]> 2009/04/07 OpenCyc Knowledge Base Copyright© 2001-2009 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. Mappings between OpenCyc terms and Wikipedia article names provided by Olena Medelyan and Catherine Legg, University of Waikato, NZ under a Creative Commons Attribution 3.0 license. 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. RationalNumber A specialization of <a href="http://sw.opencyc.org/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. A number NUM is an instance of <a href="http://sw.opencyc.org/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. rational number most rational rational numbers more rational rational

Rational number

http://en.wikipedia.org/wiki/Rational_number http://www.w3.org/2006/03/wn/wn20/instances/synset-rational_number-noun-1 Integer A specialization of <a href="http://sw.opencyc.org/concept/Mx4rvVjyqpwpEbGdrcN5Y29ycA" class="cyc_term">RationalNumber</a>. Each instance of <a href="http://sw.opencyc.org/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a> is a whole number with no fractional remainder. An integer may be positive (e.g. 42), zero, or negative (e.g. -42). Note that, in the KB browser, a fixed- or floating-point number representation such as `42.00' should not be assumed to refer to the integer 42. For it might only appear to correspond to that integer within the tolerance of its representation, and might in fact be an approximation to a non-integer number such as 42.0003. Also note that, unlike <a href="http://sw.opencyc.org/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, <a href="http://sw.opencyc.org/concept/Mx4rvWbgpJwpEbGdrcN5Y29ycA" class="cyc_term">SubLInteger</a> (q.v.) is a collection of integer-denoting expressions in the SubL programming language rather than a collection of integers themselves. Still, (<a href="http://sw.opencyc.org/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> <a href="http://sw.opencyc.org/concept/Mx4rvWbgpJwpEbGdrcN5Y29ycA" class="cyc_term">SubLInteger</a> <a href="http://sw.opencyc.org/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>) holds, but only under a special interpretation of <a href="http://sw.opencyc.org/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> forced by the fact that <a href="http://sw.opencyc.org/concept/Mx4rvWbgpJwpEbGdrcN5Y29ycA" class="cyc_term">SubLInteger</a> is a #$quotedCollection (q.v).) integer The collection of all instances of <a href="http://sw.opencyc.org/concept/Mx4r_4bScKNtQdiVw7XtX-HN0Q" class="cyc_term">ClarifyingCollectionType</a> that are used by the #$KRAKEN application to resolve natural language ambiguities. KE clarifying collection type KEClarifyingCollectionType Wikipedia Article URL (<a href="http://sw.opencyc.org/concept/Mx4rNv0nbm4TTjOp7yhmnzOyqg" class="cyc_term">wikipediaArticleURL</a> THING URL) means that in <a href="http://sw.opencyc.org/concept/Mx4rtqXA6OC8QdiWC72DuLJdUw" class="cyc_term">Wikipedia_WebSite</a> THING is described by an article located at URL wikipediaArticleURL seeAlsoURI <code>(<a href="http://sw.opencyc.org/concept/Mx4riWVFR6HJSpaEaHrcWS3MSA" class="cyc_term">seeAlsoURI</a> THING URI)</code> means that a description of the resource identified by URI is likely to contain information pertinent to THING. This predicate is roughly equivalent to rdfs:seeAlso. See Also URI TestOWLExportConcept test OWL export concept A <a href="http://sw.opencyc.org/concept/Mx4ret7qgOKgEdmAAAACs6hfSg" class="cyc_term">ConceptTypeByDomain</a> (q.v.). Instances of <a href="http://sw.opencyc.org/concept/Mx4r9fut4P7NEdmAAAACs2IKaQ" class="cyc_term">TestOWLExportConcept</a> are concepts each of which tests some aspect of the new export schema. type of atemporal collection in which membership is necessarily essential AtemporalNecessarilyEssentialCollectionType A collection of collections. Each instance <code>COL</code> of <a href="http://sw.opencyc.org/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/concept/Mx4rvViA45wpEbGdrcN5Y29ycA" class="cyc_term">disjointWith</a>) <a href="http://sw.opencyc.org/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/concept/Mx4rvViAzJwpEbGdrcN5Y29ycA" class="cyc_term">Collection</a>, <a href="http://sw.opencyc.org/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, and <a href="http://sw.opencyc.org/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/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/concept/Mx4rvViAxJwpEbGdrcN5Y29ycA" class="cyc_term">TemporalThing</a>) and <a href="http://sw.opencyc.org/concept/Mx4rwP4FM5wpEbGdrcN5Y29ycA" class="cyc_term">UniqueAnatomicalPartType</a> (which, though disjoint with <a href="http://sw.opencyc.org/concept/Mx4rvViAxJwpEbGdrcN5Y29ycA" class="cyc_term">TemporalThing</a>, has instances, such as <a href="http://sw.opencyc.org/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/concept/Mx4rvrhK-JwpEbGdrcN5Y29ycA" class="cyc_term">CollectionUnionFn</a> (<a href="http://sw.opencyc.org/concept/Mx4rvVjkdpwpEbGdrcN5Y29ycA" class="cyc_term">TheSet</a> <a href="http://sw.opencyc.org/concept/Mx4rvVjrdZwpEbGdrcN5Y29ycA" class="cyc_term">PrimeNumber</a> TodaysWinningLotteryNumbers)) This collection is clearly disjoint with <a