<html xml:lang="en" lang="en"> <head xmlns:m="http://www.w3.org/1998/Math/MathML"><meta http-equiv="Content-Type" content="text/html; charset=utf-8"><link rel="Alternate" type="text/xml" title="RDF" href="http://b2e.ex-code.com/xmlsrv/rdf.php?blog=8"><link rel="Alternate" type="text/xml" title="RSS .92" href="http://b2e.ex-code.com/xmlsrv/rss.php?blog=8"><link rel="Alternate" type="text/xml" title="RSS 2.0" href="http://b2e.ex-code.com/xmlsrv/rss2.php?blog=8"><link rel="Alternate" type="application/atom+xml" title="Atom" href="http://b2e.ex-code.com/xmlsrv/atom.php?blog=8"><meta http-equiv="Last-Modified" content="2005-11-07T10:32:13+0500"> <title>License for Theory of Formulas Online Text</title> <meta name="Description" content="Theory of Formulas is licensed under GFDL (GNU Free Documentation License)"> <meta http-equiv="Content-Script-Type" content="text/javascript"> <link rel="Stylesheet" type="text/css" href="article-html.css"> <link rel="Stylesheet" type="text/css" href="article-math.css"> <style type="text/css"> .ad { font-family: "Arial", "Helvetica", sans-serif; width: auto } </style> <meta name="Keywords" content="mathematical expressions theory, mathematical formulas theory, mathematical theory of formulas, mathematical theory of expressions, theory of mathematical formulas, theory of mathematical expressions, formulae, axiomatic theory, math logic, mathematical logic, foundation of math, foundation of mathematics, math foundations, variable substitution, morphisms, multidimensional relation, multi dimensional relation, composition of multidimensional relations, composition of multi dimensional relations, representation of formulas, representation of expressions, expression representations, algebraic logic, subexpression, subformula, indexes, indices, reindexation, category theory, theory of categories, n-ary relation, nary relation, composition relations, abstract mathematical theory, abstract theory, abstract math theory, abstract mathematics, abstract math, mathematical abstraction, math abstraction, triplet, functional dependency, functional dependencies, variable dependency, variable dependencies, dependency of variables, dependencies of variables, dependency of parameters, dependencies of parameters, X and Y, X, Y and Z"><meta name="Author" content="Victor Porton"><meta name="Copyright" content="Copyright © 2005 Victor Porton"><meta name="Date" content="2005-11-07T10:32:13+0500"><script type="text/javascript">function clk(e,id){e=window.event?window.event:e;if(e.preventDefault)e.preventDefault();else e.returnValue=false;var a=document.getElementById?document.getElementById(id):document.all[id];window.open(a.attributes.href.value,'_top');}</script><script src="mathml-in-html.js"> </script><link rel="Stylesheet" type="text/css" href="article-wrap.css"><object id="mathplayer" classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987"> </object><?import namespace="m" implementation="#mathplayer"></head> <body xmlns:m="http://www.w3.org/1998/Math/MathML" onload="convert_mathml();"><div class="center"><script type="text/javascript">google_ad_client = "pub-9523722979947731";
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</script><script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script></div><div class="body-ad-wrap"><p class="frame-nav"><a href="/">Home</a> <a href="http://b2e.ex-code.com/index.php/math">News</a> <a href="/donate.html">Donate</a> || <a href="http://www.spreadfirefox.com/?q=affiliates&amp;id=41324" title="Best Web browser, replace IE">Math Web browser</a></p><div class="titlepage"><h1>License for Theory of Formulas Online Text</h1><p>Use <a href="http://www.spreadfirefox.com/?q=affiliates&amp;id=41324">MathML compatible browser</a> to view formulas.</p><p class="author-line"><span class="parahead">Author:</span> <a href="http://porton.ex-code.com">Victor Porton</a></p><p class="keywords"> <span class="parahead">Keywords:</span> mathematical expressions theory, mathematical formulas theory, mathematical theory of formulas, mathematical theory of expressions, theory of mathematical formulas, theory of mathematical expressions, formulae, axiomatic theory, math logic, mathematical logic, foundation of math, foundation of mathematics, math foundations, variable substitution, morphisms, multidimensional relation, multi dimensional relation, composition of multidimensional relations, composition of multi dimensional relations, representation of formulas, representation of expressions, expression representations, algebraic logic, subexpression, subformula, indexes, indices, reindexation, category theory, theory of categories, n-ary relation, nary relation, composition relations, abstract mathematical theory, abstract theory, abstract math theory, abstract mathematics, abstract math, mathematical abstraction, math abstraction, triplet, functional dependency, functional dependencies, variable dependency, variable dependencies, dependency of variables, dependencies of variables, dependency of parameters, dependencies of parameters, X and Y, X, Y and Z</p></div><p><a href="/theory-of-formulas-index.html">Axiomatic Theory of Formulas pages on this site</a>.</p><p><strong>This document is rough unfinished draft</strong>. See also an <a href="/formulas-theory.html">older version</a> of formulas theory article.