikipedia INCITE
- William of Ockham
- Yangism
- Zen
- Zoroastrianism
- Zurvanism
- Alan Ross Anderson
- Alan Turing
- Alexander Bain
- Alfred Tarski
- Alonzo Church
- Aristotle
- Augustus De Morgan
- Averroes
- Averroism
- Avicenna
- Bertrand Russell
- Chrysippus
- David Hilbert
- Duns Scotus
- Ernst Schröder
- Ernst Zermelo
- Georg Cantor
- George Boole
- George Boolos
- Gerhard Gentzen
- Giuseppe Peano
- Gottlob Frege
- Haskell Curry
- Henk Tijms
- Hilary Putnam
- Jon Barwise
- Kurt Gödel
- Leopold Löwenheim
- Ludwig Wittgenstein
- Mazdak
- Paul Bernays
- Peter Geach
- Peter Norvig
- Plato
- Raymond Smullyan
- Romanian philosophy
- Rudolf Carnap
- Saul Kripke
- Sherlock Holmes
- Socrates
- Stephen Cole Kleene
- Thoralf Skolem
- William of Ockham
Send this Playlist by SMS
Email this Page
Making Inferences
- Order: Reorder
- Duration: 5:32
- Updated: 23 Apr 2013
Third grade students from Mr. Salsich's class (http://jmsalsich.edublogs.org/) at Deans Mill School explain how to make inferences while reading.
http://wn.com/Making_Inferences
Third grade students from Mr. Salsich's class (http://jmsalsich.edublogs.org/) at Deans Mill School explain how to make inferences while reading.
Inferences Song
- Order: Reorder
- Duration: 4:37
- Updated: 24 Apr 2013
Inferences are where you make educated guesses based on what you've read in the story. For example, if you read a story where people are starving on a 20 day...
http://wn.com/Inferences_Song
Inferences are where you make educated guesses based on what you've read in the story. For example, if you read a story where people are starving on a 20 day...
- published: 06 Nov 2011
- views: 27579
- author: Michael Coone
Inference
- Order: Reorder
- Duration: 2:11
- Updated: 20 Apr 2013
Inference Song.
http://wn.com/Inference
Inference and Drawing Conclusions
- Order: Reorder
- Duration: 5:33
- Updated: 17 Apr 2013
http://wn.com/Inference_and_Drawing_Conclusions
What is Inference
- Order: Reorder
- Duration: 2:31
- Updated: 03 Mar 2013
What is inference??
http://wn.com/What_is_Inference
Observation vs. Inference
- Order: Reorder
- Duration: 2:27
- Updated: 17 Apr 2013
Explaining the difference between observations and inferences through a discrepant event.
http://wn.com/Observation_vs_Inference
Explaining the difference between observations and inferences through a discrepant event.
- published: 28 Jun 2008
- views: 20003
- author: Traci Bricker
Precision Teaching: Inference Game
- Order: Reorder
- Duration: 4:08
- Updated: 12 Dec 2012
In this clip, students are actively engaged in a game that reinforces their understanding of the term "inference." The teacher pulls unfamiliar objects from ...
http://wn.com/Precision_Teaching_Inference_Game
In this clip, students are actively engaged in a game that reinforces their understanding of the term "inference." The teacher pulls unfamiliar objects from ...
- published: 02 Nov 2011
- views: 7947
- author: Knatim
SAT & ACT Reading: Making Inferences
- Order: Reorder
- Duration: 3:29
- Updated: 26 Mar 2013
Learn SAT and ACT test strategies about how to answer questions that ask you to infer the answer based on a reading passage by predicting an answer and looki...
http://wn.com/SAT_ACT_Reading_Making_Inferences
Learn SAT and ACT test strategies about how to answer questions that ask you to infer the answer based on a reading passage by predicting an answer and looki...
- published: 21 Sep 2010
- views: 7908
- author: KaplanSATACT
The Ladder of Inference Creates Bad Judgment
- Order: Reorder
- Duration: 3:34
- Updated: 23 Apr 2013
http://www.groupharmonics.com - Award-winning author Ed Muzio describes Chris Argyris' "Ladder of Inference" model and how you can use it to avoid making inc...
http://wn.com/The_Ladder_of_Inference_Creates_Bad_Judgment
http://www.groupharmonics.com - Award-winning author Ed Muzio describes Chris Argyris' "Ladder of Inference" model and how you can use it to avoid making inc...
