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Zeroth order logic (view source)

Revision as of 16:04, 8 November 2015

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'''''Zeroth order logic''''' is a term in popular use among practitioners for the common principles underlying the [[algebra of sets]], [[boolean algebra]], [[boolean function]]s, [[logical connective]]s, [[monadic predicate calculus]], [[propositional calculus]], and sentential logic. The term serves to mark a level of abstraction in which the more inessential differences among these subjects can be subsumed under the appropriate [[isomorphism]]s.
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<font size="3">&#9758;</font> This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].
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'''''Zeroth order logic''''' is an informal term that is sometimes used to indicate the common principles underlying the algebra of sets, boolean algebra, [[boolean functions]], logical connectives, monadic predicate calculus, [[propositional calculus]], and sentential logic.&nbsp; The term serves to mark a level of abstraction in which the more inessential differences among these subjects can be subsumed under the appropriate isomorphisms.
    
==Propositional forms on two variables==
 
==Propositional forms on two variables==
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By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions of concrete type ''X''&nbsp;&times;&nbsp;''Y''&nbsp;&rarr;&nbsp;'''B''' and abstract type '''B'''&nbsp;&times;&nbsp;'''B'''&nbsp;&rarr;&nbsp;'''B''' in a number of different languages for zeroth order logic.
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By way of initial orientation, Table 1 lists equivalent expressions for the sixteen functions of concrete type <math>X \times Y \to \mathbb{B}</math> and abstract type <math>\mathbb{B} \times \mathbb{B} \to \mathbb{B}</math> in a number of different languages for zeroth order logic.
    
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* Language '''L<sub>6</sub>''' expresses the sixteen functions in one of several notations that are commonly used in formal logic.
 
* Language '''L<sub>6</sub>''' expresses the sixteen functions in one of several notations that are commonly used in formal logic.
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==See also==
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==Translations==
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* [http://zh.wikipedia.org/wiki/%E9%9B%B6%E9%98%B6%E9%80%BB%E8%BE%91 &#20013;&#25991; : &#38646;&#38454;&#36923;&#36753;]
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==Syllabus==
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===Focal nodes===
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* [[Inquiry Live]]
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* [[Logic Live]]
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===Peer nodes===
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* [http://intersci.ss.uci.edu/wiki/index.php/Zeroth_order_logic Zeroth Order Logic @ InterSciWiki]
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* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic @ MyWikiBiz]
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* [http://ref.subwiki.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Subject Wikis]
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* [http://en.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Wikiversity Beta]
    
===Logical operators===
 
===Logical operators===
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{{col-break}}
 
{{col-break}}
 
* [[Ampheck]]
 
* [[Ampheck]]
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* [[Boolean algebra]]
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* [[Boolean algebra topics]]
   
* [[Boolean domain]]
 
* [[Boolean domain]]
 
* [[Boolean function]]
 
* [[Boolean function]]
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* [[Boolean logic]]
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* [[Boolean-valued function]]
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* [[Differential logic]]
 
{{col-break}}
 
{{col-break}}
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* [[Boolean-valued function]]
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* [[Entitative graph]]
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* [[Existential graph]]
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* [[First order logic]]
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* [[Indicator function]]
   
* [[Logical graph]]
 
* [[Logical graph]]
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* [[Minimal negation operator]]
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* [[Multigrade operator]]
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* [[Parametric operator]]
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* [[Peirce's law]]
 
{{col-break}}
 
{{col-break}}
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* [[Logical value]]
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* [[Minimal negation operator]]
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* [[Monadic predicate calculus]]
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* [[Operation (mathematics)|Operation]]
   
* [[Propositional calculus]]
 
* [[Propositional calculus]]
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* [[Sole sufficient operator]]
 
* [[Truth table]]
 
* [[Truth table]]
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* [[Universe of discourse]]
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* [[Zeroth order logic]]
 
