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In [[logic]] and [[mathematics]], a '''propositional calculus''' (or a '''sentential calculus''') is a [[formal system]] that represents the materials and the principles of ''propositional logic'' (or ''sentential logic'').  Propositional logic is a domain of formal subject matter that is, up to [[isomorphism]], constituted by the structural relationships of mathematical objects called ''[[proposition (mathematics)|proposition]]s''.
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A '''propositional calculus''' (or a '''sentential calculus''') is a [[formal system]] that represents the materials and the principles of ''propositional logic'' (or ''sentential logic'').  Propositional logic is a domain of formal subject matter that is, up to [[isomorphism]], constituted by the structural relationships of mathematical objects called ''[[proposition (mathematics)|proposition]]s''.
    
In general terms, a calculus is a [[formal system]] that consists of a set of syntactic expressions (''well-formed formulas'' or ''wffs''), a distinguished subset of these expressions, plus a set of transformation rules that define a [[binary relation]] on the space of expressions.   
 
In general terms, a calculus is a [[formal system]] that consists of a set of syntactic expressions (''well-formed formulas'' or ''wffs''), a distinguished subset of these expressions, plus a set of transformation rules that define a [[binary relation]] on the space of expressions.   
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* [[Elliot Mendelson|Mendelson, Elliot]] (1964), ''Introduction to Mathematical Logic'', D. Van Nostrand Company.
 
* [[Elliot Mendelson|Mendelson, Elliot]] (1964), ''Introduction to Mathematical Logic'', D. Van Nostrand Company.
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==See also==
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==Resources==
===Logical levels===
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* [[Zeroth order logic]]
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* [[Kevin C. Klement|Klement, Kevin C.]] (2006), "Propositional Logic", in James Fieser and Bradley Dowden (eds.), ''[[Internet Encyclopedia of Philosophy]]'', [http://www.iep.utm.edu/p/prop-log.htm Eprint].
* [[First order logic]]
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* [[Second order logic]]
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* [http://www.ltn.lv/~podnieks/mlog/ml2.htm Introduction to Mathematical Logic]
* [[Higher order logic]]
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* [http://www.visualstatistics.net/Scaling/Propositional%20Calculus/Elements%20of%20Propositional%20Calculus.htm Elements of Propositional Calculus]
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* ''[http://www.fecundity.com/logic/ forall x: an introduction to formal logic]'', by P.D. Magnus, covers formal semantics and proof theory for sentential logic.
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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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{{col-end}}
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===Peer nodes===
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===Building blocks===
   
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* [[Exclusive disjunction]]
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* [http://beta.wikiversity.org/wiki/Propositional_calculus Propositional Calculus @ Beta Wikiversity]
* [[Logical conjunction]]
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* [[Logical disjunction]]
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* [[Logical equality]]
   
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* [[Logical implication]]
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* [http://mywikibiz.com/Propositional_calculus Propositional Calculus @ MyWikiBiz]
* [[Logical NAND]]
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* [[Logical NNOR]]
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* [[Negation]]
   
{{col-end}}
 
{{col-end}}
    
===Related topics===
 
===Related topics===
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{{col-begin}}
 
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{{col-break}}
 
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* [[Ampheck]]
 
* [[Ampheck]]
* [[Boolean algebra]]
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* [[Boolean algebra topics]]
   
* [[Boolean domain]]
 
* [[Boolean domain]]
 
* [[Boolean function]]
 
* [[Boolean function]]
* [[Boolean logic]]
   
* [[Boolean-valued function]]
 
* [[Boolean-valued function]]
* [[Categorical logic]]
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* [[Combinational logic]]
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* [[Combinatory logic]]
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* [[Conceptual graph]]
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* [[Disjunctive syllogism]]
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* [[Entitative graph]]
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* [[Existential graph]]
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* [[Frege's propositional calculus]]
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* [[Implicational propositional calculus]]
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* [[Intuitionistic propositional calculus]]
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* [[Laws of Form]]
   
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{{col-break}}
 
* [[Logical graph]]
 
* [[Logical graph]]
* [[Logical value]]
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* [[Logical matrix]]
 
* [[Minimal negation operator]]
 
* [[Minimal negation operator]]
* [[Multigrade operator]]
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* [[Operation (mathematics)|Operation]]
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* [[Parametric operator]]
   
* [[Peirce's law]]
 
* [[Peirce's law]]
* [[Symmetric difference]]
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{{col-break}}
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* [[Propositional calculus]]
 
* [[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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===Related works===
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===Related articles===
 
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* [[Douglas Hofstadter|Hofstadter, D.R.]], ''[[Gödel, Escher, Bach]]''
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==External links==
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* [[Kevin C. Klement|Klement, Kevin C.]] (2006), "Propositional Logic", in James Fieser and Bradley Dowden (eds.), ''[[Internet Encyclopedia of Philosophy]]'', [http://www.iep.utm.edu/p/prop-log.htm Eprint].
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* [http://www.ltn.lv/~podnieks/mlog/ml2.htm Introduction to Mathematical Logic]
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, “Propositional Equation Reasoning Systems”]
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* [http://www.visualstatistics.net/Scaling/Propositional%20Calculus/Elements%20of%20Propositional%20Calculus.htm Elements of Propositional Calculus]
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* [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, “Differential Propositional Calculus”]
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* ''[http://www.fecundity.com/logic/ forall x: an introduction to formal logic]'', by P.D. Magnus, covers formal semantics and proof theory for sentential logic.
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* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, “Differential Logic : Introduction”]
    
==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.
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* [http://www.getwiki.net/-Propositional_Calculus&oldid=1695 "Propositional calculus"], [http://www.getwiki.net/ GetWiki].
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    revision as of 11:58, 29 Nov 2006 by Jon Awbrey
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* [http://mywikibiz.com/Propositional_calculus Propositional Calculus], [http://mywikibiz.com/ MyWikiBiz]
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* [http://beta.wikiversity.org/wiki/Propositional_calculus Propositional Calculus], [http://beta.wikiversity.org/ Beta Wikiversity]
 
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* [http://planetmath.org/encyclopedia/PropositionalCalculus.html Propositional Calculus], [http://planetmath.org/ PlanetMath]
* [http://www.wikinfo.org/index.php?title=Propositional_calculus&oldid=28000 "Propositional calculus"], [http://www.wikinfo.org/ Wikinfo].
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* [http://www.getwiki.net/-Propositional_Calculus Propositional Calculus], [http://www.getwiki.net/ GetWiki]
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    revision as of 18:34, 19 November 2006 by Jon Awbrey
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* [http://www.textop.org/wiki/index.php?title=Propositional_calculus Propositional Calculus], [http://www.textop.org/wiki/ Textop Wiki]
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* [http://www.wikinfo.org/index.php/Propositional_calculus Propositional Calculus], [http://www.wikinfo.org/ Wikinfo]
 
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* [http://en.wikipedia.org/w/index.php?title=Propositional_calculus&oldid=77110794 Propositional Calculus], [http://en.wikipedia.org/ Wikipedia]
* [http://en.wikipedia.org/w/index.php?title=Propositional_calculus&oldid=74069381 "Propositional calculus"], [http://en.wikipedia.org/ Wikipedia].
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