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Analogy
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'''Analogy''' in a more simple understanding is a similar [[structure]] to a given structure or the use of a similar [[example]] or [[model]] to explain something.
To be more precise one can say that it is both the [[wiktionary:cognitive|cognitive]] process of transferring [[information]] from a particular subject (the analogue or source) to another particular subject (the target), and a [[language|linguistic]] expression corresponding to such a process.
==See also==
* [[Conceptual metaphor]]
* [[Metaphor]]
* [[Allegory]]
==Other websites and references==
{{Wiktionarypar|analogy}}
* [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-09 ''Dictionary of the History of Ideas:''] Analogy in Early Greek Thought.
* [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-10 ''Dictionary of the History of Ideas'':] Analogy in Patristic and Medieval Thought.
* [http://plato.stanford.edu/entries/analogy-medieval/ ''Stanford Encyclopedia of Philosophy'':] Medieval Theories of Analogy.
*[http://www.psych.northwestern.edu/psych/people/faculty/gentner/allpubs.htm Dedre Gentner's publications page], most of them on analogy and available for download.
*[http://www.coe.uga.edu/twa/ Shawn Glynn’s publications page], all on teaching with analogies and some available for download.
*[http://reasoninglab.psych.ucla.edu/KeithPublications.htm Keith Holyoak's publications page], many on analogy and available for download.
* Chalmers, D.J. et al. (1991). Chalmers, D.J., French, R.M., Hofstadter, D., [http://consc.net/papers/highlevel.pdf High-Level Perception, Representation, and Analogy].
* Forbus, K. et al. (1998). [http://www.psych.northwestern.edu/psych/people/faculty/gentner/newpdfpapers/ForbusGentner98.pdf Analogy just looks like high-level perception].
* Gentner, D., Holyoak, K.J., Kokinov, B. (Eds.) (2001). [http://cognet.mit.edu/library/books/view?isbn=0262571390 The Analogical Mind: Perspectives from Cognitive Science.] Cambridge, MA, MIT Press, ISBN 0-262-57139-0
* Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company.
* Juthe, A. (2005). [http://www.cs.hut.fi/Opinnot/T-93.850/2005/Papers/juthe2005-analogy.pdf "Argument by Analogy"], in Argumentation (2005) 19: 1–27.
* Holland, J.H., Holyoak, K.J., Nisbett, R.E., and Thagard, P. (1986). [http://cognet.mit.edu/library/books/view?isbn=0262580969 Induction: Processes of Inference, Learning, and Discovery]. Cambridge, MA, MIT Press, ISBN 0-262-58096-9.
* Holyoak, K.J., and Thagard, P. (1995). [http://cognet.mit.edu/library/books/view?isbn=0262581442 Mental Leaps: Analogy in Creative Thought]. Cambridge, MA, MIT Press, ISBN 0-262-58144-2.
* Holyoak, K.J., and Thagard, P. (1997). [http://cogsci.uwaterloo.ca/Articles/Pages/Analog.Mind.html The Analogical Mind].
*Hummel, J.E., and Holyoak, K.J. (2005). [http://reasoninglab.psych.ucla.edu/KH%20pdfs/hummel&holyoak_cdips_2005.pdf Relational Reasoning in a Neurally Plausible Cognitive Architecture]
* Lamond, G. (2006). [http://plato.stanford.edu/entries/legal-reas-prec/ Precedent and Analogy in Legal Reasoning], in Stanford Encyclopedia of Philosophy.
* Turney, P.D., and Littman, M.L. (2005). [http://arxiv.org/abs/cs.LG/0508103 Corpus-based learning of analogies and semantic relations]. Machine Learning, 60 (1-3), 251-278.
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Begging the question
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'''Begging the question''' requires two or more [[idea]]s. Each of these ideas may or may not be [[true]]. The [[speaker]] of these ideas tries to show that one idea is true by saying a second idea proves it, but the second idea is only true if the first idea is true already.
Begging the question is commonly known as [[circular reasoning]], though they are not exactly the same.[http://en.wikipedia.org/wiki/Begging_the_question#Related_fallacies]
Begging the question is a [[fallacy]].
