Zeroth order logic - Revision history

Jon Awbrey: update

2015-11-09T03:08:28Z

update

← Older revision		Revision as of 03:08, 9 November 2015
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	==Propositional forms on two variables==		==Propositional forms on two variables==

	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.		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.

	<br>		<br>
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	These six languages for the sixteen boolean functions are conveniently described in the following order:		These six languages for the sixteen boolean functions are conveniently described in the following order:

	* Language ~~'''L~~<~~sub~~>3</~~sub~~>~~'''~~ describes each boolean function ''f'' : ~~'''~~B~~'''<sup>~~2</~~sup~~> ~~→ '''B'''~~ by means of the sequence of four boolean values ~~(''~~f''(1,1), ''f''(1,0), ''f''(0,1), ''f''(0,0)). Such a sequence, perhaps in another order, and perhaps with the logical values ''F'' and ''T'' instead of the boolean values 0 and 1, respectively, would normally be displayed as a column in a [[truth table]].		* Language <math>\mathcal{L}_{3}\!</math> describes each boolean function <math>f : \mathbb{B}^2 \to \mathbb{B}\!</math> by means of the sequence of four boolean values, <math>f(1,1),\!</math> <math>f(1,0),\!</math> <math>f(0,1),\!</math> <math>f(0,0).\!</math>  Such a sequence, perhaps in another order, and perhaps with the logical values <math>\mathrm{F}\!</math> and <math>\mathrm{T}\!</math> instead of the boolean values <math>0\!</math> and <math>1,\!</math> respectively, would normally be displayed as a column in a [[truth table]].

	* Language ~~'''L~~<~~sub~~>2</~~sub~~>~~'''~~ lists the sixteen functions in the form ~~'''f~~<~~sub~~>i</~~sub~~>~~''',~~ where the index ~~'''~~i~~'''~~ is a [[bit string]] formed from the sequence of boolean values in ~~'''L~~<~~sub~~>3</~~sub~~>~~'''.~~		* Language <math>\mathcal{L}_{2}\!</math> lists the sixteen functions in the form <math>f_i,\!</math> where the index <math>i\!</math> is a bit string formed from the sequence of boolean values in <math>\mathcal{L}_{3}.\!</math>

	* Language ~~'''L~~<~~sub~~>1</~~sub~~>~~'''~~ notates the boolean functions ~~'''f~~<~~sub~~>i</~~sub~~>~~'''~~ with an index ~~'''~~i~~'''~~ that is the decimal equivalent of the binary numeral index in ~~'''L~~<~~sub~~>2</~~sub~~>~~'''.~~		* Language <math>\mathcal{L}_{1}\!</math> notates the boolean functions <math>f_i\!</math> with an index <math>i\!</math> that is the decimal equivalent of the binary numeral index in <math>\mathcal{L}_{2}.\!</math>

	* Language ~~'''L~~<~~sub~~>4</~~sub~~>~~'''~~ expresses the sixteen functions in terms of ~~logical~~ [[conjunction]], indicated by concatenating function names or proposition expressions in the manner of products, plus the family of ''[[minimal negation operator]]s'', the first few of which are given in the following variant notations:		* Language <math>\mathcal{L}_{4}\!</math> expresses the sixteen functions in terms of [[logical conjunction]], indicated by concatenating function names or proposition expressions in the manner of products, plus the family of ''[[minimal negation operator]]s'', the first few of which are given in the following variant notations:

	: <math>\begin{matrix}		{\| align="center" cellpadding="8" style="text-align:center"
	(\ ) & = & 0 & = & \~~mbox~~{false} \\		\|
	(x) & = & \tilde{x} & = & x' \\		<math>\begin{matrix}
	(x, y) & = & \tilde{x}y \lor x\tilde{y} & = & x'y \lor ~~xy'~~ \\		\texttt{()}
	(x, y, z) & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} & = & x~~'yz~~ \lor ~~xy'~~z \lor ~~xyz'~~		& = & 0
	\end{matrix}</math>		& = & \mathrm{false}
			\\[6pt]
			\texttt{(} x \texttt{)}
			& = & \tilde{x}
			& = & x^\prime
			\\[6pt]
			\texttt{(} x \texttt{,} y \texttt{)}
			& = & \tilde{x}y \lor x\tilde{y}
			& = & x^\prime y \lor x y^\prime
			\\[6pt]
			\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}
			& = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z}
			& = & x^\prime y z \lor x y^\prime z \lor x y z^\prime
			\end{matrix}\!</math>
			\|}

