View source for Philosophy:Inference

{{Short description|Steps in reasoning}}
{{For multi|the 1992 album by pianist Marilyn Crispell and saxophonist Tim Berne|Inference (album)|the process in statistics and machine learning|Statistical inference}}

'''Inferences''' are steps in [[Philosophy:Reason|reason]]ing, moving from [[Premise|premise]]s to [[Logical consequence|logical consequence]]s; etymologically, the word ''infer'' means to "carry forward". Inference is theoretically traditionally divided into [[Deductive reasoning|deduction]] and [[Philosophy:Inductive reasoning|induction]], a distinction that in Europe dates at least to [[Biography:Aristotle|Aristotle]] (300s BCE). Deduction is inference [[Formal proof|deriving]] [[Logical consequence|logical conclusions]] from premises known or assumed to be [[Truth|true]], with the [[Rule of inference|laws of valid inference]] being studied in [[Logic|logic]]. Induction is inference from [[Physics:Particular|particular]] evidence to a [[Philosophy:Universal (metaphysics)|universal]] conclusion. A third type of inference is sometimes distinguished, notably by [[Biography:Charles Sanders Peirce|Charles Sanders Peirce]], contradistinguishing [[Abductive reasoning|abduction]] from induction.

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 [[Philosophy:Cognitive psychology|cognitive psychology]]; [[Artificial intelligence|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.

==Definition==
The process by which a conclusion is inferred from multiple observations is called [[Philosophy:Inductive reasoning|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." {{clarify|reason=Some information, probably encoded by different type fonts in the dictionary, seems to have got lost. I assume, under the keyword 'induction ([[Logic|logic]])', the dictionary says 'the inference of a general law from particular instances'. Please check with the source and clarify.|date=August 2013}}) The definition given thus applies only when the "conclusion" is general.

Two possible definitions of "inference" are:
# A conclusion reached on the basis of evidence and reasoning.
# The process of reaching such a conclusion.

==Examples==
===Example for definition #1===
[[Philosophy:Ancient Greek philosophy|Ancient Greek philosophers]] defined a number of [[Philosophy:Syllogism|syllogism]]s, correct three part inferences, that can be used as building blocks for more complex reasoning. We begin with a famous example:
# All humans are mortal.
# All Greeks are humans.
# All Greeks are 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 some 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 meat comes from animals.
#All beef is meat.
#Therefore, all beef comes from animals.

If the premises are true, then the conclusion is necessarily true, too.

Now we turn to an invalid form.
#All A are B.
#All C are B.
#Therefore, all C are 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. (True)
#All bananas are fruit. (True)
#Therefore, all bananas are apples. (False)

A valid argument with a false premise may lead to a false conclusion, (this and the following examples do not follow the Greek syllogism):
#All tall people are French. (False)
#John Lennon was tall. (True)
#Therefore, John Lennon was French. (False)

When a valid argument is used to derive a false conclusion from a false premise, 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 a false premise:
#All tall people are musicians. (Valid, False)
#John Lennon was tall. (Valid, True)
#Therefore, John Lennon was a musician. (Valid, True)

In this case we have one false premise and one true premise where a true conclusion has been inferred.

===Example for definition #2===

Evidence: It is the early 1950s and you are an American stationed in the [[Place:Soviet Union|Soviet Union]]. You read in the [[Place:Moscow|Moscow]] newspaper that a soccer team from a small city in Siberia starts winning game after game. The team even defeats the Moscow team. Inference: The small city in Siberia is not a small city anymore. The Soviets are working on their own nuclear or high-value secret weapons program.

Knowns: The Soviet Union is a command economy: people and material are told where to go and what to do. The small city was remote and historically had never distinguished itself; its soccer season was typically short because of the weather.

