ÿþFile: KEHOME/doc/Ontology View Definition Nothing Space Time.txt

Subject: Ontology View Definition Nothing Space Time

From: "Richard H. McCullough" <rhm@cdepot.net>

Date: May 11, 2003



This document consists of some notes on the above topics.

I use an extended n-tuple notation where n is 4 or 7.

My extensions are:

add 1 optional "modifier" element for a Statement;

add 3 space.time,view "context" elements for a Proposition;

permit each element of a tuple to be a list;

permit names which are not absolute URIs.



Contents:

1. View and EPS LATTICE

2. Context and ECP LATTICE

3. GenusDifferentia Definitions

4. Nothing

5. Space Time

6. Implications for OWL

7. Examples



1. View and EPS LATTICE

A View is a set of propositions.  A View can be constructed for

any Ontology, and can be simplified by using subClassOf and

subPropertyOf inferences and Definitions.

(See KEHOME/doc/simplifylattice.html and KEHOME/xml/*.ku.)

It is useful to display a View as an Entity-Property-Statement (EPS)

LATTICE.  Statements are represented by 4-tuples.



    <subject> <predicate> <object> <modifier> ;



2. Context and ECP LATTICE

To combine two or more views, we need a Context mechanism to

distinguish the Views.  We do this by extending the Statement concept

to a Proposition.  Propositions are represented by 7-tuples.



    <space> <time> <view>

    	<subject> <predicate> <object> <modifier> ;



For a proposition:

space, time, view are the context of the sentence;

subject, predicate, object, modifier are the sentence,

which may be a statement, question, command or assignment.



3. Genus-Differentia Definition

A Genus-Differntia Definition is a Statement which identifies

the nature of the Individuals (units) which are subsumed by

a Class (concept).  Although a Definition can be composed

from 3-tuples, it is advantageoous to use a single 4-tuple.



    <subject> <predicate> <object> <modifier> ;



For a genus-differentia definition:

the subject is the Individual or Class or Property being defined;

the predicate is mkr:isDefinedAs;

the object is the genus Class of the subject;

the modifier is the differentia -- the Property restrictions which

are the essential characteristics of the subject.



The subject and object are adjacent elements in the View LATTICE.



The 4-tuple is also an excellent representation for action predicates.

For an action predicate:

the subject is the entity which performs the action;

the predicate is the action;

the object is the action event (instance);

the modifier is a list of "adverb phrases".



4. Nothing

Nothing is the class of things that do not exist.

Nothing has no extension.

Nothing is not part of the View LATTICE.



5. Space Time

The View LATTICE is, in general, space-time dependent.  The space,

time attributes measure changes, i.e., action predicates.  Including

space,time in the context of a proposition facilitates the isolation

of space-time dependencies.



6. Implications for OWL

To represent the concepts described in these notes, OWL needs these

new Properties



	space

	time

	view

	individualOf

	properSubClassOf

	properSubPropertyOf

	isDefinedAs



and these new Classes



	Set

	LATTICE

	Lattice

	Hierarchy

	View

	Context

	Proposition



7. Examples

GenusDifferentia Definitions.



	<man> <isDefinedAs> <animal> <rational> ;

	<woman> <isDefinedAs> <person> <sex = female> ;

	<lattice> <isDefinedAs> <LATTICE> <ambiguous genus> ;

	<hierarchy> <isDefinedAs> <LATTICE> <unique genus> ;



An EPS LATTICE



	Thing

	    Entity

	        Person

		    John Doe

		    Mary Doe

	    Property

	        sex

		    male

		    female

	    Statement

	        <John Doe> <sex> <male> ;

		<Mary Doe> <sex> <female> ;



An ECP LATTICE



	Thing

	    Entity

	        Person

		    John Doe

		    Mary Doe

		    Dick McCullough

	    Characteristic

	        action

		    work

		        work_001

		    make

		        make_002

		    write

		        write_003

		attribute

		    space

		        London

			London home

			Pioneer home

		    time

		        week day

	  		6 pm

			2003-05-06 5:00 pm

		    view

		        week day routine

			every day routine

			Semantic Web activity

	            sex

		        male

		        female

	    Proposition

	        <London> <week day> <week day routine>

			<John Doe> <work> <work_001> <from 9 am to 5 pm> ;

		<London home> <6 pm> <every day routine>

			<Mary Doe> <make> <make_002> <dinner> ;

		<Pioneer home> <2003-05-06 5:00 pm> <Semantic Web activity>

			<Dick McCullough> <write> <write_003> <this email> ;



============ 

Dick McCullough 

knowledge := man do identify od existent done;

knowledge haspart proposition list;