	It may ~~also~~ be noted that <math>(x, y)\!</math> is the same function as <math>x + y\!</math> and <math>x \ne y</math>~~, and that the~~ inclusive disjunctions indicated for <math>(x, y)\!</math> and for <math>(x, y, z)\!</math> may be replaced with exclusive disjunctions without affecting the meaning, ~~because~~ the terms disjoined are already disjoint. However, the function <math>(x, y, z)\!</math> is not the same thing as the function <math>x + y + z\!</math>.		It may be noted that <math>\texttt{(} x \texttt{,} y \texttt{)}\!</math> is the same function as <math>x + y\!</math> and <math>x \ne y.</math> The inclusive disjunctions indicated for <math>\texttt{(} x \texttt{,} y \texttt{)}\!</math> and for <math>\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}\!</math> may be replaced with exclusive disjunctions without affecting the meaning, since the terms disjoined are already disjoint. However, the function <math>\texttt{(} x \texttt{,} y \texttt{,} z \texttt{)}\!</math> is not the same thing as the function <math>x + y + z.\!</math>

	* Language ~~'''L~~<~~sub~~>5</~~sub~~>~~'''~~ lists ordinary language expressions for the sixteen functions. Many other paraphrases are possible, but these afford a sample of the simplest equivalents.		* Language <math>\mathcal{L}_{5}\!</math> lists ordinary language expressions for the sixteen functions. Many other paraphrases are possible, but these afford a sample of the simplest equivalents.

	* Language ~~'''L~~<~~sub~~>6</~~sub~~>~~'''~~ expresses the sixteen functions in one of several notations that are commonly used in formal logic.		* Language <math>\mathcal{L}_{6}\!</math> expresses the sixteen functions in one of several notations that are commonly used in formal logic.

	==Translations==		==Translations==

Jon Awbrey: update with TeX table

2015-11-08T15:50:18Z

update with TeX table

Show changes

Jon Awbrey: update

2015-11-08T03:44:42Z

update

← Older revision		Revision as of 03:44, 8 November 2015
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	<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].		<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].

	'''''Zeroth order logic''''' is an informal term that is sometimes used to indicate 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~~.		'''''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.

	==Propositional forms on two variables==		==Propositional forms on two variables==
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	===Focal nodes===		===Focal nodes===

	~~{{col-begin}}~~
	~~{{col-break}}~~
	* [[Inquiry Live]]		* [[Inquiry Live]]
	~~{{col-break}}~~
	* [[Logic Live]]		* [[Logic Live]]
	~~{{col-end}}~~

	===Peer nodes===		===Peer nodes===

	~~{{col-begin}}~~		* [http://intersci.ss.uci.edu/wiki/index.php/Zeroth_order_logic Zeroth Order Logic @ InterSciWiki]
	~~{{col-break}}~~
	* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic @ MyWikiBiz]		* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic @ MyWikiBiz]
	* [http://mathweb.org/wiki/Zeroth_order_logic Zeroth Order Logic @ MathWeb Wiki]
	* [http://netknowledge.org/wiki/Zeroth_order_logic Zeroth Order Logic @ NetKnowledge]
	* [http://wiki.oercommons.org/mediawiki/index.php/Zeroth_order_logic Zeroth Order Logic @ OER Commons]
	~~{{col-break}}~~
	* [http://p2pfoundation.net/Zeroth_Order_Logic Zeroth Order Logic @ P2P Foundation]
	* [http://semanticweb.org/wiki/Zeroth_order_logic Zeroth Order Logic @ SemanticWeb]
	* [http://ref.subwiki.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Subject Wikis]		* [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]		* [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Wikiversity Beta]
	~~{{col-end}}~~

