]> 2008/06/10 OpenCyc Knowledge Base Copyright© 2001-2008 Cycorp, Inc., http://www.cyc.com/, Austin, TX, USA This file contains an OWL representation of information contained in the OpenCyc Knowledge Base. The content of this OWL file is licensed under the Creative Commons Attribution 3.0 license whose text can be found at http://creativecommons.org/licenses/by/3.0/legalcode. The content of this OWL file, including the OpenCyc content it represents, constitutes the "Work" referred to in the Creative Commons license. The terms of this license equally apply to, without limitation, renamings and other logically equivalent reformulations of the content of this OWL file (or portions thereof) in any natural or formal language, as well as to derivations of this content or inclusion of it in other ontologies. externalID A unique, language-neutral, variable-sized identifier for a concept that can be used to refer unambiguously to that concept across OWL exports or across Cyc inference engines. label A natural-language representation for a concept that is both human readable and readable by the Cyc inference engine. These terms are not guaranteed to refer to the same concept across time but are guaranteed to be consistent within a particular OWL export. Use 'cycAnnot:externalID' for unambiguously referring to a concept across OWL exports or across Cyc inference engines. A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xA</code>, is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQSKaIHb0QdmeFP53_RWUlg" class="cyc_term">AlgebraicNumber</a> if and only if it is the solution to some polynomial equation of the form <pre> anxn + an-1xn-1 + ... + a1x + a0 = 0 </pre> where the <code>ai</code> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>s. The smallest <code>n</code> for which <code>xA</code> is the solution to some polynomial equation of order <code>n</code> is called the degree of <code>xA</code>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>. algebraic number AlgebraicNumber http://en.wikipedia.org/wiki/Algebraic_number algebraic numbers rational number A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. A number NUM is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyqpwpEbGdrcN5Y29ycA" class="cyc_term">RationalNumber</a> just in case NUM can be expressed as the quotient of two integers. For example, 3/4, 2 1/8, 0.3333333..., 11/5. RationalNumber <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvr2CBJwpEbGdrcN5Y29ycA" class="cyc_term">GoldenRatio_Number</a> is the mathematical constant which represents the Golden Ratio and is defined to be (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAq5wpEbGdrcN5Y29ycA" class="cyc_term">QuotientFn</a> (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViArpwpEbGdrcN5Y29ycA" class="cyc_term">PlusFn</a> 1 (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjxBZwpEbGdrcN5Y29ycA" class="cyc_term">SquareRootFn</a> 5)) 2). The Golden Ratio has many surprising and curious mathematical properties. It is also sometimes called the 'Divine Proportion', and has been extensively used in architecture because objects in this proportion tend to be visually appealing. Although <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvr2CBJwpEbGdrcN5Y29ycA" class="cyc_term">GoldenRatio_Number</a> is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a>, a reasonable rational approximation is 1.6180340 GoldenRatio-Number the golden ratio A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xA</code>, is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQSKaIHb0QdmeFP53_RWUlg" class="cyc_term">AlgebraicNumber</a> if and only if it is the solution to some polynomial equation of the form <pre> anxn + an-1xn-1 + ... + a1x + a0 = 0 </pre> where the <code>ai</code> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>s. The smallest <code>n</code> for which <code>xA</code> is the solution to some polynomial equation of order <code>n</code> is called the degree of <code>xA</code>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>. algebraic number AlgebraicNumber Pretty String (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwLSVCpwpEbGdrcN5Y29ycA" class="cyc_term">prettyString</a> TERM STRING) means that STRING is the English word or expression (sequence of words) commonly used to refer to TERM. The predicate <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwLSVCpwpEbGdrcN5Y29ycA" class="cyc_term">prettyString</a> is used by the code which generates CycL to English paraphrases, but its applicability is not restricted to this use. prettyString A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xA</code>, is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQSKaIHb0QdmeFP53_RWUlg" class="cyc_term">AlgebraicNumber</a> if and only if it is the solution to some polynomial equation of the form <pre> anxn + an-1xn-1 + ... + a1x + a0 = 0 </pre> where the <code>ai</code> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>s. The smallest <code>n</code> for which <code>xA</code> is the