File: 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;