	===Logical operators===		===Logical operators===
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	===Related articles===		===Related articles===

	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Semiotic_Information Jon Awbrey, “Semiotic Information”~~]		{{col-begin}}
			{{col-break}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Introduction_to_Inquiry_Driven_Systems Jon Awbrey, “Introduction To Inquiry Driven Systems”~~]		* [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://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Essays~~/~~Prospects_For_Inquiry_Driven_Systems Jon Awbrey, “Prospects For Inquiry Driven~~ Systems~~”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Propositional_Equation_Reasoning_Systems Propositional Equation Reasoning Systems]
			{{col-break}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Inquiry_Driven_Systems Jon Awbrey, “Inquiry Driven Systems~~ : ~~Inquiry Into Inquiry”~~]		* [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://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Propositional_Equation_Reasoning_Systems Jon Awbrey, “~~Propositional ~~Equation Reasoning Systems”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 Differential Logic and Dynamic Systems]
			{{col-break}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory:Jon_Awbrey~~/~~Papers~~/~~Differential_Logic_:_Introduction Jon Awbrey, “~~Differential Logic ~~: Introduction”~~]		* [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://~~planetmath~~.~~org~~/~~encyclopedia~~/~~DifferentialPropositionalCalculus~~.~~html Jon Awbrey, “Differential Propositional Calculus”~~]		* [http://intersci.ss.uci.edu/wiki/index.php/Inquiry_Driven_Systems Inquiry Driven Systems : Inquiry Into Inquiry]
			{{col-end}}
	* [http://~~mywikibiz~~.~~com~~/~~Directory~~:~~Jon_Awbrey~~/~~Papers~~/~~Differential_Logic_and_Dynamic_Systems_2~~.~~0 Jon Awbrey, “Differential Logic and Dynamic~~ Systems~~”~~]

	==Document history==		==Document history==
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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.		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.

	~~{{col-begin}}~~		* [http://intersci.ss.uci.edu/wiki/index.php/Zeroth_order_logic Zeroth Order Logic], [http://intersci.ss.uci.edu/ InterSciWiki]
	~~{{col-break}}~~
	* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic], [http://mywikibiz.com/ MyWikiBiz]		* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic], [http://mywikibiz.com/ MyWikiBiz]
	* [http://planetmath.org~~/encyclopedia~~/ZerothOrderLogic~~.html~~ Zeroth Order Logic], [http://planetmath.org/ PlanetMath]		* [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://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic], [http://beta.wikiversity.org/ Wikiversity Beta]
	* [http://getwiki.net/-Zeroth-Order_Logic Zeroth Order Logic], [http://getwiki.net/ GetWiki]
	~~{{col-break}}~~
	* [http://wikinfo.org/index.php/Zeroth_order_logic Zeroth Order Logic], [http://wikinfo.org/ Wikinfo]
	* [http://textop.org/wiki/index.php?title=Zeroth_order_logic Zeroth Order Logic], [http://textop.org/wiki/ Textop Wiki]
	* [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]
	* [http://altheim.com/cs/zol.html Zeroth Order Logic], [http://altheim.com/cs Altheim.com]		* [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]
	~~{{col-end}}~~

	[[Category:Inquiry]]		[[Category:Inquiry]]

Jon Awbrey: + article

2010-06-23T14:04:42Z

+ article

New page

☞ This page belongs to resource collections on [[Logic Live|Logic]] and [[Inquiry Live|Inquiry]].

'''''Zeroth order logic''''' is an informal term that is sometimes used to indicate 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.

==Propositional forms on two variables==

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.