== Examples ==
* "If such actions were not illegal, then they would not be prohibited by the law."[http://www.nizkor.org/features/fallacies/begging-the-question.html]
* "We know God exists because we can see the perfect order of His Creation, an order which demonstrates supernatural intelligence in its design."[http://skepdic.com/begging.html]
== Modern usage ==
"This begs the question" has recently been used to mean "this raises the question." This usage is often [[wiktionary:criticize|criticized]] as [[wiktionary:inappropriate|inappropriate]].
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Category:Logic
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[[zh:Category:邏輯]]
Common sense
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'''Common sense''' means what people would agree about. It is actually a personal judgement based on the situation and facts.<ref>{{cite web|url=http://mw1.merriam-webster.com/dictionary/common%20sense|title=Definition of common sense|publisher= Merriam Webster dictionary|accessdate = 2007-09-09}}</ref> Common sense is sometimes the best guide to what is acceptable by others.
== References ==
{{reflist}}
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Connotation
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{{wiktionarypar|connotation}}
'''Connotation''' is a meaning that is suggested or implied, as opposed to a [[denotation]], or literal [[definition]].
==Usage==
Today the word has different meanings, but it is always used for the contrast of a word or phrase with its primary, [[literal]] meaning (known as a denotation). That can be an implied value judgement or feelings.
*A stubborn person may be described as being either ''strong-willed'' or ''pig-headed''. Although these have the same literal meaning (i.e. ''stubborn''), ''strong-willed'' connotes admiration for the level of someone's will, while ''pig-headed'' '''connotes''' frustration in dealing with someone. Likewise, ''used car'' and ''previously owned car'' have the same literal meaning, but many dealerships prefer the latter, since it is thought to have fewer ''negative'' ''connotations''.
*It is often useful to avoid words with strong connotations (especially [[pejorative|negative]] ones) when striving to achieve a neutral point of view. A desire for more positive connotations, or fewer negative ones, is one of the main reasons for using [[euphemism]]s.
== Other websites ==
* [http://portal.acm.org/citation.cfm?id=505555&dl=ACM&coll=portal Connotations of problem solving]
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Denotation
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:''For the opposite of Denotation see [[Connotation]].''
{{wiktionary|denote}}
*In [[logic]], [[linguistics]] and [[semiotics]], a '''denotation''' of a [[word]] or [[phrase]] is a part of its meaning.
==Examples==
In order to understand fully the difference between denotation and [[connotation]] in the media studies and semiotics uses it is necessary to become familiar with some examples:
{|
|-
| [[Image:Cartoony red rose.svg|100px|left|Example one.]]
The denotation of this example is a red [[rose]] with a green [[Plant stem|stem]]. The connotation is that it is a '''symbol''' of passion and love - this is what the rose represents.
|-
| [[Image:Cartoony cross.svg|100px|left|Example two.]]
The denotation is a brown cross. The connotation is a '''symbol''' of [[religion]], according to the media connotation. However, to be more specific this is a '''symbol''' of Christianity.
|-
| [[Image:Cartoony heart.svg|100px|left|Example seven
.]]
The denotation is a [[Representation (arts)|representation]] of a cartoon heart. The connotation is a '''symbol''' of love and affection, not in the way of a rose, but a symbol of true love.
|-
|}:
== Different aspects of meaning ==
Several parts of meaning may be called denotation. That depends on the contrast being drawn.
** ''[[Connotation and denotation]]'' are either
***in basic [[semantics]] and [[literary theory]], the ''figurative'' and ''literal'' meanings of a word, or
***in philosophy, logic and parts of linguistics, the [[intension]] and [[extension]] of a word
** ''Denotation'' can be synonymous with '''reference''' in the [[sense and reference]] in philosophy of language.
* In [[Computer science]], [[denotational semantics]] is contrasted with [[operational semantics]].
* In [[Semiotics]], [[denotation (Semiotics)|denotation]] also has its own meaning.
*In [[mass media|media]]-studies terminology, '''denotation''' is the first level of analysis: what the audience can visually see on a page. Denotation often refers to something literal, and avoids being a [[metaphor]]. Here it is usually coupled with [[connotation]] which is the second level of analysis, being what the denotation represents
In logic and semantics, denotational always attracts the [[Extension_(semantics)|extension]] meaning "in the pair", but the other element genuinely varies. See [[intension]] for some more discussion.
