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In [[classical logic]] '''disjunctive syllogism'''<ref>{{cite book |ref=harv |last=Copi |first=Irving M. |last2=Cohen |first2=Carl |title=Introduction to Logic |publisher=Prentice Hall |year=2005 |page=362 |isbn=}}</ref><ref>{{cite book |title=A Concise Introduction to Logic 4th edition |last=Hurley |first=Patrick |authorlink= |coauthors= |year=1991 |publisher=Wadsworth Publishing |location= |isbn= |page= |pages=320–1 |url= |accessdate=}}</ref> (historically known as '''modus tollendo ponens''') is a [[validity|valid]] [[argument form]]  which is a [[syllogism]] having a [[Logical disjunction|disjunctive statement]] for one of its [[premise]]s.<ref>Hurley</ref><ref>Copi and Cohen</ref>
 
:Either the breach is a safety violation, or it is not subject to fines.
:The breach is not a safety violation.
:Therefore, it is not subject to fines.
 
In [[propositional calculus|propositional logic]], '''disjunctive syllogism''' (also known as '''disjunction elimination''' and '''or elimination''', or abbreviated '''∨E'''),<ref>Sanford, David Hawley. 2003. ''If P, Then Q: Conditionals and the Foundations of Reasoning''. London, UK: Routledge: 39</ref><ref>Hurley</ref><ref>Copi and Cohen</ref><ref>Moore and Parker</ref> is a valid [[rule of inference]]. If we are told that at least one of two statements is true; and also told that it is not the former that is true; we can [[inference|infer]] that it has to be the latter that is true. If either ''P'' or ''Q'' is true and ''P'' is false, then ''Q'' is true. The reason this is called "disjunctive syllogism" is that, first, it is a syllogism, a three-step [[argument]], and second, it contains a logical disjunction, which simply means an  "or" statement.  "Either P or Q" is a disjunction; P and Q are called the statement's ''disjuncts''. The rule makes it possible to eliminate a [[logical disjunction|disjunction]] from a [[formal proof|logical proof]]. It is the rule that:
 
:<math>\frac{P \or Q, \neg P}{\therefore Q}</math>
 
where the rule is that whenever instances of "<math>P \or Q</math>", and "<math>\neg P</math>" appear on lines of a proof, "<math>Q</math>" can be placed on a subsequent line.
 
Disjunctive syllogism is closely related and similar to [[hypothetical syllogism]], in that it is also type of syllogism, and also the name of a rule of inference.
 
== Formal notation ==
The ''disjunctive syllogism'' rule may be written in [[sequent]] notation:
 
: <math> P \lor Q, \lnot P \vdash Q </math>
 
where <math>\vdash</math> is a [[metalogic]]al symbol meaning that <math>Q</math> is a [[logical consequence|syntactic consequence]] of <math>P \lor Q</math>, and <math>\lnot P</math> in some [[formal system|logical system]];
 
and expressed as a truth-functional [[tautology (logic)|tautology]] or [[theorem]] of propositional logic:
 
:<math> ((P \or Q) \and \neg P) \to Q</math>
 
where <math>P</math>, and <math>Q</math> are propositions expressed in some formal system.
 
== Natural language examples ==
Here is an example:
:Either I will choose soup or I will choose salad.
:I will not choose soup.
:Therefore, I will choose salad.
 
Here is another example:
:It is either red or blue.
:It is not blue.
:Therefore, it is red.
 
== Inclusive and exclusive disjunction ==
Please observe that the disjunctive syllogism works whether 'or' is considered 'exclusive' or 'inclusive' disjunction. See below for the definitions of these terms.
 
There are two kinds of logical disjunction:
 
* ''[[logical disjunction|inclusive]]'' means "and/or"  - at least one of them is true, or maybe both.
* ''[[xor|exclusive]]'' ("xor") means exactly one must be true, but they cannot both be.
 