{{col-end}}
 
{{col-end}}
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==Translations==
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===Relational concepts===
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* [http://zh.wikipedia.org/wiki/%E9%9B%B6%E9%98%B6%E9%80%BB%E8%BE%91 &#20013;&#25991; : &#38646;&#38454;&#36923;&#36753;]
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{{col-begin}}
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{{col-break}}
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==Document history==
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* [[Continuous predicate]]
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* [[Hypostatic abstraction]]
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* [[Logic of relatives]]
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* [[Logical matrix]]
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{{col-break}}
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* [[Relation (mathematics)|Relation]]
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* [[Relation composition]]
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* [[Relation construction]]
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* [[Relation reduction]]
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{{col-break}}
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* [[Relation theory]]
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* [[Relative term]]
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* [[Sign relation]]
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* [[Triadic relation]]
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{{col-end}}
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Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
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===Information, Inquiry===
    
{{col-begin}}
 
{{col-begin}}
 
{{col-break}}
 
{{col-break}}
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* [[Inquiry]]
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* [[Dynamics of inquiry]]
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{{col-break}}
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* [[Semeiotic]]
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* [[Logic of information]]
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{{col-break}}
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* [[Descriptive science]]
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* [[Normative science]]
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{{col-break}}
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* [[Pragmatic maxim]]
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* [[Truth theory]]
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{{col-end}}
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* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic], [http://mywikibiz.com/ MyWikiBiz]
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===Related articles===
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* [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic], [http://beta.wikiversity.org/ Beta Wikiversity]
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* [http://planetmath.org/encyclopedia/ZerothOrderLogic.html Zeroth Order Logic], [http://planetmath.org/ PlanetMath]
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* [http://www.getwiki.net/-Zeroth-Order_Logic Zeroth Order Logic], [http://www.getwiki.net/ GetWiki]
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{{col-begin}}
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{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language]
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* [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs]
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* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
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{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus]
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* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
 
{{col-break}}
 
{{col-break}}
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* [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems]
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* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
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{{col-end}}
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* [http://www.wikinfo.org/index.php/Zeroth_order_logic Zeroth Order Logic], [http://www.wikinfo.org/ Wikinfo]
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==Document history==
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* [http://www.textop.org/wiki/index.php?title=Zeroth_order_logic Zeroth Order Logic], [http://www.textop.org/wiki/ Textop Wiki]
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Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
    +
* [http://intersci.ss.uci.edu/wiki/index.php/Zeroth_order_logic Zeroth Order Logic], [http://intersci.ss.uci.edu/ InterSciWiki]
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* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic], [http://mywikibiz.com/ MyWikiBiz]
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* [http://planetmath.org/ZerothOrderLogic Zeroth Order Logic], [http://planetmath.org/ PlanetMath]
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* [http://wikinfo.org/w/index.php/Zeroth_order_logic Zeroth Order Logic], [http://wikinfo.org/w/ Wikinfo]
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* [http://en.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic], [http://en.wikiversity.org/ Wikiversity]
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* [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic], [http://beta.wikiversity.org/ Wikiversity Beta]
 
* [http://en.wikipedia.org/w/index.php?title=Zeroth-order_logic&oldid=77109225 Zeroth Order Logic], [http://en.wikipedia.org/ Wikipedia]
 
* [http://en.wikipedia.org/w/index.php?title=Zeroth-order_logic&oldid=77109225 Zeroth Order Logic], [http://en.wikipedia.org/ Wikipedia]
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* [http://web.archive.org/web/20050323065233/http://www.altheim.com/cs/zol.html Zeroth Order Logic], [http://web.archive.org/web/20070305032442/http://www.altheim.com/cs/ Altheim.com]
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* [http://www.altheim.com/cs/zol.html Zeroth Order Logic], [http://www.altheim.com/cs Altheim.com]
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[[Category:Inquiry]]
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[[Category:Open Educational Resource]]
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[[Category:Peer Educational Resource]]
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[[Category:Computer Science]]
 
[[Category:Computer Science]]
 
[[Category:Formal Languages]]
 
[[Category:Formal Languages]]
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[[Category:Mathematics]]
 
[[Category:Mathematics]]
 
[[Category:Normative Sciences]]
 
[[Category:Normative Sciences]]
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[[Category:Semiotics]]
Jon Awbrey
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