A denotation is the strict, literal, dictionary definition of a word, devoid of any emotion, attitude, or colour.
Denotation often links with [[symbolism]], as the denotation of a particular media text often represents something further; a hidden meaning (or an Engima Code) is often encoded into a media text (such as the images below).
==Other websites==
* [http://www.aber.ac.uk/media/Documents/S4B/sem06.html Semiotics for Beginners]
* [http://bcs.bedfordstmartins.com/virtualit/poetry/denotate_def.html VirtuaLit Elements of Poetry]
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Eclusive disjunction
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#REDIRECT [[Exclusive disjunction]]
Exclusive disjunction
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wiktionary definitions using [[Project:AWB|AWB]]
'''Exclusive disjunction''' (also called '''eclusive or''', '''Xor''') is a [[Logic]] [[operation]]. It normally takes two [[value]]s. It will be true, if exactly one of the two values is true. Otherwise it will be false.
This is [[wikt:difference|different]] from [[inclusive disjunction]].
{{stub}}
[[Category:Logic]]
[[en:Exclusive disjunction]]
False
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False means [[untrue]]. If some''thing'' is false, it means it is not [[real]]. A falsehood is anything said that is not [[true]]. A falsehood can also be a series of [[lie]]s, told to 'prove' something that is false itself.
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Framework
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'''Framework''' is a [[term]] describing [[established]] [[practice|practices]] in a [[society]], [[science]], [[software development]], or [[hardware]] [[design]] that can be [[repeat|repeatedly]] applied to [[solving]] [[problem|problems]]. The problems are solved [[uniformly]] (in the same or very similar way) in a framework.
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Inclusive disjunction
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'''Inclusive disjunction''' (also called '''or''') is a [[Logic]] operation. It normally takes two inputs. It is false, when both inputs are false. Otherwise it is true.
This is different from the [[exclusive disjunction]].
{{stub}}
[[Category:Logic]]
[[en:Logical disjunction]]
Logic
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wikt: links using [[Project:AutoWikiBrowser|AWB]]
'''Logic''' is the [[science]] of [[wikt:reason|reasoning]]. Logic helps [[wikt:people|people]] decide whether something is [[true]] or [[false]].
A popular example, given by [[Aristotle]]:
#All humans are mortal (They die at some point)
#Aristotle is a human
#Therefore, Aristotle is mortal.
<math>\land</math> is read like "and", meaning both of the two.
<math>\lor</math> is read like "or", meaning at least one of the two.
<math>\Rightarrow</math> is read like "implies", or "If ... then ...".
<math>\lnot</math> is read like "not", or "it is not the case that ...".
This is the same example using logic symbols:
:<math> (human \Rightarrow mortal) \land (Aristotle \Rightarrow human) \Rightarrow (Aristotle\Rightarrow mortal) </math>
And this is the same example using general terms:
:<math> (a \Rightarrow b) \land (c \Rightarrow a) \Rightarrow (c \Rightarrow b) </math>
Finally, those talking about ''logic'' talk about ''logic clauses''. A clause is simply something like "Aristole is human" or "all humans are mortal".
Clauses have a [[truth value]]; they are either true or false, but not both. Mistakes in logic are called "[[fallacy|fallacies]]".
There are statements that are always true.
<math>(a \lor \lnot a)</math> is always true. It is called a ''tautology''. (for example: "It rains, or it does not rain")
Logic is used by [[computer]]s in what is called an [[algorithm]]. An ''algorithm'' is sort of like a cooking recipe; it tells the computer what to do and when to do it.
Logic is used in [[mathematics]]. People who study math create [[proof]]s that use logic to show that math facts are correct. There is an area of mathematics called [[mathematical logic]] that studies logic using mathematics.
Logic is also studied in [[philosophy]].
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Logic equality
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'''Logical equality''' is a [[logical]] operation. It takes two inputs. It returns true, if either both inputs are true, or both inputs are false. Otherwise (when they are different) it returns false.
