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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. | + | <font size="3">☞</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. 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. |
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| ==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'' × ''Y'' → '''B''' and abstract type '''B''' × '''B''' → '''B''' in a number of different languages for zeroth order logic. | + | 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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| <br> | | <br> |
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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== | + | ==Translations== |
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| + | * [http://zh.wikipedia.org/wiki/%E9%9B%B6%E9%98%B6%E9%80%BB%E8%BE%91 中文 : 零阶逻辑] |
| + | |
| + | ==Syllabus== |
| + | |
| + | ===Focal nodes=== |
| + | |
| + | * [[Inquiry Live]] |
| + | * [[Logic Live]] |
| + | |
| + | ===Peer nodes=== |
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| + | * [http://intersci.ss.uci.edu/wiki/index.php/Zeroth_order_logic Zeroth Order Logic @ InterSciWiki] |
| + | * [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic @ MyWikiBiz] |
| + | * [http://ref.subwiki.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Subject Wikis] |
| + | * [http://en.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Wikiversity] |
| + | * [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Wikiversity Beta] |
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| ===Logical operators=== | | ===Logical operators=== |
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| {{col-break}} | | {{col-break}} |
| * [[Ampheck]] | | * [[Ampheck]] |
− | * [[Boolean algebra]]
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− | * [[Boolean algebra topics]]
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| * [[Boolean domain]] | | * [[Boolean domain]] |
| * [[Boolean function]] | | * [[Boolean function]] |
− | * [[Boolean logic]] | + | * [[Boolean-valued function]] |
| + | * [[Differential logic]] |
| {{col-break}} | | {{col-break}} |
− | * [[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]]
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| * [[Logical graph]] | | * [[Logical graph]] |
| + | * [[Minimal negation operator]] |
| + | * [[Multigrade operator]] |
| + | * [[Parametric operator]] |
| + | * [[Peirce's law]] |
| {{col-break}} | | {{col-break}} |
− | * [[Logical value]]
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− | * [[Minimal negation operator]]
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− | * [[Monadic predicate calculus]]
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− | * [[Operation (mathematics)|Operation]]
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| * [[Propositional calculus]] | | * [[Propositional calculus]] |
| + | * [[Sole sufficient operator]] |
| * [[Truth table]] | | * [[Truth table]] |
| + | * [[Universe of discourse]] |
| + | * [[Zeroth order logic]] |
| {{col-end}} | | {{col-end}} |
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− | ==Other languages== | + | ===Relational concepts=== |
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− | * [http://zh.wikipedia.org/wiki/%E9%9B%B6%E9%98%B6%E9%80%BB%E8%BE%91 中文 : 零阶逻辑] | + | {{col-begin}} |
| + | {{col-break}} |
| + | * [[Continuous predicate]] |
| + | * [[Hypostatic abstraction]] |
| + | * [[Logic of relatives]] |
| + | * [[Logical matrix]] |
| + | {{col-break}} |
| + | * [[Relation (mathematics)|Relation]] |
| + | * [[Relation composition]] |
| + | * [[Relation construction]] |
| + | * [[Relation reduction]] |
| + | {{col-break}} |
| + | * [[Relation theory]] |
| + | * [[Relative term]] |
| + | * [[Sign relation]] |
| + | * [[Triadic relation]] |
| + | {{col-end}} |
| + | |
| + | ===Information, Inquiry=== |
| + | |
| + | {{col-begin}} |
| + | {{col-break}} |
| + | * [[Inquiry]] |
| + | * [[Dynamics of inquiry]] |
| + | {{col-break}} |
| + | * [[Semeiotic]] |
| + | * [[Logic of information]] |
| + | {{col-break}} |
| + | * [[Descriptive science]] |
| + | * [[Normative science]] |
| + | {{col-break}} |
| + | * [[Pragmatic maxim]] |
| + | * [[Truth theory]] |
| + | {{col-end}} |
| + | |
| + | ===Related articles=== |
| + | |
| + | {{col-begin}} |
| + | {{col-break}} |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Cactus_Language Cactus Language] |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Futures_Of_Logical_Graphs Futures Of Logical Graphs] |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems] |
| + | {{col-break}} |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_:_Introduction Differential Logic : Introduction] |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Propositional_Calculus Differential Propositional Calculus] |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems] |
| + | {{col-break}} |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Prospects_for_Inquiry_Driven_Systems Prospects for Inquiry Driven Systems] |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Introduction_to_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems] |
| + | * [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry] |
| + | {{col-end}} |
| + | |
| + | ==Document history== |
| + | |
| + | 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] |
| + | * [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic], [http://mywikibiz.com/ MyWikiBiz] |
| + | * [http://planetmath.org/ZerothOrderLogic Zeroth Order Logic], [http://planetmath.org/ PlanetMath] |
| + | * [http://wikinfo.org/w/index.php/Zeroth_order_logic Zeroth Order Logic], [http://wikinfo.org/w/ Wikinfo] |
| + | * [http://en.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic], [http://en.wikiversity.org/ Wikiversity] |
| + | * [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://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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| + | [[Category:Inquiry]] |
| + | [[Category:Open Educational Resource]] |
| + | [[Category:Peer Educational Resource]] |
| [[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]] |
− | | + | [[Category:Semiotics]] |
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