href="http://sw.opencyc.org/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/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/concept/Mx4rGeylLJTfEdqAAAACs0uFOQ" class="cyc_term">PragmaticallyDecontextualizedCollection</a>. Pretty String (<a href="http://sw.opencyc.org/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/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 RationalNumber A specialization of <a href="http://sw.opencyc.org/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. A number NUM is an instance of <a href="http://sw.opencyc.org/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. rational number UnitOfMeasureConcept A <a href="http://sw.opencyc.org/concept/Mx4ret7qgOKgEdmAAAACs6hfSg" class="cyc_term">ConceptTypeByDomain</a> (q.v.). Instances of <a href="http://sw.opencyc.org/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/concept/Mx4rvViAqpwpEbGdrcN5Y29ycA" class="cyc_term">UnitOfMeasure</a>, major specializations or <a href="http://sw.opencyc.org/concept/Mx4rvViAp5wpEbGdrcN5Y29ycA" class="cyc_term">ScalarInterval</a>, and relations that are important to measurement theory are instances of this collection. unit of measure concept RealNumber real number The collection of real numbers; a specialization of both <a href="http://sw.opencyc.org/concept/Mx4rvVjzL5wpEbGdrcN5Y29ycA" class="cyc_term">IntervalOnNumberLine</a> and <a href="http://sw.opencyc.org/concept/Mx4rvViCW5wpEbGdrcN5Y29ycA" class="cyc_term">ScalarPointValue</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/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/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, <a href="http://sw.opencyc.org/concept/Mx4rvVjyqpwpEbGdrcN5Y29ycA" class="cyc_term">RationalNumber</a>, and <a href="http://sw.opencyc.org/concept/Mx4rwP4D45wpEbGdrcN5Y29ycA" class="cyc_term">NegativeNumber</a>. Note that <a href="http://sw.opencyc.org/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> is also a specialization of <a href="http://sw.opencyc.org/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/concept/Mx4rwL5mhJwpEbGdrcN5Y29ycA" class="cyc_term">ImaginaryNumber</a>). MeasurableScalarIntervalType type of measurable scalar interval A collection of collections and a specialization of <a href="http://sw.opencyc.org/concept/Mx4r91ZApkTvEdaAAACgye4oEQ" class="cyc_term">TotallyOrderedScalarIntervalType</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> is a collection of <a href="http://sw.opencyc.org/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/concept/Mx4rnVZQSiCmEdaAAACgyZzFrg" class="cyc_term">NumericInterval</a>) or quantities that can be assigned a numeric value (see <a href="http://sw.opencyc.org/concept/Mx4rr-2NGp7sQdidoL5VyxYMGg" class="cyc_term">MeasurableQuantity</a>). Instances of <a href="http://sw.opencyc.org/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> include <a href="http://sw.opencyc.org/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, <a href="http://sw.opencyc.org/concept/Mx4rvVjfYJwpEbGdrcN5Y29ycA" class="cyc_term">ProbabilityInterval</a>, <a href="http://sw.opencyc.org/concept/Mx4rvViYB5wpEbGdrcN5Y29ycA" class="cyc_term">RateOfRotation</a>, and <a href="http://sw.opencyc.org/concept/Mx4rvViApZwpEbGdrcN5Y29ycA" class="cyc_term">Time_Quantity</a>. Specializations include <a href="http://sw.opencyc.org/concept/Mx4rwDcy85wpEbGdrcN5Y29ycA" class="cyc_term">IntegerTypeByRange</a> and <a href="http://sw.opencyc.org/concept/Mx4rlsKf-MukQdiEYr6WbI2G4Q" class="cyc_term">MeasurableQuantityType</a>. RationalNumber A specialization of <a href="http://sw.opencyc.org/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. A number NUM is an instance of <a href="http://sw.opencyc.org/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. rational number <a href="http://sw.opencyc.org/concept/Mx4rF1b-lO_eEdmAAAACs2IKaQ" class="cyc_term">OwlSemanticDataType</a> is the collection of Owl data types. The datatypes can be characterized in two ways -- (1) by the type of thing it is; e.g. a positive integer, (2) by the way it is denoted; e.g. positive integers that are denoted by instances of <a href="http://sw.opencyc.org/concept/Mx4r3_R5Nk2iEdaCwAACs0x8nw" class="cyc_term">SubLPositiveInteger</a>. owl semantic data type OwlSemanticDataType A <a href="http://sw.opencyc.org/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, <code>xA</code>, is an <a href="http://sw.opencyc.org/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/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/concept/Mx4rNg-zlHbzQdmFOasy86iwmw" class="cyc_term">TranscendentalNumber</a>. AlgebraicNumber algebraic number wikipediaArticleName (<a href="http://sw.opencyc.org/concept/Mx4rTv-jk9SPTXa991kk5mAvHg" class="cyc_term">wikipediaArticleName</a> THING NAME) means that in <a href="http://sw.opencyc.org/concept/Mx4rtqXA6OC8QdiWC72DuLJdUw" class="cyc_term">Wikipedia_WebSite</a> THING is described by an article with the title NAME Wikipedia Article Name numbers-math-topic Numbers-Math-Topic RationalNumber A specialization of <a href="http://sw.opencyc.org/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. A number NUM is an instance of <a href="http://sw.opencyc.org/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. rational number