</p><h2 id="d15e45">Table of Contents</h2><ul class="ToC"><li><a href="#d16e17">Licensing etc.</a><ul class="ToC"><li><a href="#d16e22">About the Original Method Authorship</a></li><li><a href="#d16e50">License</a></li></ul></li></ul><h2 id="d16e17">Licensing etc.</h2><h3 id="d16e22">About the Original Method Authorship</h3><p><a href="http://www.mathematics21.org/method.html">21st Century Math Method</a>, <a href="http://www.mathematics21.org/theory-of-formulas-index.html">Operator Theory of Formulas</a>, and <a href="http://www.mathematics21.org/algebraic-general-topology.html">Algebraic General Topology and Math Synthesis</a> were developed by Victor Porton (<a href="http://ex-code.com/~porton/">http://ex-code.com/~porton/</a>). See <a href="http://www.mathematics21.org">www.mathematics21.org</a></p><p>Please <a href="http://www.mathematics21.org/donate.html">donate</a> to the method author to help in further research.</p><h3 id="d16e50">License</h3><p>Permission is granted to copy, distribute and/or modify this document under the terms of the <a href="/gfdl-1.2.html">GNU Free Documentation License</a>, Version 1.2 published by the Free Software Foundation; with the Invariant Sections being</p><ul><li>Trademarks,</li><li>About the Original Method Authorship,</li></ul><p>with the Front-Cover Texts being</p><ul><li>More on the site <a href="http://www.mathematics21.org">www.mathematics21.org</a>, </li></ul><p>and with the Back-Cover Texts being</p><ul><li>This method was developed by <a href="http://ex-code.com/~porton/">Victor Porton</a> during his revolutionary research <a href="http://www.mathematics21.org/algebraic-general-topology.html">Algebraic General Topology and Math Synthesis</a>. See the Web site <a href="http://www.mathematics21.org">www.mathematics21.org</a> </li></ul><p>For using this document in Wiki like collaboration areas this license requirement is weakened by allowing to apply to front and back covers invariant sections rules instead of front and back cover rules in Wiki collaboration areas.</p><h2 id="d18e195">Related Links</h2><ul><li><a href="/theory-of-formulas-index.html">Axiomatic Theory of Formulas pages on this site</a>.</li><li><a href="/formulas.xml">This article as one <abbr>XHTML</abbr>+<acronym>MathML</acronym> file</a>.</li><li><strong>Axiomatic Theory of Formulas</strong> (old version of this theory, essentially based on universal algebra; but a more ready document than this). <a href="http://ex-code.com/~porton/">Victor Porton</a>. 2005. <ul><li><a href="/formulas-theory.html">first part</a>;</li><li><a href="/representation-of-formulas.html">second part</a> (<q>Representation Related Properties of Formulas</q>).</li></ul> </li><li><a href="http://b2e.ex-code.com/index.php/math/2005/08/12/definition_of_category_with_multiple_sou">Definition of category with multiple domains and ranges</a>.</li><li><a href="/method.html">21 Century Math Method</a> (rough draft), a logical method which will use this theory of formulas.</li><li><a href="/programming.html">21 Century Math Method in Programming</a> (rough draft).</li><li><a href="/news/2005-07-07-transformations-algebra.html">Algebra of transformations of formulas</a> (a <a href="/news.html">weblog</a> message by <a href="http://ex-code.com/~porton/">Victor Porton</a>).</li><li><a href="/21mm-software.html">Software for 21 Century Math Method</a>.</li><li><a href="/21mm-research-plans.html">21 Century Math Method - Further Research Plans</a>.</li><li><a href="/">www.mathematics21.org</a></li><li><a href="/journal.html">Journal of post-Axiomatic Mathematics and Logic</a>.</li></ul><h2 id="d18e289">License</h2><p><a href="/formulas/legal.xml">See here</a> about licensing of this text etc.</p><hr><h2 id="d15e59">Related Web Categories</h2><p>See also <a href="/new-categories.html">my suggestions for new mathematics classification categories</a>.</p><ul class="webdir-links"><li><a href="http://directory.google.com/Top/Computers/Computer_Science/Theoretical/">/Computers/Computer_Science/Theoretical/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Algebra/">/Science/Math/Algebra/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Logic_and_Foundations/">/Science/Math/Logic_and_Foundations/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Logic_and_Foundations/Foundations/">/Science/Math/Logic_and_Foundations/Foundations/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Logic_and_Foundations/Model_Theory/">/Science/Math/Logic_and_Foundations/Model_Theory/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Algebra/Category_Theory/">/Science/Math/Algebra/Category_Theory/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Publications/Online_Texts/">/Science/Math/Publications/Online_Texts/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Logic_and_Foundations/Education/">/Science/Math/Logic_and_Foundations/Education/</a></li><li><a href="http://directory.google.com/Top/Science/Math/Education/">/Science/Math/Education/</a></li></ul><hr><p class="copyright">Copyright © 2005 Victor Porton</p><p>Produced with <a href="http://www.mathematics21.org/xslt.html">XSLT Stylesheets for Math</a>.</p></div><div class="center"><script type="text/javascript">google_ad_client = "pub-9523722979947731";
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