Propositional calculus - Revision history

Jon Awbrey: update

2015-11-07T15:56:40Z

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Jon Awbrey: update

2013-10-06T03:38:34Z

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Jon Awbrey: trim

2013-10-06T02:40:19Z

trim

Jon Awbrey: Category:Charles Sanders Peirce

2011-10-29T19:00:22Z

Category:Charles Sanders Peirce

Jon Awbrey: /* Information, Inquiry */

2010-05-23T11:28:57Z

Information, Inquiry

Jon Awbrey: + Category:Open Educational Resource

2010-05-22T15:02:16Z

+ Category:Open Educational Resource

Jon Awbrey: /* Syllabus */ update

2010-05-22T14:48:22Z

Syllabus: update

Jon Awbrey: typo

2010-05-10T18:52:50Z

typo

Jon Awbrey: ☞ This page belongs to resource collections on Logic and Inquiry.

2010-05-10T18:52:16Z

<font size="3">☞</font> This page belongs to resource collections on Logic and Inquiry.

Jon Awbrey: cats

2010-05-03T04:44:39Z

cats

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 * [http://en.wikipedia.org/w/index.php?title=Propositional_calculus&oldid=77110794 Propositional Calculus], [http://en.wikipedia.org/ Wikipedia]
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 [[Category:Open Educational Resource]]
 [[Category:Peer Educational Resource]]
 [[Category:Computer Science]]
 [[Category:Formal Grammars]]

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 * [[Pragmatic maxim]]
-* [[Pragmatic theory of truth]]
+* [[Truth theory]]
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-* [http://beta.wikiversity.org/wiki/Propositional_calculus Propositional Calculus @ Beta Wikiversity]
+* [http://mywikibiz.com/Propositional_calculus Propositional Calculus @ MyWikiBiz]
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-* [http://mywikibiz.com/Propositional_calculus Propositional Calculus @ MyWikiBiz]
+* [[Logical implication]]
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 * [[Boolean function]]
 * [[Boolean-valued function]]
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 * [[Logical graph]]
 * [[Minimal negation operator]]
 * [[Peirce's law]]
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 * [[Propositional calculus]]
 * [[Truth table]]
 * [[Universe of discourse]]
 * [[Zeroth order logic]]
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 ===Related articles===
 * [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, &ldquo;Propositional Equation Reasoning Systems&rdquo;]
 * [http://planetmath.org/encyclopedia/DifferentialPropositionalCalculus.html Jon Awbrey, &ldquo;Differential Propositional Calculus&rdquo;]
-* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_:_Introduction Jon Awbrey, &ldquo;Differential Logic : Introduction&rdquo;]
+* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Differential_Logic_and_Dynamic_Systems_2.0 Jon Awbrey, &ldquo;Differential Logic and Dynamic Systems&rdquo;]
 ==Document history==

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 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.
-When the expressions are interpreted for mathematical purposes, the transformation rules are typically intended to preserve some type of [[semantic equivalence relation]] among the expressions.  In particular, when the expressions are intepreted as a [[logical system]], the [[semantic equivalence]] is typically intended to be [[logical equivalence]].  In this setting, the transformation rules can be used to derive logically equivalent expressions from any given expression.  These derivations include as special cases (1) the problem of ''simplifying'' expressions and (2) the problem of deciding whether a given expression is equivalent to an expression in the distinguished subset, typically interpreted as the subset of logical ''[[axiom]]s''.
+When the expressions are interpreted for mathematical purposes, the transformation rules are typically intended to preserve some type of [[semantic equivalence relation]] among the expressions.  In particular, when the expressions are interpreted as a [[logical system]], the [[semantic equivalence]] is typically intended to be [[logical equivalence]].  In this setting, the transformation rules can be used to derive logically equivalent expressions from any given expression.  These derivations include as special cases (1) the problem of ''simplifying'' expressions and (2) the problem of deciding whether a given expression is equivalent to an expression in the distinguished subset, typically interpreted as the subset of logical ''[[axiom]]s''.
 The set of axioms may be empty, a nonempty finite set, a countably infinite set, or given by axiom schemata.  A [[formal grammar]] recursively defines the expressions and well-formed formulas (wffs) of the [[formal language|language]].  In addition a [[semantics]] is given which defines truth and valuations (or interpretations).  It allows us to determine which wffs are valid, that is, are [[theorem]]s.

← Older revision		Revision as of 18:52, 10 May 2010
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		+	<font size="3">☞</font> This page belongs to resource collections on [[Logic Live\|Logic]] and [[Inquiry Live\|Inquiry]].
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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''.		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''.