]> 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. type of measurable scalar interval MeasurableScalarIntervalType 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>. types of measurable scalar interval MeasurableQuantityType measurable quantity type A collection of collections and a specialization of both <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwF4t15wpEbGdrcN5Y29ycA" class="cyc_term">TotallyOrderedQuantityType</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rlsKf-MukQdiEYr6WbI2G4Q" class="cyc_term">MeasurableQuantityType</a> is a totally-ordered collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rr-2NGp7sQdidoL5VyxYMGg" class="cyc_term">MeasurableQuantity</a>[ies] (q.v.) that is <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwNM3N5wpEbGdrcN5Y29ycA" class="cyc_term">closedUnder</a> addition (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViArpwpEbGdrcN5Y29ycA" class="cyc_term">PlusFn</a>) and subtraction (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAppwpEbGdrcN5Y29ycA" class="cyc_term">DifferenceFn</a>). Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rlsKf-MukQdiEYr6WbI2G4Q" class="cyc_term">MeasurableQuantityType</a> include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmpwpEbGdrcN5Y29ycA" class="cyc_term">Distance</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/Mx4rvVkFnZwpEbGdrcN5Y29ycA" class="cyc_term">PrimitiveMeasurableQuantityType</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVja4JwpEbGdrcN5Y29ycA" class="cyc_term">DerivedMeasurableQuantityType</a>. A collection of collections. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjS2pwpEbGdrcN5Y29ycA" class="cyc_term">MaterialStrengthType</a> is a specific collection of attributes used in determining the strength of a material. Examples: <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVixwpwpEbGdrcN5Y29ycA" class="cyc_term">Hardness</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViVXZwpEbGdrcN5Y29ycA" class="cyc_term">Malleability</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViXc5wpEbGdrcN5Y29ycA" class="cyc_term">Ductility</a>, <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViE0ZwpEbGdrcN5Y29ycA" class="cyc_term">Elasticity</a>. MaterialStrengthType type of material strength type of integer classified by range IntegerTypeByRange A collection of collections. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwDcy85wpEbGdrcN5Y29ycA" class="cyc_term">IntegerTypeByRange</a> is a collection of integers in a particular range from a minimal element to a maximal element. For example, (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rva7bcJwpEbGdrcN5Y29ycA" class="cyc_term">IntegerFromToFn</a> 1 10), the collection of integers from 1 to 10 would be a member, since it has a minimal element, a maximal element, and all integers in between are instances of the collection. See also <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvft90JwpEbGdrcN5Y29ycA" class="cyc_term">integerBetween</a>. A Real Number between -1 and 1 real minus 1 to plus 1 Real-Minus1ToPlus1 positive number PositiveNumber A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. An instance NUMBER of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> is also an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv2r7MpwpEbGdrcN5Y29ycA" class="cyc_term">PositiveNumber</a> just in case NUMBER is greater than zero. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv2r7MpwpEbGdrcN5Y29ycA" class="cyc_term">PositiveNumber</a> include 42 and 0.17, but not 0 or -5. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVi_aZwpEbGdrcN5Y29ycA" class="cyc_term">NonNegativeInteger</a> is the sub-collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a> that excludes the negative integers. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVi_aZwpEbGdrcN5Y29ycA" class="cyc_term">NonNegativeInteger</a> is a whole number greater than or equal to zero -- for example, 0, 1, 2, 3, .... non-negative integer NonNegativeInteger A specialization of <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/Mx4rvs7acpwpEbGdrcN5Y29ycA" class="cyc_term">NonPositiveInteger</a> is the collection of all integers less than or equal to zero. non-positive integer NonPositiveInteger 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 non-positive number A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. An instance REAL of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> is also an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvoHONZwpEbGdrcN5Y29ycA" class="cyc_term">NonPositiveNumber</a> just in case REAL is less than or equal to zero. NonPositiveNumber negative integer NegativeInteger A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>. An instance INT of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a> is also an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP4DHZwpEbGdrcN5Y29ycA" class="cyc_term">NegativeInteger</a> if and only if INT is less than zero. 