- published: 26 Jan 2011
- views: 20369
- author: Ed Muzio
Statistical Inference
- Order: Reorder
- Duration: 2:06
- Updated: 14 Apr 2013
The meaning and purpose of statistical inference and the tools that statisticians have created in order to enable you to estimate how close and with what con...
http://wn.com/Statistical_Inference
The meaning and purpose of statistical inference and the tools that statisticians have created in order to enable you to estimate how close and with what con...
- published: 14 Jan 2010
- views: 9819
- author: FelsInstitute
INFERENCE SONG
- Order: Reorder
- Duration: 0:42
- Updated: 22 Apr 2013
Inference Song.
http://wn.com/INFERENCE_SONG
Lecture 5 -Logical Inference
- Order: Reorder
- Duration: 59:15
- Updated: 11 Mar 2013
Discrete Mathematical Structures -Logical Inference.
http://wn.com/Lecture_5_-Logical_Inference
Discrete Mathematical Structures -Logical Inference.
- published: 04 Dec 2007
- views: 38767
- author: nptelhrd
21. Bayesian Statistical Inference I
- Order: Reorder
- Duration: 48:50
- Updated: 08 Apr 2013
MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis...
http://wn.com/21_Bayesian_Statistical_Inference_I
MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis...
- published: 09 Nov 2012
- views: 2644
- author: MIT
23. Classical Statistical Inference I
- Order: Reorder
- Duration: 49:32
- Updated: 25 Apr 2013
MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis...
http://wn.com/23_Classical_Statistical_Inference_I
MIT 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010 View the complete course: http://ocw.mit.edu/6-041F10 Instructor: John Tsitsiklis...
- published: 09 Nov 2012
- views: 1769
- author: MIT
6 Inference E
- Order: Reorder
- Duration: 11:00
- Updated: 19 Sep 2012
Statistical Inference: Actually Doing it, Part 2. An introduction to the p-value.
http://wn.com/6_Inference_E
Statistical Inference: Actually Doing it, Part 2. An introduction to the p-value.
- published: 04 Mar 2010
- views: 1084
- author: BurkeyAcademy
(ML 7.1) Bayesian inference - A simple example
- Order: Reorder
- Duration: 14:52
- Updated: 26 Mar 2013
Illustration of the main idea of Bayesian inference, in the simple case of a univariate Gaussian with a Gaussian prior on the mean (and known variances).
http://wn.com/ML_71_Bayesian_inference_A_simple_example
Illustration of the main idea of Bayesian inference, in the simple case of a univariate Gaussian with a Gaussian prior on the mean (and known variances).
- published: 23 Jun 2011
- views: 13133
- author: mathematicalmonk
Inferring Video - Bigger than Alexander - Grade 5 - Lesson
- Order: Reorder
- Duration: 2:04
- Updated: 09 Apr 2013
Video about a boy named Alexander who can't stop growing at school and has to move away. The teacher decides to bring her classroom to Alexander. Alexander b...
http://wn.com/Inferring_Video_Bigger_than_Alexander_Grade_5_Lesson
Video about a boy named Alexander who can't stop growing at school and has to move away. The teacher decides to bring her classroom to Alexander. Alexander b...
- published: 09 Sep 2011
- views: 42823
- author: Chris Francis
The Logic of Statistical Inference
- Order: Reorder
- Duration: 13:48
- Updated: 07 Apr 2013
Reviews the conceptual logic of statistical inference as the fundamental decision making process behind hypothesis testing for addressing research questions.
http://wn.com/The_Logic_of_Statistical_Inference
Reviews the conceptual logic of statistical inference as the fundamental decision making process behind hypothesis testing for addressing research questions.
- published: 16 Jul 2012
- views: 515
- author: Ray Cooksey
Logic: Argument Forms / Rules of Inference
- Order: Reorder
- Duration: 14:16
- Updated: 22 Apr 2013
Symbolic Logic!! This video offers a basic explanation of "modus ponens", "modus tollens", and "hypothetical syllogism", including examples and non-examples.
http://wn.com/Logic_Argument_Forms_Rules_of_Inference
Symbolic Logic!! This video offers a basic explanation of "modus ponens", "modus tollens", and "hypothetical syllogism", including examples and non-examples.
- published: 08 Jul 2012
- views: 1832
- author: MrDLPmath
Rules of Inference I
- Order: Reorder
- Duration: 10:00
- Updated: 20 Apr 2013
http://wn.com/Rules_of_Inference_I
Google SketchUp Technique Series: Inference Locking
- Order: Reorder
- Duration: 7:16
- Updated: 05 Apr 2013
http://sketchup.google.com/ Inference locking is the ability to draw or move in only one locked direction in SketchUp. This video will teach you how to use t...
http://wn.com/Google_SketchUp_Technique_Series_Inference_Locking
http://sketchup.google.com/ Inference locking is the ability to draw or move in only one locked direction in SketchUp. This video will teach you how to use t...
