Are there examples, particularly references to papers, regarding parallels between ontologies and set theories, specifically how both are utilized by machines?
Deb MacPherson
Sent from my iPhone It seems to me that beyond their being a *parallel* in mathematics, the concepts of term, primitive term, and construct (or open expresssion) come from and are standard in formal mathematics and model theory, since Tarski "introduction to logic and scientific method", continuing today, and applied carefully in formal renditions of everything from arithmetic to set theory to category theory, and in such collections as "Explanation and Proof in Mathematics."
For example, in an axiomatic arithmetic for the natural numbers, "0" and "successor" are primitive terms, while "+" is a defined term, and the open sentence x+successor(y) = successor (x +y)
might be one of the constructs used in the definition of "+" defintiions are expressions of the form: definedTerm (x1, xn arguments of term) means construct or
On Tue, Feb 28, 2012 at 10:42 AM, Matthew West <dr.matthew.west@xxxxxxxxx> wrote:
Dear Deborah,
Sorry, not sure what you are getting at.
Regards
Matthew West
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Hi Matthew - do you think there are parallels in mathematics - ie prime numbers? Deborah MacPherson
Sent from my iPhone
Dear Marcelino,
I’ll take a crack at these:
Construct: A syntactic structure that is itself devoid of meaning, but can have many meanings placed on it. E.g. the subject, verb, object structure can take on different meanings with the use of different subjects, objects, and verbs.
Primitive: A term that is not fully defined by logical constructs in terms of other terms in a theory (a text definition does not count). For example, a class that is defined as the intersection of two other classes is fully defined and is not primitive. A class that is defined as a subtype of anther class, but has no other axioms restricting membership is primitive – it is only partially defined.
Term: An identifier in a logical theory. In general a term has an intended interpretation, and is often named in terms of this intended interpretation. However, other models of the theory may exist.
Regards
Matthew West
Information Junction Tel: +44 1489 880185
Mobile: +44 750 3385279
Skype: dr.matthew.west matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.informationjunction.co.uk/
http://www.matthew-west.org.uk/
This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.
Registered office: 2 Brookside, Meadow Way, Letchworth Garden City, Hertfordshire, SG6 3JE.
Along my studies in the subject of ontologies, i perceived that i have some doubts about the meaning of some terms which generally appear in the literature. My doubts are (mainly) regarding to the following terms: Construct, primitive, term. What each of them means in the context of ontology? How they are related?
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