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Re: [ontolog-forum] Foundation Ontology Primitives

To: <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "sean barker" <sean.barker@xxxxxxxxxxxxx>
Date: Wed, 3 Feb 2010 13:14:46 -0000
Message-id: <33B52531673B4DF48AAE3D745DABE018@SMB>

Actually, circles, lines and points are all the same primitive - half-spaces of the plane: lines have zero curvature, points zero radius, and circles have finite radius and finite curvature. An ellipse is a circle after linear transformation.
A triangle is the intersection of three linear halfspaces.
BTW, point is not obviously a primitive, in the sense there are several different flavours of point - a 2D point is not the same as a 3D point, and a point in homogeneous co-ordinates is not quite the same as one in Cartesian co-ordinates. This is before you get to the more esoteric end of things, such a duality theory and geometry over algebraic systems other than the real numbers. I believe there is also a more generalised concept of a point called a turbine.
I'm not sure I can think of any more concrete example of the claim that an ontology is viewpoint specific

Sean Barker



From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Duane Nickull
Sent: 02 February 2010 19:54
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Foundation Ontology Primitives

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On 2/2/10 11:43 AM, "Matthew West" <dr.matthew.west@xxxxxxxxx> wrote:

>  I hope that it will not actually be necessary to try to precisely
> define
> the borderline between primitive and non-primitive.

A concept is primitive if it cannot be completely defined in terms of
concepts you already have defined.

Most OO programming languages are structured this way.  If there is any way to build such a concept with another class, then refactoring is often used.

Take drawing primitives as an example.  There is one base primitive which might be ?coordinate?.  This corresponds to a specific X,Y pair.  This is abstract so at this point it ignores all pixel resolutions etc but could generally taken to be based on a pixel grid.

The next level down would be some primitive shapes.  Candidates might be Line, Circle, Ellipse, Rectangle, Square etc.  On closer examination, circle can be stated to be a specialized type of ellipse (one with a constant radius value) and a square can be declared as a specialized type of rectangle (one with equal side lengths within a fixed unit of precision, usually the pixel resolution when implemented).  Line might also be a candidate for rectangle (a rectangle with height:width ratio exceeding certain limits) but lines could also carry the added property of an arc or path.  Therefore the true primitives might be coordinate (or point), line, ellipse and rectangle.  This represents a context of pixelated screens however.  In vector graphics (SVG et al) the primitives may be different.

A triangle then presents a test.  Is it another primitive of is it a specialized type of one of the existing graphic primitives.  One could create another primitive called ?fill? that takes parameters of a ?boundary? expressed in terms of lines.  This could then make up all other shapes such as polygon, triangle, star, etc..


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