- published: 16 Jun 2008
- views: 172474
- author: SketchUpVideo
TOEFL iBT Reading Section Inference Questions - Video Lesson | www.i-Courses.org
- Order: Reorder
- Duration: 5:35
- Updated: 23 Apr 2013
Visit http://i-Courses.org Short video lesson presenting the Inference question type in TOEFL iBT Reading part. This type of questions tests your ability to ...
http://wn.com/TOEFL_iBT_Reading_Section_Inference_Questions_Video_Lesson_|_wwwi-Coursesorg
Visit http://i-Courses.org Short video lesson presenting the Inference question type in TOEFL iBT Reading part. This type of questions tests your ability to ...
- published: 03 Jan 2013
- views: 760
- author: iCourses TOEFL
Observation & Inference
- Order: Reorder
- Duration: 7:54
- Updated: 22 Aug 2012
Unit 1 Lesson 2 video covering the basics of observation and inference.
http://wn.com/Observation_Inference
Unit 1 Lesson 2 video covering the basics of observation and inference.
- published: 22 Aug 2012
- views: 522
- author: Kelly Williams
photo: AP / A.M. Ahad
24 Apr 2013
Dhaka. At least 100 people were killed and over 600 injured Wednesday when an eight-storeyed building crumbled on the outskirts of capital Dhaka. Rescued workers complained they were forced to get back to work though the building was evacuated just a day earlier after cracks appeared. Those trapped under the rubble screamed for help as rescuers scrambled to get them out. The building, "Rana Plaza", collapsed around 8.45 am ... IANS ... ....(size: 2.7Kb)
Newstrack India
26 Apr 2013
Tweet. Wellington, Apr 26 (ANI) ... Stating that he was not aware of any facts that could support inferences contained in "The Taylor Affair", Parker said he was wrong in inferring that Hesson acted in a dishonest, improperly motivated or a manipulative way as coach of the Black Caps, Stuff.co.nz reports ... (ANI). Read More ... ) .. ). ... . . . . . .. . . .. ....(size: 1.8Kb)
Stockhouse
26 Apr 2013
Gold Tonnes (g/t) Ounces Main Vein Measured Mineral Resources 5,064 32.46 5,269 Main Vein Indicated Mineral Resources 21,423 29.14 20,006 Total Measured and Indicated Mineral Resources 26,487 29,77 25,275 Main Vein Inferred Mineral Resources 69,440 27.83 61,940 Highway Vein Inferred Mineral Resources 8,490 12.21 3,323 Parallel Vein Inferred Mineral Resources 7,647 24.98 6,123 Total Inferred Mineral Resources 85,577 26.03 71,385 ... ....(size: 7.2Kb)
Stuff
26 Apr 2013
In a written statement, John Parker confirmed that he was not aware of any facts that could support inferences contained in “The Taylor Affair” that Mike Hesson had been dishonest, improperly motivated or acted in a ......(size: 1.2Kb)
Otago Daily Times
26 Apr 2013
The Guardian
26 Apr 2013
Is George Osborne the worst chancellor?. As in worst chancellor of the exchequer ever? Probably not. There have been some real clowns ... Osborne, as far as we know, has never done this, although you do see some of his policies and think. "He must have made that up in the car.". Is George Osborne evil?. Nah. He just looks it ... If we infer from this that a chancellor requires no financial expertise whatsoever then Osborne isn't just qualified ... ....(size: 2.5Kb)
noodls
26 Apr 2013
Maiden JORC Inferred Resource completed at the Medcalf Project ... Audalia received notification from the Department of Mines and Petroleum (DMP) in February 2013 that the proposed drill programme designed to test the vanadium-titanium mineralisation to quantify an inferred resource was approved....(size: 14.9Kb)
Independent online (SA)
26 Apr 2013
Johannesburg - Former Ekurhuleni metro police chief Robert McBride knew from the start that he was not guilty of drunken driving, and the fact that he had won his appeal came as no surprise ... The judges drew the inference that the three were under pressure to change their original statements on the drunken driving charge and that their statements should have been rejected ... Pretoria News. ....(size: 3.1Kb)
Stockhouse
26 Apr 2013
http.//at.marketwire.com/accesstracking/AccessTrackingLogServlet?docid=0869228001&sourceType=1http.//media3.marketwire.com/logos/20120524-focusgraphite_200.jpg ... and certain other parties ... The Lac Knife project hosts a NI 43-101 compliant Measured and Indicated mineral resource of 4.972 Mt grading 15.7% carbon as crystalline graphite with an additional Inferred mineral resource of 3.000 Mt grading 15.6% crystalline graphite ... Mr ... 101 ... ....(size: 2.9Kb)
Zeenews
26 Apr 2013
Washington ... Sarah Ballard, a post-doctoral researcher at the UW, is using the technique, known as "characterization by proxy," to infer the properties of small, relatively cool stars too distant for measurement, by comparing them to closer stars that now can be directly observed. Ballard is lead author of a study that used this method and observations from the Kepler Space Telescope to learn the nature of the distant star Kepler-61 ... ....(size: 3.5Kb)
