|To:||ian@xxxxxxxxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||Jawit Kien <jawit.kien@xxxxxxxxx>|
|Date:||Tue, 2 Feb 2010 10:11:27 -0600|
On Tue, Feb 2, 2010 at 3:53 AM, Ian Bailey <ian@xxxxxxxxxxxxxxxx> wrote:In the hope that we can actually discuss some details about ontologies and
Hi Pat (I won't qualify which Pat, as I'm pretty sure the other one has me
useful primitives, I submit the following table:
Table 1. Current set of semantic relation types in MindNet
This is from:
MindNet: acquiring and structuring semantic
information from text
Stephen D. Richardson, William B. Dolan, Lucy Vanderwende
One Microsoft Way
Redmond, WA 98052
which is in a file: tr-98-23.doc which I downloaded from http://research.microsoft.com
following some trail that John Sowa started me following recently.
This is related to MNEX at http://stratus.research.microsoft.com/mnex/Main.aspx
would probably be useful to someone looking to get more information.
I note that Pat Cassidy has a list of "connectives" at http://micra.com/dictionary/tagset.txt
But realistically, making a list of connectors is not the the interesting issue, in my mind.
If you focus on making this list, as your first problem, you lose sight of the second problem,
which is more interesting on this list i.e.: what axioms/true statements/rules exist that implicitly
define these connectives?
What I mean is, can we create a list of axioms for Color, or Purpose similar to the axioms for
Part which are mentioned on the page: http://en.wikipedia.org/wiki/Mereology#Axioms_and_primitive_notions
i.e.: (stealing from that page)
Axioms and primitive notions
It is possible to formulate a "naive mereology" analogous to naive set theory. Doing so gives rise to paradoxes analogous to Russell's paradox. Let there be an object O such that every object that is not a proper part of itself is a proper part of O. Is O a proper part of itself? No, because no object is a proper part of itself; and yes, because it meets the specified requirement for inclusion as a proper part of O. (Every object is, of course, an improper part of itself. Another, though differently structured, paradox can be made using improper part instead of proper part; and another using improper or proper part.) Hence mereology requires an axiomatic formulation.
A mereological "system" is a first-order theory (with identity) whose universe of discourse consists of wholes and their respective parts, collectively called objects. Mereology is a collection of nested and non-nested axiomatic systems, not unlike the case with modal logic.
The treatment, terminology, and hierarchical organization below follow Casati and Varzi (1999: chpt. 3) closely. For a more recent treatment, correcting certain misconceptions, see Hovda (2008). Lower-case letters denote variables ranging over objects. Following each symbolic axiom or definition is the number of the corresponding formula in Casati and Varzi, written in bold.
A mereological system requires at least one primitive binary relation (dyadic predicate). The most conventional choice for such a relation is Parthood (also called "inclusion"), "x is a part of y", written Pxy. Nearly all systems require that Parthood partially order the universe. The following defined relations, required for the axioms below, follow immediately from Parthood alone:
Systems vary in what relations they take as primitive and as defined. For example, in extensional mereologies (defined below), Parthood can be defined from Overlap as follows:
The axioms are:
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