Explanation: In a command economy, people and material are moved where they are needed. 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. In addition, you put your best and brightest in places where they can do the most good—such as on high-value weapons programs. It is an anomaly for a small city to field such a good team. The anomaly indirectly described a condition by which the observer inferred a new meaningful pattern—that the small city was no longer small. Why would you put a large city of your best and brightest in the middle of nowhere? To hide them, of course.

==Incorrect inference==
An incorrect inference is known as a [[Fallacy|fallacy]]. Philosophers who study [[Philosophy:Informal logic|informal logic]] have compiled large lists of them, and cognitive psychologists have documented many [[Philosophy:Cognitive bias|biases in human reasoning]] that favor incorrect reasoning.

==Applications==

===Inference engines===

AI systems first provided automated logical inference and these were once extremely popular research topics, leading to industrial applications under the form of [[Expert system|expert system]]s and later business rule engines. More recent work on [[Automated theorem proving|automated theorem proving]] has had a stronger
basis in formal logic.

An inference system's job is to extend a knowledge base automatically. The [[Knowledge base|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 [[Relevance|relevant]] to its task.

Additionally, the term 'inference' has also been applied to the process of generating predictions from trained [[Artificial neural network|neural networks]]. In this context, an 'inference engine' refers to the system or hardware performing these operations. This type of inference is widely used in applications ranging from image recognition to [[Natural language processing|natural language processing]].

====Prolog engine====
[[Prolog]] (for "Programming in Logic") is a [[Programming language|programming language]] based on a [[Subset|subset]] of [[Philosophy:Predicate calculus|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|backward chaining]].

Let us return to our [[Biography:Socrates|Socrates]] [[Philosophy:Syllogism|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 {{imp}} Q'' (if P then Q) then in Prolog we would code ''Q''':-'''P'' (Q if P).)<br />
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 [[Biography:Plato|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)<br />
[[Prolog]] can be used for vastly more complicated inference tasks. See the corresponding article for further examples.

===Semantic web===
Recently automatic reasoners found in semantic web a new field of application. Being based upon [[Description logic|description logic]], knowledge expressed using one variant of [[Web Ontology Language|OWL]] can be logically processed, i.e., inferences can be made upon it.

===Bayesian statistics and probability logic===
{{main|Bayesian inference}}

Philosophers and scientists who follow the [[Bayesian inference|Bayesian framework]] for inference use the mathematical rules of [[Probability|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]].

===Fuzzy logic===

{{main||Fuzzy logic}}


=== Non-monotonic logic ===


A relation of inference is [[Philosophy:Monotonicity of entailment|monotonic]] if the addition of premises does not undermine previously reached conclusions; otherwise the relation is non-monotonic.
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 non-monotonic 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 [[Abductive reasoning|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==
* {{Annotated link|A priori and a posteriori|''A priori'' and ''a posteriori''}}
* {{Annotated link|Abductive reasoning}}
* {{Annotated link|Deductive reasoning}}
* {{Annotated link|Inductive reasoning}}
* {{Annotated link|Entailment}}
* {{Annotated link|Epilogism}}
* {{Annotated link|Analogy}}
* {{Annotated link|Axiom system}}
** {{Annotated link|Axiom}}
* {{Annotated link|Immediate inference}}
* {{Annotated link|Inferential programming}}
* {{Annotated link|Inquiry}}
* {{Annotated link|Logic}}
* {{Annotated link|Logic of information}}
* {{Annotated link|Logical assertion}}
* {{Annotated link|Logical graph}}
* {{Annotated link|Rule of inference}}
* {{Annotated link|List of rules of inference}}
* {{Annotated link|Theorem}}
* {{Annotated link|Transduction (machine learning)}}

