]> 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. irrational number The collection of all irrational numbers. A type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. The collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and a #$UnitOfMeasureCollection. IrrationalNumber irrational irrational numbers more irrational most irrational http://en.wikipedia.org/wiki/Irrational_number TranscendentalNumber transcendental number A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a>. A <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xT</code>, is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a> if and only if for all <code>n>0</code> <code>xT</code> is not the solution to any 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. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rQSKaIHb0QdmeFP53_RWUlg" class="cyc_term">AlgebraicNumber</a>. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>s are important in the history of mathematics because their investigation provided the first proof that it is impossible using only a straightedge and compass to construct a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjUVZwpEbGdrcN5Y29ycA" class="cyc_term">Square</a> of equal area to a given <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rmSmWUM7yEdmAAAACs0uFOQ" class="cyc_term">Circle</a>. The impossibility of such a construction follows from the proof that <pre>(<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBBJwpEbGdrcN5Y29ycA" class="cyc_term">isa</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvzKZSJwpEbGdrcN5Y29ycA" class="cyc_term">Pi_Number</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>). <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 The collection of all irrational numbers. A type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. The collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and a #$UnitOfMeasureCollection. irrational number IrrationalNumber The collection of all irrational numbers. A type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. The collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and a #$UnitOfMeasureCollection. irrational number IrrationalNumber The collection of all irrational numbers. A type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. The collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and a #$UnitOfMeasureCollection. irrational number IrrationalNumber 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 AtemporalNecessarilyEssentialCollectionType A collection of collections. Each instance <code>COL</code> of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rqEYnNVMqEdaSKAACs0x8nw" class="cyc_term">AtemporalNecessarilyEssentialCollectionType</a> (ANECT) is a collection satisfying three conditions: (1) <code>COL</code> is disjoint with (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViA45wpEbGdrcN5Y29ycA" class="cyc_term">disjointWith</a>) <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAxJwpEbGdrcN5Y29ycA" class="cyc_term">TemporalThing</a>, (2) every instance <code>INST</code> of <code>COL</code> is an instance of <code>COL</code> essentially (i.e. <code>INST</code> is an instance of <code>COL</code>, and could not exist without being an instance of <code>COL</code>), and (3) condition (2) is a necessary truth about <code>COL</code>. Positive examples of ANECTs include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAzZwpEbGdrcN5Y29ycA" class="cyc_term">Relation</a> (each of which is a collection of atemporals and is such that, necessarily, all of its instances are in it essentially). Negative examples include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjpUZwpEbGdrcN5Y29ycA" class="cyc_term">SpatialThing</a> (though arguably it is necessary that all of its instances are essentially instances of it, it is not disjoint with <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAxJwpEbGdrcN5Y29ycA" class="cyc_term">TemporalThing</a>) and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP4FM5wpEbGdrcN5Y29ycA" class="cyc_term">UniqueAnatomicalPartType</a> (which, though disjoint with <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAxJwpEbGdrcN5Y29ycA" class="cyc_term">TemporalThing</a>, has instances, such as <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjvDpwpEbGdrcN5Y29ycA" class="cyc_term">Heart</a>, that could exist even if they weren't instances of it; e.g. it might have been the case that every creature with a heart had at least two hearts). There are no known examples of Cyc-reified collections satisfying conditions (1) and (2) but not (3), but one can be contrived. Suppose that all of today's winning lottery numbers were primes. Now consider the collection: (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvrhK-JwpEbGdrcN5Y29ycA" class="cyc_term">CollectionUnionFn</a> (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjkdpwpEbGdrcN5Y29ycA" class="cyc_term">TheSet</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrdZwpEbGdrcN5Y29ycA" class="cyc_term">PrimeNumber</a> TodaysWinningLotteryNumbers)) This collection is clearly disjoint with <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAxJwpEbGdrcN5Y29ycA" class="cyc_term">TemporalThing</a> and, by hypothesis, all of its instances are in it essentially (as each prime number is essentially a prime number). But this last fact is not necessarily true of this collection: the collection might have had instances that belonged to it only contingently (i.e. not essentially), as it might have been the case that one of today's winning lottery numbers was non-prime, and no number is such that it is essentially one of today's winning lottery numbers. When asserting that something is an instance or specialization of a given instance of ANECT, it is appropriate to do so in the <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r3_SgQU2iEdaCwAACs0x8nw" class="cyc_term">UniversalVocabularyMt</a> (q.v.). Indeed, ANECT was specially defined to facilitate the movement of appropriate assertions to that microtheory. Cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rGeylLJTfEdqAAAACs0uFOQ" class="cyc_term">PragmaticallyDecontextualizedCollection</a>. type of atemporal collection in which membership is necessarily essential 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 The collection of all irrational numbers. A type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. The collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and a #$UnitOfMeasureCollection. irrational number IrrationalNumber 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 all irrational numbers. A type of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. The collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyaZwpEbGdrcN5Y29ycA" class="cyc_term">IrrationalNumber</a> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and a #$UnitOfMeasureCollection. irrational number IrrationalNumber 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