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 non-zero number NonZeroNumber A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>, and the binary union of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv2r7MpwpEbGdrcN5Y29ycA" class="cyc_term">PositiveNumber</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP4D45wpEbGdrcN5Y29ycA" class="cyc_term">NegativeNumber</a>. It is disjoint with the singleton set of 0. Real-Minus1ToPlus1-1 A Real Number between -1 and 1 real minus 1 to plus 1 1 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/Mx4rLOwZCvkjQdea-sfI2QK3kQ" class="cyc_term">ScalarProperInterval</a> (qq.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rrMRklqndQdiFxe5MQvukaA" class="cyc_term">ProperIntervalOnNumberLine</a> is an proper interval -- i.e. not just a single point (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvxwC-ZwpEbGdrcN5Y29ycA" class="cyc_term">Number_General</a>) -- on the real number line. For example, the phrase "numbers greater than zero and less than or equal to 10" describes such an interval. ProperIntervalOnNumberLine proper interval on number line NonNegativeNumber non-negative number <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyK5wpEbGdrcN5Y29ycA" class="cyc_term">NonNegativeNumber</a> is the sub-collection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> that excludes the negative reals. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyK5wpEbGdrcN5Y29ycA" class="cyc_term">NonNegativeNumber</a> is a number greater than or equal to zero -- for example, 0, 0.173, Pi, 4, and 101. Quantities measured in units -- for example, (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrsZwpEbGdrcN5Y29ycA" class="cyc_term">SecondsDuration</a> 4) and (<a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVi3VJwpEbGdrcN5Y29ycA" class="cyc_term">Mile</a> 42) -- are not instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyK5wpEbGdrcN5Y29ycA" class="cyc_term">NonNegativeNumber</a>, but rather are instances of its super-collection <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv3ockJwpEbGdrcN5Y29ycA" class="cyc_term">NonNegativeScalarInterval</a>. Interval On Number Line From Fn 0 60 (IntervalOnNumberLineFromFn 0 60) ImaginaryNumber imaginary number A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVi4CpwpEbGdrcN5Y29ycA" class="cyc_term">ComplexNumber</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwL5mhJwpEbGdrcN5Y29ycA" class="cyc_term">ImaginaryNumber</a> is a number of the type a+ib, where: (1) i is the square root of negative one (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvx4CzZwpEbGdrcN5Y29ycA" class="cyc_term">I_TheNumber</a>), (2) a and b are real numbers (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>), and (3) b is non-zero. Real0-1 A number between 0 and 1 real number between zero and one 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 even number A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>. An instance INT of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a> is also an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rv_RnYJwpEbGdrcN5Y29ycA" class="cyc_term">EvenNumber</a> if and only if INT is divisible (without remainder) by two. EvenNumber 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 odd number OddNumber A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>. An integer is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvssIH5wpEbGdrcN5Y29ycA" class="cyc_term">OddNumber</a> if and only if it is not divisible by 2 without remainder. It might be positive or negative. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjzL5wpEbGdrcN5Y29ycA" class="cyc_term">IntervalOnNumberLine</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rORcxXKnuQdiDj8CiPrnh2w" class="cyc_term">ContinuousIntervalOnNumberLine</a> is either a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> or a continuous proper interval on the real number line. For example, the phrase "real numbers greater than zero and less than or equal to 10" describes such an interval, but the phrase "integers greater than zero and less than or equal to 10" does not (cf. <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwTGgF5wpEbGdrcN5Y29ycA" class="cyc_term">IntegerExtent</a>). ContinuousIntervalOnNumberLine continuous interval on number line interval IntervalOnNumberLine A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rnVZQSiCmEdaAAACgyZzFrg" class="cyc_term">NumericInterval</a> (q.v.). Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjzL5wpEbGdrcN5Y29ycA" class="cyc_term">IntervalOnNumberLine</a> is either a particular <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> or a proper interval on the real number line (see <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rrMRklqndQdiFxe5MQvukaA" class="cyc_term">ProperIntervalOnNumberLine</a>). For example, the phrase "numbers greater than zero and less than or equal to 10" describes such an interval. Note that an interval on the real number line need not be continuous. E.g. the phrase "even integers between Pi and the square root of 1000" describes a noncontinuous instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjzL5wpEbGdrcN5Y29ycA" class="cyc_term">IntervalOnNumberLine</a>. Cf. the specialization <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rORcxXKnuQdiDj8CiPrnh2w" class="cyc_term">ContinuousIntervalOnNumberLine</a>. 