==References==
{{Reflist}}

==Further reading==
{{refbegin}}
* {{cite book
 |first=Ian |last=Hacking
 |title=An Introduction to Probability and Inductive Logic
 |publisher=Cambridge University Press
 |year=2001

 |ref=Hacking, 2001
 |isbn=978-0-521-77501-4
}}
* {{cite book
 |first=Edwin Thompson
 |last=Jaynes
 |url=http://titles.cambridge.org/catalogue.asp?isbn=0521592712
 |title=Probability Theory: The Logic of Science
 |publisher=Cambridge University Press
 |year=2003
 |isbn=978-0-521-59271-0
 |ref=Jaynes, 2003
 |access-date=2004-11-29
 |archive-url=https://web.archive.org/web/20041011085524/http://titles.cambridge.org/catalogue.asp?isbn=0521592712
 |archive-date=2004-10-11
 |url-status=dead
 }}
* {{cite book
 |title=Information Theory, Inference, and Learning Algorithms
 |publisher=Cambridge University Press
 |year=2003
 |isbn=978-0-521-64298-9
 |url=http://www.inference.phy.cam.ac.uk/mackay/itila/book.html
 |ref=McKay, 2003
}}
* {{Russell Norvig 2003}}
* {{cite book
 |title=Understanding Probability
 |url=https://archive.org/details/understandingpro0000tijm |url-access=registration |publisher=Cambridge University Press
 |year=2004
 |ref=Tijms, 2004
 |isbn=978-0-521-70172-3
}}
{{refend}}

'''Inductive inference:'''
* {{cite book| title=Studies in Inductive Logic and Probability| year=1971| volume=1| publisher=The University of California Press| editor1-first=Rudolf |editor1-last=Carnap |editor2-first=Richard C. |editor2-last=Jeffrey}}
* {{cite book| title=Studies in Inductive Logic and Probability| year=1980| volume=2| publisher=The University of California Press| editor-first=Richard C. |editor-last=Jeffrey|url=https://books.google.com/books?id=Qfe0SEazn3oC| isbn=9780520038264}}
* {{cite thesis| type=Ph.D.| first=Dana |last=Angluin| title=An Application of the Theory of Computational Complexity to the Study of Inductive Inference| year=1976| publisher=University of California at Berkeley}}
* {{cite journal| first=Dana |last=Angluin| title=Inductive Inference of Formal Languages from Positive Data| journal=Information and Control| year=1980| volume=45|issue=2| pages=117–135| url=http://www-personal.umich.edu/~yinw/papers/Angluin80.pdf| doi=10.1016/s0019-9958(80)90285-5| doi-access=free}}
* {{cite journal| first1=Dana |last1=Angluin|first2= Carl H. |last2=Smith| title=Inductive Inference: Theory and Methods| journal=Computing Surveys|date=Sep 1983| volume=15| number=3| pages=237–269| url=http://users.dsic.upv.es/asignaturas/facultad/apr/AngluinSmith83.pdf| doi=10.1145/356914.356918|s2cid=3209224}}
* {{cite book| title=Inductive Logic| year=2009| volume=10| publisher=Elsevier| editor1-first=Dov M. |editor1-last=Gabbay |editor2-first=Stephan |editor2-last=Hartmann |editor3-first=John |editor3-last=Woods| series=Handbook of the History of Logic}}
* {{cite book| first=Nelson |last=Goodman| title=Fact, Fiction, and Forecast| year=1983| publisher=Harvard University Press|url=https://books.google.com/books?id=i97_LdPXwrAC|isbn=9780674290716}}

'''Abductive inference:'''
* {{cite book| title=Automated abduction: Inference to the best explanation| year=1997| publisher=AAAI Press| editor1-first=P. |editor1-last=O'Rourke |editor2-first=J. |editor2-last=Josephson}}
* {{cite book| first=Stathis |last=Psillos| title=An Explorer upon Untrodden Ground: Peirce on Abduction| year=2009| volume=10| pages=117–152| publisher=Elsevier| editor1-first=Dov M. |editor1-last=Gabbay |editor2-first=Stephan |editor2-last=Hartmann |editor3-first=John |editor3-last=Woods| series=Handbook of the History of Logic| url=http://users.uoa.gr/~psillos/PapersI/11-Peirce-Abduction.pdf}}
* {{cite thesis| type=Ph.D.| first=Oliver |last=Ray| title=Hybrid Abductive Inductive Learning|date=Dec 2005| publisher=University of London, Imperial College| citeseerx = 10.1.1.66.1877}}