noodls
26 Apr 2013
(Source. Energy Ventures Ltd). L EV EL 1. 8 C OL I N S TR EE T. W EST P ER T H WA 600 5. PO B OX 886 ... ABN 89 106 52 3 611 ... 36.7 Mlb eU3O8 at a grade of 253 ppm eU3O8, and an Inferred Resource of 1.2 Mlb eU3O8 at a grade of ... The information contained in this announcement has been presented in accordance with the JORC Code and references to "Measured", "Indicated" and "Inferred Resources" are to those terms as defined in the JORC Code....(size: 10.4Kb)
Sun Sentinel
26 Apr 2013
University degree requirements sometimes require students to complete a rigorous final project, called a thesis. Four students slated to graduate soon from Florida Atlantic University's master of fine arts in visual art program are displaying the fruits of those creative labors ... The sets focus on a different culinary experience ... "Uncounted Cadences" draws on musical and cinematic inferences of volume, pacing and rhythm, Lavetsky said ... ....(size: 3.7Kb)
noodls
26 Apr 2013
The Elaine JORC Inferred Resource of 27.7 million tonnes with a contained metal content of 147,000 tonnes of copper and 75,000 ounces of gold was defined in 2012 ... MKED036 was designed primarily for metallurgical testwork to obtain samples to measure copper and gold recovery rates within the previously announced 27.7Mt Elaine copper-gold Inferred Resource....(size: 16.7Kb)
Indiewire
26 Apr 2013
.. What’s up with those crazy Danish filmmakers and their compulsion to pile it on? The latest from Oscar-winning filmmaker Susanne Bier (“In A Better World”) is like watching a long game of Jenga ... And while “Love is All You Need” is by no means a disaster, it simply can’t support all that weight ... a wedding ... Brosnan’s Philip is a long-widowed workaholic prone to declaring what should be inferred quite easily by simply watching the movie....(size: 4.3Kb)
 |
This article needs attention from an expert on the subject. Please add a reason or a talk parameter to this template to explain the issue with the article. WikiProject Logic may be able to help recruit an expert. (November 2008) |
 |
This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (April 2010) |
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true.[1] The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.
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 allows for inference from quantitative data.
Contents |
Definition of inference[link]
The process by which a conclusion is inferred from multiple observations is called inductive reasoning. The conclusion may be correct or incorrect, or correct to within a certain degree of accuracy, or correct in certain situations. Conclusions inferred from multiple observations may be tested by additional observations.
This definition is disputable (due to its lack of clarity. Ref: Oxford English dictionary: "induction ... 3. Logic the inference of a general law from particular instances.") The definition given thus applies only when the "conclusion" is general.
1. A conclusion reached on the basis of evidence and reasoning. 2. The process of reaching such a conclusion: "order, health, and by inference cleanliness".
Examples of inference[link]
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 the most famous of them all:
- All men are mortal
- Socrates is a man
- Therefore, Socrates is mortal.
The reader can check that the premises and conclusion are true, but Logic is concerned with inference: does the truth of the conclusion follow from that of the premises?
The validity of an inference depends on the form of the inference. 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. An inference can be valid even if the parts are false, and can be invalid even if the parts are true. But a valid form with true premises will always have a true conclusion.
For example, consider the form of the following symbological track:
- All fruits are sweet.
- A banana is a fruit.
- Therefore, a banana is sweet.
For the conclusion to be necessarily true, the premises need to be true.
Now we turn to an invalid form.
- All A are B.
- C is a B.
- Therefore, C is an A.
To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion.
- All apples are fruit. (Correct)
- Bananas are fruit. (Correct)
- Therefore, bananas are apples. (Wrong)
A valid argument with false premises may lead to a false conclusion:
- All fat people are Greek.
- John Lennon was fat.
- Therefore, John Lennon was Greek.
When a valid argument is used to derive a false conclusion from false premises, the inference is valid because it follows the form of a correct inference.