{{stub}}
[[Category:Logic]]
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[[it:Algebra di Boole#XNOR]]
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Logical
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#redirect [[logic]]
Logical conjunction
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{{complex}}
'''Logical conjunction''' (very often called '''and''') is a [[Logic]] operation. Usually it takes two inputs. It is true, when both inputs are true. Otherwise it is false.
[[Category:Logic]]
[[en:Logical conjunction]]
Logical disjunction
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'''Logical disjunction''' is a concept from [[Logic]]. It can refer to
*[[Inclusive disjunction]] (also known as ''logical or''): At least one of the [[argument]]s is true
*[[Exclusive disjunction]] (also known as ''XOR'': Exactly one of the arguments is true.
{{disambiguation}}
{{stub}}
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[[uk:Диз'юнкція (логічна)]]
Logical implication
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/* Examples */
'''Logical implication''' (also known as '''implies''', or ''' If ... then''') is a [[logical]] operation. It takes two arguments. It returns false, only if the first term is true, and the second term is false.
This may be problematic, because it means that from a false proposition, anyithing can follow.
==Examples==
The following shows a (valid) implication
# All [[human]]s are mortal (they die).
# [[Aristotle]] is human
# Therefore Aristotle is mortal
Now look at ''If I am healthy, I will come to class''. There are four possibilities
# I am healthy, and I come to class. I have kept my promise.
#I am healthy, and I do not come to class. I have not kept my promise
#I am not healthy, and I do come to class. I have kept my promise.
#I am not healthy,and I do not come to class. I have kept my promise.
{{stub}}
[[Category:Logic]]
[[en:Logical implication]]
Logical negation
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'''Logical negation''' (also known as '''not''') is a [[logic]] operation. It takes one input. It flips the value of the input as the output. If the input was true, it returns false. If the input was false, it returns true.
{{stub}}
[[Category:Logic]]
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Logician
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#redirect [[logic]]
Oximoron
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#redirect [[oxymoron]]
Oxymoron
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An '''oxymoron''' consists of two or more [[word]]s that seem to contradict (go against, or be the opposite of) each other, or actually do contradict each other.
For example, the words "Wise fool", "Warm freezer", "Legal murder" each have two words. In each case, the one word appears to be the opposite of the other word. More than one word is possible when one of the two terms is a compound word.
It is possible to have words that seem to contradict each other, but where it is possible and correct to place them together. For example, a "warm freezer" may actually be possible. It would occur if the freezer was not working and it was in a warm place.
Words that actually do contradict each other, would be words which are [[logic]]ally or [[physical]]ly impossible when placed together. For example, a "circular square" is physically impossible.
Because of the tension between the words, oxymorons often appear in [[joke]]s. Sometimes, the joke is simply to claim that certain pairs of words ''are'' an oxymoron. For example, a common joke says that "military intelligence" is an oxymoron. This plays with two meanings of "intelligence": (1) intellect, use of the brain and (2) knowledge, especially knowledge about an enemy country.
==See also==
*[[Paradox]]
[[Category:Logic]]
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Paradox
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[[Image:Boyle'sSelfFlowingFlask.png|thumb|[[Robert Boyle]]'s self-flowing flask fills itself in this picture, but [[Perpetual motion|perpetual motion machines]] cannot exist.]]
A '''paradox''' is a sentence in [[logic]] that cannot be [[true]] but also cannot be [[false]]. Many famous problems of this kind exist.
One of most famous paradoxes is called the '''liar's paradox'''. It is the simple sentence "This sentence is a [[lying|lie]]."
If the sentence is true, then it is a lie, as it says. But if it is a lie, how can it be true? A lie cannot also be the [[truth]]. So the sentence being true makes it a lie.
If the sentence is a lie, then it is not as it says, it is true. But that is just what the sentence says. So that makes it true. So the sentence being a lie makes it true.
This paradox is not just true in English but in any language powerful enough for a sentence to make a claim about itself. This is true of [[mathematics]] as well. Paradox can never be removed from any [[symbol]] system that makes claims about itself.
Another example is the statement that [[there is no cabal]]. Only a cabal can know if there is no cabal, so this is either a guess, or, it is a cabal trying to pretend it does not exist.