 

{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:90%"
|+ '''Table 1. Propositional Forms on Two Variables'''
|- style="background:#e6e6ff"
! style="width:15%" | L1
! style="width:15%" | L2
! style="width:15%" | L3
! style="width:15%" | L4
! style="width:15%" | L5
! style="width:15%" | L6
|- style="background:#e6e6ff"
|  
| align="right" | x :
| 1 1 0 0
|  
|  
|  
|- style="background:#e6e6ff"
|  
| align="right" | y :
| 1 0 1 0
|  
|  
|  
|-
| f0 || f0000 || 0 0 0 0 || ( ) || false || 0
|-
| f1 || f0001 || 0 0 0 1 || (x)(y) || neither x nor y || ¬x &and; ¬y
|-
| f2 || f0010 || 0 0 1 0 || (x) y || y and not x || ¬x &and; y
|-
| f3 || f0011 || 0 0 1 1 || (x) || not x || ¬x
|-
| f4 || f0100 || 0 1 0 0 || x (y) || x and not y || x &and; ¬y
|-
| f5 || f0101 || 0 1 0 1 || (y) || not y || ¬y
|-
| f6 || f0110 || 0 1 1 0 || (x, y) || x not equal to y || x ≠ y
|-
| f7 || f0111 || 0 1 1 1 || (x y) || not both x and y || ¬x &or; ¬y
|-
| f8 || f1000 || 1 0 0 0 || x y || x and y || x &and; y
|-
| f9 || f1001 || 1 0 0 1 || ((x, y)) || x equal to y || x = y
|-
| f10 || f1010 || 1 0 1 0 || y || y || y
|-
| f11 || f1011 || 1 0 1 1 || (x (y)) || not x without y || x → y
|-
| f12 || f1100 || 1 1 0 0 || x || x || x
|-
| f13 || f1101 || 1 1 0 1 || ((x) y) || not y without x || x ← y
|-
| f14 || f1110 || 1 1 1 0 || ((x)(y)) || x or y || x &or; y
|-
| f15 || f1111 || 1 1 1 1 || (( )) || true || 1
|}

 

These six languages for the sixteen boolean functions are conveniently described in the following order:

* Language '''L3''' describes each boolean function ''f'' : '''B'''2 → '''B''' by means of the sequence of four boolean values (''f''(1,1), ''f''(1,0), ''f''(0,1), ''f''(0,0)). Such a sequence, perhaps in another order, and perhaps with the logical values ''F'' and ''T'' instead of the boolean values 0 and 1, respectively, would normally be displayed as a column in a [[truth table]].

* Language '''L2''' lists the sixteen functions in the form '''fi''', where the index '''i''' is a [[bit string]] formed from the sequence of boolean values in '''L3'''.

* Language '''L1''' notates the boolean functions '''fi''' with an index '''i''' that is the decimal equivalent of the binary numeral index in '''L2'''.

* Language '''L4''' expresses the sixteen functions in terms of logical [[conjunction]], indicated by concatenating function names or proposition expressions in the manner of products, plus the family of ''[[minimal negation operator]]s'', the first few of which are given in the following variant notations:

: <math>\begin{matrix}
(\ ) & = & 0 & = & \mbox{false} \\
(x) & = & \tilde{x} & = & x' \\
(x, y) & = & \tilde{x}y \lor x\tilde{y} & = & x'y \lor xy' \\
(x, y, z) & = & \tilde{x}yz \lor x\tilde{y}z \lor xy\tilde{z} & = & x'yz \lor xy'z \lor xyz'
\end{matrix}</math>

It may also be noted that <math>(x, y)\!</math> is the same function as <math>x + y\!</math> and <math>x \ne y</math>, and that the inclusive disjunctions indicated for <math>(x, y)\!</math> and for <math>(x, y, z)\!</math> may be replaced with exclusive disjunctions without affecting the meaning, because the terms disjoined are already disjoint. However, the function <math>(x, y, z)\!</math> is not the same thing as the function <math>x + y + z\!</math>.

* Language '''L5''' lists ordinary language expressions for the sixteen functions. Many other paraphrases are possible, but these afford a sample of the simplest equivalents.