A valid argument can also be used to derive a true conclusion from false premises:
- All fat people are musicians
- John Lennon was fat
- Therefore, John Lennon was a musician
In this case we have two false premises that imply a true conclusion.
Incorrect inference[link]
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.
Automatic logical inference[link]
AI systems first provided automated logical inference and these were once extremely popular research topics, leading to industrial applications under the form of expert systems and later business rule engines.
An inference system's job is to extend a knowledge base automatically. The knowledge base (KB) is a set of propositions that represent what the system knows about the world. Several techniques can be used by that system to extend KB by means of valid inferences. An additional requirement is that the conclusions the system arrives at are relevant to its task.
Example using Prolog[link]
Prolog (for "Programming in Logic") is a programming language based on a subset of predicate calculus. Its main job is to check whether a certain proposition can be inferred from a KB (knowledge base) using an algorithm called backward chaining.
Let us return to our Socrates syllogism. We enter into our Knowledge Base the following piece of code:
mortal(X) :- man(X). man(socrates).
( Here :- can be read as "if". Generally, if P Failed to parse (Missing texvc executable; please see math/README to configure.): \to
Q (if P then Q) then in Prolog we would code Q:-P (Q if P).)
This states that all men are mortal and that Socrates is a man. Now we can ask the Prolog system about Socrates:
?- mortal(socrates).
(where ?- signifies a query: Can mortal(socrates). be deduced from the KB using the rules) gives the answer "Yes".
On the other hand, asking the Prolog system the following:
?- mortal(plato).
gives the answer "No".
This is because Prolog does not know anything about Plato, and hence defaults to any property about Plato being false (the so-called closed world assumption). Finally ?- mortal(X) (Is anything mortal) would result in "Yes" (and in some implementations: "Yes": X=socrates)
Prolog can be used for vastly more complicated inference tasks. See the corresponding article for further examples.
Use with the semantic web[link]
Recently automatic reasoners found in semantic web a new field of application. Being based upon first-order logic, knowledge expressed using one variant of OWL can be logically processed, i.e., inferences can be made upon it.
Bayesian statistics and probability logic[link]
Philosophers and scientists who follow the Bayesian framework for inference use the mathematical rules of probability to find this best explanation. The Bayesian view has a number of desirable features—one of them is that it embeds deductive (certain) logic as a subset (this prompts some writers to call Bayesian probability "probability logic", following E. T. Jaynes).
Bayesians identify probabilities with degrees of beliefs, with certainly true propositions having probability 1, and certainly false propositions having probability 0. To say that "it's going to rain tomorrow" has a 0.9 probability is to say that you consider the possibility of rain tomorrow as extremely likely.
Through the rules of probability, the probability of a conclusion and of alternatives can be calculated. The best explanation is most often identified with the most probable (see Bayesian decision theory). A central rule of Bayesian inference is Bayes' theorem.
See Bayesian inference for examples.
[edit] Nonmonotonic logic[2]
A relation of inference is monotonic if the addition of premises does not undermine previously reached conclusions; otherwise the relation is nonmonotonic. Deductive inference, is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added.
By contrast, everyday reasoning is mostly nonmonotonic because it involves risk: we jump to conclusions from deductively insufficient premises. We know when it is worth or even necessary (e.g. in medical diagnosis) to take the risk. Yet we are also aware that such inference is defeasible—that new information may undermine old conclusions. Various kinds of defeasible but remarkably successful inference have traditionally captured the attention of philosophers (theories of induction, Peirce’s theory of abduction, inference to the best explanation, etc.). 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.
See also[link]
References[link]
 |
Look up inference or infer in Wiktionary, the free dictionary. |
- Hacking, Ian (2011). An Introduction to Probability and Inductive Logic. Cambridge University Press. ISBN 0-521-77501-9.
- Jaynes, Edwin Thompson (2003). Probability Theory: The Logic of Science. Cambridge University Press. ISBN 0-521-59271-2. http://titles.cambridge.org/catalogue.asp?isbn=0521592712.
- McKay, David J.C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press. ISBN 0-521-64298-1. http://www.inference.phy.cam.ac.uk/mackay/itila/book.html.
- Russell, Stuart J.; Norvig, Peter (2003), Artificial Intelligence: A Modern Approach (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN 0-13-790395-2, http://aima.cs.berkeley.edu/
- Tijms, Henk (2004). Understanding Probability. Cambridge University Press. ISBN 0-521-70172-4.
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
http://wn.com/Inference
This page contains text from Wikipedia, the Free Encyclopedia - http://en.wikipedia.org/wiki/Inference
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
