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Formal Language:
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| CircularArc(circular arc) |
| appearance as argument number 1 |
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| (instance CircularArc OneDimensionalFigure) | Mid-level-ontology.kif 5797-5797 | Circular arc is an instance of one dimensional figure |
| (documentation CircularArc EnglishLanguage "A CircularArc is the arc of a circle between a pair of distinct points on a Circle.[Wikipedia]") | Mid-level-ontology.kif 5798-5799 | Circular arc is an instance of one dimensional figure |
| appearance as argument number 2 |
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| appearance as argument number 3 |
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| (domain arcLength 1 CircularArc) | Mid-level-ontology.kif 5832-5832 | The number 1 argument of arc length is an instance of circular arc |
| antecedent |
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| (=> (equal ?A CircularArc) (exists (?C) (and (equal ?C Circle) (geometricPart ?A ?C)))) |
Mid-level-ontology.kif 5806-5811 | If equal X and circular arc, then there exists Y such that equal Y, circle, and Y is a geometric part of X |
| (=> (and (equal ?A CircularArc) (pointOfFigure ?P ?A)) (exists (?C ?P2) (and (geometricPart ?A ?C) (equal ?C Circle) (pointOfFigure ?P2 ?C) (equal ?P ?P2)))) |
Mid-level-ontology.kif 5815-5824 | If equal X and circular arc and Y is a vertex of X, then All of the following hold: (1) there exist Z (2) W such that Z is a geometric part of X (3) equal Z (4) circle (5) W is a vertex of Z (6) equal Y (7) W |
| (=> (and (arcLength ?A ?L) (equal ?A CircularArc)) (exists (?P ?P2) (and (pointOfFigure ?P ?A) (pointOfFigure ?P2 ?A) (not (equal ?P ?P2)) (geometricDistance ?P ?P2 ?L)))) |
Mid-level-ontology.kif 5841-5851 | If X is the LengthMeasure of Y and equal Y and circular arc, then there exist Z, W such that Z is a vertex of Y, W is a vertex of Y, equal Z, W, and Z is geometric distance W for X |
| (=> (and (equal ?S CircularSegment) (equal ?A CircularArc) (geometricPart ?A ?S) (equal ?C ChordOfACircle) (geometricPart ?C ?S)) (exists (?P1 ?P2) (and (not (equal ?P1 ?P2)) (endPointsOfLine ?P1 ?P2 ?C) (pointOfIntersection ?A ?C ?P1) (pointOfIntersection ?A ?C ?P2)))) |
Mid-level-ontology.kif 6046-6059 | If equal X and circular segment, equal Y and circular arc, X is a geometric part of Y, equal Z and chord of a circle, and X is a geometric part of Z, then All of the following hold: (1) there exist W (2) V such that equal W (3) V (4) W (5) V are endPointsOfLine of Z (6) Y is point of intersection Z for W (7) Y is point of intersection Z for V |
| consequent |
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| (=> (equal ?S CircleSector) (exists (?C ?A) (and (equal ?C Circle) (geometricPart ?S ?C) (equal ?A CircularArc) (geometricPart ?A ?C) (sideOfFigure ?A ?S) (sideOfIntersection ?S ?C ?A)))) |
Mid-level-ontology.kif 5763-5772 | If equal X and circle sector, then All of the following hold: (1) there exist Y (2) Z such that equal Y (3) circle (4) Y is a geometric part of X (5) equal Z (6) circular arc (7) Y is a geometric part of Z (8) the size of X is Z (9) Z is the intersection X (10) Y |
| (=> (equal ?S CircleSector) (exists (?A ?AC) (and (equal ?A CentralAngle) (angleOfFigure ?A ?S) (equal ?AC CircularArc) (sideOfFigure ?AC ?S)))) |
Mid-level-ontology.kif 5774-5781 | If equal X and circle sector, then All of the following hold: (1) there exist Y (2) Z such that equal Y (3) central angle (4) Y is the angle found in X (5) equal Z (6) circular arc (7) the size of X is Z |
| (=> (and (equal ?S CircleSector) (equal ?A CentralAngle) (angleOfFigure ?A ?S) (equal ?L ClosedLineSegment) (sideOfFigure ?L ?A) (sideOfIntersection ?A ?S ?L) (lineMeasure ?L ?R)) (exists (?AC) (and (equal ?AC CircularArc) (sideOfFigure ?AC ?S) (arcLength ?AC ?R) (angularMeasure ?A (MeasureFn 1 Radian))))) |
Mid-level-ontology.kif 5910-5924 | If All of the following hold: (1) equal X and circle sector (2) equal Y and central angle (3) Y is the angle found in X (4) equal Z and closed line segment (5) the size of Y is Z (6) Z is the intersection Y and X (7) W is a line measure of Z, then there exists V such that equal V and circular arc and the size of X is V and W is the LengthMeasure of V and 1 radian(s) is an angular measure of Y |
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