Other famous examples:
*[[Xeno's paradox]] of [[motion]]
*[[Simpson's paradox]] in [[statistics]]
A paradox can also arise in [[ethics]]. Taking [[power]] over others is often required to protect them, but also, one of the things being protected is their ability to do as they please, which this power interferes with. There is another article on [[ethical dilemma]] which means "a paradox arising in ethics".
Because a paradox forces us to think "[[out of the box]]", about possibilities other than true or false in [[logic]], right or wrong in [[morality]], it is considered very important in [[education]]. People who do not see a paradox where others do, are likely to be too [[certain]] they are right.
==See also==
*[[Irony]]
*[[Oxymoron]]
[[Category:Logic]]
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Problem
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A '''problem''' is a situation which is difficult to deal with. The word comes from a Greek word meaning an "obstacle" (something that is in your way). If someone has a problem, they have to find a way of ''solving'' the problem. The way to solve it is called a ''solution''.
== Examples ==
"John has locked his car keys inside his car so that he cannot get at them. John has a big problem".
=== Social examples ===
We can also talk about a child with "behaviour problems".
=== Entertainment examples ===
Some problems are made up for fun. These are like puzzles. Some of them can be solved with [[logic]], others can be solved by trial and error (this is called ''[[heuristic]]'').
=== Mathematical examples ===
Here is an example of a mathematical problem:
"John is three times as old as Mary. In three years time he will be twice as old as Mary. How old are John and Mary?"
Children often like to give one another problems that can be solved by "lateral thinking". This means using the [[imagination]] rather than strict logic. Here is an example:
"Peter, Ruth, Samuel and Jessica live in the same house. Peter and Ruth went out. When they returned they found Jessica lying dead, surrounded by glass. They were sure Samuel had done it. Why did they not call the police?" The answer is: Samuel was the cat and Jessica was a goldfish.
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Proof by contradiction
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#REDIRECT[[Reductio ad absurdum]]
Reductio ad absurdum
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'''Reductio ad absurdum''' is a [[Latin language|Latin]] phrase. It can be translated as ''reduction to the impossible''. Generally, it is also known as '''Proof by contradiction'''. In [[Logic]] and [[mathematics]] it is a method of [[proof|proving]] something.
The phrase can be traced back to the [[Greek language|Greek]] ''η εις άτοπον απαγωγή'' (''hê eis átopon apagogê''). This phrase means "reduction to the impossible". It was often used by [[Aristotle]].
The method of proving something works by first stating something is true. Then other things are deduced from that. In the end, there is a contradiction. This contradiction then shows that thing stated first cannot be true.
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[[en:Reductio ad absurdum]]
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A '''riddle''' can be classed as a statement with a solution. This solution, however, need not have a [[logic|logical]] solution. Solving riddles usually involve thinking about the question with great concentration, and putting it into a context.
E.g. "If seven nines are ace, how many by thorn"
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#REDIRECT [[Riddle]]
True
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A thing is '''true''' if it is [[correct]]. A thing is true if it is a [[fact]].
===Example===
For example, it is true that a [[dog]] is an [[animal]]. It is ''untrue'' (not true) that a dog is a [[plant]].
===Other words===
Something untrue is [[false]]. A half truth is something true mixed with something false.
If the things you say are true, then you speak the truth, or speak truly. Saying something untrue can be called 'a [[lie]]', if the person saying it knows it is untrue.
==True and False in [[Logic]]==
''True'' is also one of the two [[basic]] [[value]]s of [[classical logic]]. The other such value is usually called ''false''.
Classical logic is also known as [[boolean algebra]]
==See Also==
* [[Number]]
* [[Mathematics]]
{{stub}}
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Truth
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#redirect [[True]]
Truth value
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In [[logic]], the '''truth value''' of a logical statement says how much it is true. Usually, the truth value can only be "true" or "false". For example, "The [[car]] is [[red]]" is true when the car is red and false when it is not.
In [[multi-valued logic]]s, the truth value can be other values as well. For example, one could use a value between 0 and 1 to say how much it is true. Zero would mean that it is completely false and one would mean that is completely true. When the car is [[orange]] (half red, half [[yellow]]), the truth value could be 0.5 because the statement is half true and half false.
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#REDIRECT [[Exclusive disjunction]]