'''Psychological investigations about human reasoning:'''
* '''deductive:'''
**{{cite book| first1 = Philip Nicholas |last1 = Johnson-Laird|  first2 = Ruth M. J. | last2 = Byrne| title=Deduction| year=1992| publisher=Erlbaum}}
**{{cite journal| first1=Ruth M. J.| last1=Byrne| first2=P. N.| last2=Johnson-Laird|  title="If" and the Problems of Conditional Reasoning| journal=Trends in Cognitive Sciences| year=2009| volume=13| number=7| pages=282–287| url=https://psych.princeton.edu/psychology/research/johnson_laird/pdfs/2009ifandtheproblemof.pdf| doi=10.1016/j.tics.2009.04.003| pmid=19540792| s2cid=657803| access-date=2013-08-09| archive-url=https://web.archive.org/web/20140407061602/https://psych.princeton.edu/psychology/research/johnson_laird/pdfs/2009ifandtheproblemof.pdf| archive-date=2014-04-07| url-status=dead}}
**{{cite journal | first1 = Markus | last1 = Knauff | first2 = Thomas | last2 = Fangmeier | first3 = Christian C. | last3 = Ruff | first4 = P. N. | last4 = Johnson-Laird |  title = Reasoning, Models, and Images: Behavioral Measures and Cortical Activity | journal = Journal of Cognitive Neuroscience | year = 2003 | volume = 15 | number = 4 | pages = 559–573 | url = http://www.uni-giessen.de/cms/fbz/fb06/psychologie/abt/kognition/dateien/kfrjl_JOCN.pdf | doi = 10.1162/089892903321662949 | pmid = 12803967 | hdl = 11858/00-001M-0000-0013-DC8B-C | citeseerx = 10.1.1.318.6615 | s2cid = 782228 | access-date = 2013-08-09 | archive-url = https://web.archive.org/web/20150518094338/http://www.uni-giessen.de/cms/fbz/fb06/psychologie/abt/kognition/dateien/kfrjl_JOCN.pdf | archive-date = 2015-05-18 | url-status = dead }}
**{{cite book| first = Philip N. | last = Johnson-Laird|  title=Mental Models, Deductive Reasoning, and the Brain| year=1995| pages=999–1008| publisher=MIT Press| editor-first = M. S. | editor-last = Gazzaniga| url=http://nbu.bg/cogs/events/2002/materials/Markus/mental_models.pdf}}
**{{cite book| first1 = Sangeet | last1 = Khemlani | first2 = P. N. | last2 = Johnson-Laird|  chapter=Illusory Inferences about Embedded Disjunctions| title=Proceedings of the 30th Annual Conference of the Cognitive Science Society. Washington/DC| year=2008| pages=2128–2133| chapter-url=http://mentalmodels.princeton.edu/papers/2008disjillusions.pdf}}
* '''statistical:'''
**{{cite journal | first1 = Rachel | last1 = McCloy | first2 = Ruth M. J. | last2 = Byrne | first3 = Philip N. | last3 = Johnson-Laird |  title = Understanding Cumulative Risk | journal = The Quarterly Journal of Experimental Psychology | year = 2009 | pages = 499–515 | url = http://psych.princeton.edu/psychology/research/johnson_laird/pdfs/2009%20Understanding%20cumulative%20risk.pdf | doi = 10.1080/17470210903024784 | pmid = 19591080 | volume = 63 | issue = 3 | s2cid = 7741180 | access-date = 2013-08-09 | archive-url = https://web.archive.org/web/20150518073242/http://psych.princeton.edu/psychology/research/johnson_laird/pdfs/2009%20Understanding%20cumulative%20risk.pdf | archive-date = 2015-05-18 | url-status = dead }}
**{{cite journal| first = Philip N. | last = Johnson-Laird |  title=Mental Models and Probabilistic Thinking| journal=Cognition| year=1994| volume=50| issue = 1–3 | pages=189–209| url=http://mentalmodels.princeton.edu/papers/1994probabilistic.pdf| doi=10.1016/0010-0277(94)90028-0| pmid = 8039361 | s2cid = 9439284 }},
* '''analogical:'''