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>). integer A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjyqpwpEbGdrcN5Y29ycA" class="cyc_term">RationalNumber</a>. Each instance of <a href="http://sw.opencyc.org/2008/06/10/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/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>, <a href="http://sw.opencyc.org/2008/06/10/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/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWbgpJwpEbGdrcN5Y29ycA" class="cyc_term">SubLInteger</a> <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>) holds, but only under a special interpretation of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBDpwpEbGdrcN5Y29ycA" class="cyc_term">genls</a> forced by the fact that <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvWbgpJwpEbGdrcN5Y29ycA" class="cyc_term">SubLInteger</a> is a #$quotedCollection (q.v).) Integer A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a>. An instance INT of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVieEpwpEbGdrcN5Y29ycA" class="cyc_term">Integer</a> is an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVie2ZwpEbGdrcN5Y29ycA" class="cyc_term">PositiveInteger</a> just in case INT is an integer greater than 0. positive integer PositiveInteger A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a>. An instance REAL of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> is also an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rwP4D45wpEbGdrcN5Y29ycA" class="cyc_term">NegativeNumber</a> just in case REAL is less than 0. negative number NegativeNumber real number greater than or equal to one Real1-Infinity <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVs2MZwpEbGdrcN5Y29ycA" class="cyc_term">Real1_Infinity</a> is the subcollection of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAmJwpEbGdrcN5Y29ycA" class="cyc_term">RealNumber</a> that excludes numbers less than 1. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVs2MZwpEbGdrcN5Y29ycA" class="cyc_term">Real1_Infinity</a> is a number greater than or equal to 1. A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rORcxXKnuQdiDj8CiPrnh2w" class="cyc_term">ContinuousIntervalOnNumberLine</a> (q.v.). This is the collection of all continuous numeric intervals (both real numbers and proper intervals on the real line) between 0 and 1 inclusive. Each instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjfYJwpEbGdrcN5Y29ycA" class="cyc_term">ProbabilityInterval</a> can be used as an argument to <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r1wAZXoIvEdqAAACQJw5drg" class="cyc_term">ProbabilityFn</a> (q.v.) to represent the <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjfYJwpEbGdrcN5Y29ycA" class="cyc_term">ProbabilityInterval</a> (q.v.) that a sentence is true. ProbabilityInterval probability Real0-100 A number between 0 and 100 used to denote the real0-100age of what ever. real number one through one hundred PrimeNumber prime number A specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVie2ZwpEbGdrcN5Y29ycA" class="cyc_term">PositiveInteger</a>. An integer <code>N</code> is a <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjrdZwpEbGdrcN5Y29ycA" class="cyc_term">PrimeNumber</a> if and only if it is greater than 1 and its only integral divisors are 1 and <code>N</code> itself. The collection of all specializations of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>, that is, of all collections of (first-order) collections, and an instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHUFI8h_TEdaAAABQ2rksLw" class="cyc_term">ThirdOrderCollection</a>. Instances of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> are collections of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a>s. Any instance of any instance of any instance of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHQdVmB_TEdaAAABQ2rksLw" class="cyc_term">SecondOrderCollection</a> is an <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjaApwpEbGdrcN5Y29ycA" class="cyc_term">Individual</a>. SecondOrderCollection second-order Cyc collection 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>. 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>. scalar intervals quantity topic ScalarIntervals-Quantity-Topic 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 A collection of collections and a specialization of <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rsY6gaGxxQdefg9tLUtQ-BQ" class="cyc_term">TotallyOrderedCollection</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rHIBS0h_TEdaAAABQ2rksLw" class="cyc_term">FirstOrderCollection</a> (qq.v.). Each <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4r91ZApkTvEdaAAACgye4oEQ" class="cyc_term">TotallyOrderedScalarIntervalType</a> is a totally-ordered collection all of whose instances are <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViAp5wpEbGdrcN5Y29ycA" class="cyc_term">ScalarInterval</a>s (q.v.) Specializations of this collection include <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvVjZs5wpEbGdrcN5Y29ycA" class="cyc_term">MeasurableScalarIntervalType</a> and <a href="http://sw.opencyc.org/2008/06/10/concept/Mx4rvViBKpwpEbGdrcN5Y29ycA" class="cyc_term">PrimitiveOrderedQuantityType</a>. totally ordered scalar interval type TotallyOrderedScalarIntervalType