The widely used English language concept of ''or'' is often ambiguous between these two meanings, but the difference is pivotal in evaluating disjunctive arguments.  
 
This argument:
:Either P or Q.
:Not P.
:Therefore, Q.
 
is valid and indifferent between both meanings. However, only in the ''exclusive'' meaning is the following form valid:
 
:Either P or Q (exclusive).
:P.
:Therefore, not Q.
 
With the ''inclusive'' meaning you could draw no conclusion from the first two premises of that argument. See [[affirming a disjunct]].
 
==Related argument forms==
 
Unlike [[modus ponendo ponens]] and [[modus ponendo tollens]], with which it should not be confused, disjunctive syllogism is often not made an explicit rule or axiom of [[logical system]]s, as the above arguments can be proven with a (slightly devious) combination of [[reductio ad absurdum]] and [[disjunction elimination]].
 
''Other forms of syllogism:''
*[[hypothetical syllogism]]
*[[categorical syllogism]]
 
Disjunctive syllogism holds in classical propositional logic and [[intuitionistic logic]], but not in some [[paraconsistent logic]]s.<ref>Chris Mortensen, [http://plato.stanford.edu/entries/mathematics-inconsistent/ Inconsistent Mathematics], ''Stanford encyclopedia of philosophy'', First published Tue Jul 2, 1996; substantive revision Thu Jul 31, 2008</ref>
 
==References==
<references />
 
[[Category:Rules of inference]]
[[Category:Theorems in propositional logic]]
[[Category:Classical logic]]
 
[[is:Jákvæð neitunarregla]]
[[ja:選言三段論法]]
[[pt:Silogismo disjuntivo]]
[[zh:选言三段论]]

Latest revision as of 20:06, 13 December 2014

It is time to address the slow computer issues whether or not you do not understand how. Just considering the computer is working thus slow or keeps freezing up; does not imply to not address the issue and fix it. You may or might not be aware which any computer owner must learn which there are certain aspects which your computer requires to keep the greatest performance. The sad truth is the fact that numerous folks that own a program have no idea that it needs routine repair merely like their cars.

Carry out window's system restore. It is important to do this because it removes wrong changes which have happened in the system. Some of the errors outcome from inability of the program to create restore point regularly.

So what if you look for whenever you compare registry cleaners. Many of the registry products accessible now, have quite similar attributes. The principal ones which we should be hunting for are these.

In order to remove the programs on a computer, Windows Installer should be inside a healthy state. If its installation is corrupted you might obtain error 1721 in Windows 7, Vista and XP throughout the system removal procedure. Simply re-registering its component files would resolve a issue.

The 2nd step to fixing these errors is to utilize a system called a "registry reviver" to scan from a computer and fix some of the registry errors which may furthermore be leading for this error. A registry cleaner is a software system that may scan by a computer and repair any of the problems that Windows has inside, allowing a computer to "remember" all the settings it has when it loads up. Although the registry is continually being selected to help load up a big number of programs on a PC, it's continually being saved incorrectly - leading to a big amount of mistakes to be formed. To fix this problem, it's recommended we download a registry cleaner within the Internet and install it on the Pc, allowing Windows to run smoother again.

Active X controls are used across the whole spectrum of computer plus internet technologies. These controls are referred to as the building blocks of the web plus as the glue that puts it all together. It is a standard which is chosen by all developers to create the web more useful plus interactive. Without these control guidelines there would basically be no public web.

Your registry is the region all a significant configurations for hardware, software plus user profile configurations plus needs are stored. Every time 1 of these items is changed, the database then begins to expand. Over time, the registry will become bloated with unwanted files. This causes a general slow down yet in extreme cases may result important tasks plus programs to stop working all together.

A program plus registry cleaner is downloaded from the web. It's user friendly plus the task refuses to take long. All it does is scan plus then when it finds mistakes, it might fix and clean those mistakes. An error free registry usually safeguard the computer from mistakes and give you a slow PC fix.

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