solution to some polynomial equation of order <code>n</code> is called the degree of <code>xA</code>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>. algebraic number AlgebraicNumber The collection of all instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r_4bScKNtQdiVw7XtX-HN0Q" class="cyc_term">ClarifyingCollectionType</a> that are used by the #$KRAKEN application to resolve natural language ambiguities. KE clarifying collection type KEClarifyingCollectionType MeasurableScalarIntervalType type of measurable scalar interval A collection of collections and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r91ZApkTvEdaAAACgye4oEQ" class="cyc_term">TotallyOrderedScalarIntervalType</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> is a collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAp5wpEbGdrcN5Y29ycA" class="cyc_term">ScalarInterval</a>s that are quantifiable; i.e. they are either purely numeric (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rnVZQSiCmEdaAAACgyZzFrg" class="cyc_term">NumericInterval</a>) or quantities that can be assigned a numeric value (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rr-2NGp7sQdidoL5VyxYMGg" class="cyc_term">MeasurableQuantity</a>). Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjfYJwpEbGdrcN5Y29ycA" class="cyc_term">ProbabilityInterval</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViYB5wpEbGdrcN5Y29ycA" class="cyc_term">RateOfRotation</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViApZwpEbGdrcN5Y29ycA" class="cyc_term">Time_Quantity</a>. Specializations include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwDcy85wpEbGdrcN5Y29ycA" class="cyc_term">IntegerTypeByRange</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rlsKf-MukQdiEYr6WbI2G4Q" class="cyc_term">MeasurableQuantityType</a>. The collection of real numbers; a specialization of both <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjzL5wpEbGdrcN5Y29ycA" class="cyc_term">IntervalOnNumberLine</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViCW5wpEbGdrcN5Y29ycA" class="cyc_term">ScalarPointValue</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> is a single point on the real number line, which has no upper or lower bounds. Specializations of this collection include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyqpwpEbGdrcN5Y29ycA" class="cyc_term">RationalNumber</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP4D45wpEbGdrcN5Y29ycA" class="cyc_term">NegativeNumber</a>. Note that <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> is also a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVi4CpwpEbGdrcN5Y29ycA" class="cyc_term">ComplexNumber</a> (q.v.), and any instance of the former constitutes a degenerate case of the latter, in that the value along the real's "imaginary axis" is zero (cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwL5mhJwpEbGdrcN5Y29ycA" class="cyc_term">ImaginaryNumber</a>). RealNumber real number A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xA</code>, is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQSKaIHb0QdmeFP53_RWUlg" class="cyc_term">AlgebraicNumber</a> if and only if it is the solution to some polynomial equation of the form <pre> anxn + an-1xn-1 + ... + a1x + a0 = 0 </pre> where the <code>ai</code> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>s. The smallest <code>n</code> for which <code>xA</code> is the solution to some polynomial equation of order <code>n</code> is called the degree of <code>xA</code>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>. algebraic number AlgebraicNumber A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4ret7qgOKgEdmAAAACs6hfSg" class="cyc_term">ConceptTypeByDomain</a> (q.v.). Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rC-8cJgBpEdqAAAACs0uFOQ" class="cyc_term">UnitOfMeasureConcept</a> are collections and relations having to do with unit of measurement functions and the kinds of quantities they return as values. Important specializations and instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAqpwpEbGdrcN5Y29ycA" class="cyc_term">UnitOfMeasure</a>, major specializations or <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAp5wpEbGdrcN5Y29ycA" class="cyc_term">ScalarInterval</a>, and relations that are important to measurement theory are instances of this collection. UnitOfMeasureConcept unit of measure concept A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xA</code>, is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQSKaIHb0QdmeFP53_RWUlg" class="cyc_term">AlgebraicNumber</a> if and only if it is the solution to some polynomial equation of the form <pre> anxn + an-1xn-1 + ... + a1x + a0 = 0 </pre> where the <code>ai</code> are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>s. The smallest <code>n</code> for which <code>xA</code> is the solution to some polynomial equation of order <code>n</code> is called the degree of <code>xA</code>. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>. algebraic number AlgebraicNumber