Changes

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''.

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.   

* [[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.

==See also==

==Resources==

===Logical levels===

* [[Zeroth order logic]]

* [[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]]

 

* [[Second order logic]]

* [http://www.ltn.lv/~podnieks/mlog/ml2.htm Introduction to Mathematical Logic]

* [[Higher order logic]]

 

 

* ''[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.

 

 

 

* [[Inquiry Live]]

* [[Logic Live]]

 

{{col-begin}}

{{col-begin}}

{{col-break}}

{{col-break}}

* [[Exclusive disjunction]]

* [http://beta.wikiversity.org/wiki/Propositional_calculus Propositional Calculus @ Beta Wikiversity]

* [[Logical equality]]

{{col-break}}

{{col-break}}

* [[Logical implication]]

* [http://mywikibiz.com/Propositional_calculus Propositional Calculus @ MyWikiBiz]

* [[Negation]]

{{col-end}}

{{col-end}}

===Related topics===

===Related topics===

{{col-begin}}

{{col-begin}}

{{col-break}}

{{col-break}}

* [[Ampheck]]

* [[Ampheck]]

* [[Boolean domain]]

* [[Boolean domain]]

* [[Boolean function]]

* [[Boolean function]]

* [[Boolean-valued function]]

* [[Boolean-valued function]]

{{col-break}}

{{col-break}}

* [[Logical graph]]

* [[Logical graph]]

* [[Logical value]]

* [[Logical matrix]]

* [[Minimal negation operator]]

* [[Minimal negation operator]]

* [[Peirce's law]]

* [[Peirce's law]]

* [[Symmetric difference]]

* [[Propositional calculus]]

* [[Truth table]]

* [[Truth table]]

{{col-end}}

{{col-end}}

===Related works===

===Related articles===

 

 

 

* [http://www.ltn.lv/~podnieks/mlog/ml2.htm Introduction to Mathematical Logic]

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

* [http://www.visualstatistics.net/Scaling/Propositional%20Calculus/Elements%20of%20Propositional%20Calculus.htm Elements of Propositional Calculus]

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

* ''[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.

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

==Document history==

==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.

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://www.getwiki.net/-Propositional_Calculus&oldid=1695 "Propositional calculus"], [http://www.getwiki.net/ GetWiki].

<!--via GetWiki: Propositional calculus

 

* [http://www.wikinfo.org/index.php?title=Propositional_calculus&oldid=28000 "Propositional calculus"], [http://www.wikinfo.org/ Wikinfo].

* [http://www.getwiki.net/-Propositional_Calculus Propositional Calculus], [http://www.getwiki.net/ GetWiki]

<!--via Wikinfo: Propositional calculus

{{col-break}}

    revision as of 18:34, 19 November 2006 by Jon Awbrey

* [http://www.textop.org/wiki/index.php?title=Propositional_calculus Propositional Calculus], [http://www.textop.org/wiki/ Textop Wiki]

//-->

* [http://www.wikinfo.org/index.php/Propositional_calculus Propositional Calculus], [http://www.wikinfo.org/ Wikinfo]

 

* [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].

{{col-end}}

//-->

<br><sharethis />

<br><sharethis />