**{{cite journal| first = B. D. | last = Burns| title=Meta-Analogical Transfer: Transfer Between Episodes of Analogical Reasoning| journal=Journal of Experimental Psychology: Learning, Memory, and Cognition| year=1996| volume=22| number=4| pages=1032–1048| doi=10.1037/0278-7393.22.4.1032}}
* '''spatial:'''
**{{cite journal| first1 = Georg | last1 = Jahn | first2 = Markus | last2 = Knauff | first3 = P. N. | last3 = Johnson-Laird|  title=Preferred mental models in reasoning about spatial relations| journal=Memory & Cognition| year=2007| volume=35| number=8| pages=2075–2087| url=http://mentalmodels.princeton.edu/papers/2007preferredmodels.pdf| doi=10.3758/bf03192939| pmid = 18265622 | s2cid = 25356700 | doi-access = free}}
**{{cite journal| first1 = Markus | last1 = Knauff | first2 = P. N. | last2 = Johnson-Laird |  title=Visual imagery can impede reasoning| journal=Memory & Cognition| year=2002| volume=30| number=3| pages=363–371| url=http://mentalmodels.princeton.edu/papers/2002imagery.pdf| doi=10.3758/bf03194937| pmid = 12061757 | s2cid = 7330724 | doi-access=free}}
**{{cite journal| first1 = James A. | last1 = Waltz | first2 = Barbara J. | last2 = Knowlton | first3 = Keith J. | last3 = Holyoak | first4 = Kyle B. | last4 = Boone | first5 = Fred S. | last5 = Mishkin | first6 = Marcia | last6 = de Menezes Santos | first7 = Carmen R. | last7 = Thomas | first8 = Bruce L. | last8 = Miller| title=A System for Relational Reasoning in Human Prefrontal Cortex| journal=Psychological Science|date=Mar 1999| volume=10| number=2| pages=119–125| url=https://www.researchgate.net/publication/228906574| doi=10.1111/1467-9280.00118| s2cid = 44019775 }}
* '''moral:'''
**{{cite journal| first1 = Monica | last1 = Bucciarelli | first2 = Sangeet | last2 = Khemlani | first3 = P. N. | last3 = Johnson-Laird |  title=The Psychology of Moral Reasoning| journal=Judgment and Decision Making|date=Feb 2008| volume=3| number=2| pages=121–139| doi = 10.1017/S1930297500001479 | s2cid = 327124 | url=http://journal.sjdm.org/jdm8105.pdf}}

== External links ==

* {{PhilPapers|category|inference}}
* [http://philosophyterms.com/inference/ Inference example and definition]
* {{InPho|taxonomy|2397}}

{{Logic}}
{{Philosophy topics}}


[[Category:Inference| ]]
[[Category:Concepts in epistemology]]
[[Category:Concepts in logic]]
[[Category:Concepts in metaphilosophy]]
[[Category:Concepts in metaphysics]]
[[Category:Concepts in the philosophy of mind]]
[[Category:History of logic]]
[[Category:Logic]]
[[Category:Logic and statistics]]
[[Category:Logical consequence]]
[[Category:Metaphysics of mind]]
[[Category:Reasoning]]
[[Category:Sources of knowledge]]
[[Category:Thought]]

{{Sourceattribution|Inference}}