* Language '''L6''' expresses the sixteen functions in one of several notations that are commonly used in formal logic.

==Translations==

* [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===

{{col-begin}}
{{col-break}}
* [[Inquiry Live]]
{{col-break}}
* [[Logic Live]]
{{col-end}}

===Peer nodes===

{{col-begin}}
{{col-break}}
* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic @ MyWikiBiz]
* [http://mathweb.org/wiki/Zeroth_order_logic Zeroth Order Logic @ MathWeb Wiki]
* [http://netknowledge.org/wiki/Zeroth_order_logic Zeroth Order Logic @ NetKnowledge]
* [http://wiki.oercommons.org/mediawiki/index.php/Zeroth_order_logic Zeroth Order Logic @ OER Commons]
{{col-break}}
* [http://p2pfoundation.net/Zeroth_Order_Logic Zeroth Order Logic @ P2P Foundation]
* [http://semanticweb.org/wiki/Zeroth_order_logic Zeroth Order Logic @ SemanticWeb]
* [http://ref.subwiki.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Subject Wikis]
* [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic @ Wikiversity Beta]
{{col-end}}

===Logical operators===

{{col-begin}}
{{col-break}}
* [[Exclusive disjunction]]
* [[Logical conjunction]]
* [[Logical disjunction]]
* [[Logical equality]]
{{col-break}}
* [[Logical implication]]
* [[Logical NAND]]
* [[Logical NNOR]]
* [[Logical negation|Negation]]
{{col-end}}

===Related topics===

{{col-begin}}
{{col-break}}
* [[Ampheck]]
* [[Boolean domain]]
* [[Boolean function]]
* [[Boolean-valued function]]
* [[Differential logic]]
{{col-break}}
* [[Logical graph]]
* [[Minimal negation operator]]
* [[Multigrade operator]]
* [[Parametric operator]]
* [[Peirce's law]]
{{col-break}}
* [[Propositional calculus]]
* [[Sole sufficient operator]]
* [[Truth table]]
* [[Universe of discourse]]
* [[Zeroth order logic]]
{{col-end}}

===Relational concepts===

{{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===

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Semiotic_Information Jon Awbrey, “Semiotic Information”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Introduction_to_Inquiry_Driven_Systems Jon Awbrey, “Introduction To Inquiry Driven Systems”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems Jon Awbrey, “Prospects For Inquiry Driven Systems”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Inquiry_Driven_Systems Jon Awbrey, “Inquiry Driven Systems : Inquiry Into Inquiry”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, “Propositional Equation Reasoning Systems”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, “Differential Logic : Introduction”]

* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, “Differential Propositional Calculus”]

* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, “Differential Logic and Dynamic Systems”]

==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.

{{col-begin}}
{{col-break}}
* [http://mywikibiz.com/Zeroth_order_logic Zeroth Order Logic], [http://mywikibiz.com/ MyWikiBiz]
* [http://planetmath.org/encyclopedia/ZerothOrderLogic.html Zeroth Order Logic], [http://planetmath.org/ PlanetMath]
* [http://beta.wikiversity.org/wiki/Zeroth_order_logic Zeroth Order Logic], [http://beta.wikiversity.org/ Wikiversity Beta]
* [http://getwiki.net/-Zeroth-Order_Logic Zeroth Order Logic], [http://getwiki.net/ GetWiki]
{{col-break}}
* [http://wikinfo.org/index.php/Zeroth_order_logic Zeroth Order Logic], [http://wikinfo.org/ Wikinfo]
* [http://textop.org/wiki/index.php?title=Zeroth_order_logic Zeroth Order Logic], [http://textop.org/wiki/ Textop Wiki]
* [http://en.wikipedia.org/w/index.php?title=Zeroth-order_logic&oldid=77109225 Zeroth Order Logic], [http://en.wikipedia.org/ Wikipedia]
* [http://altheim.com/cs/zol.html Zeroth Order Logic], [http://altheim.com/cs Altheim.com]
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