Lecture from Prof. Navjyoti Singh's course on Vaiseshika System of Formal Ontologies.

1. Context, History, Concepts and Tools

2. Basic stance of ontology is –
meanings are entities, events and relations
Meanings occur in Cognition
Meanings are impressed in cognition and meanings are expressed in natural language
impress-meanings recur
Ontology seeks entitative account of such recurrence
Ontological engineering seeks automation of such account
Central issue of ontological engineering is –
how to specify meaning for robots or computational agents

3. Problem of the Specification of Meanings
For human agents –
dictionaries (terms), glosses (usages of term) and thesauri (relation of terms) do the job
Reusable term can often be seen as a class (concept) of objects
class and sub-class inheritances become computable
Lower terms inherit meanings from higher ones: vegetation:plant:flower:rose
Another dimension to computing meaning is added by
seeing object as having properties (roles)
multiple inheritances in objects become computable
„Red-rose‟ inherits meanings from quality:color:red as well as vegetation genus

4. Top-down and bottom-up approaches for computing meaning
WORDS
class|sub-class
Foundatio *
nal
Ontologies object|property
*
whole|part
* Domain
action|event Ontologies
*
etc.
?
PARTICULARS
Bottom-up approach takes particular entities as primitives and not terms
Ontology is a theory of actual particulars and their change
and not a theory of their representation
Bottom-up approach depends on rigorous foundational ontology
that is independent of natural language

5. Comprehensive
Foundational Ontologies
Aristotelian Ontology Vaiśes Ontology
ika
relation among real entities are relation among real entities are
logical real entities
different categories of reals have hierarchy of universals is valid across
different highest universal categories of reals
„Existence‟ is a declaration „Existence‟ is a specific entity
Declarative Categories Differentiated Categories
Descriptive Ontologies

6. Aristotelian Categories (ta onta)
ousia sumbebhkota
substance accident
ousia poion poson pros ti pou pote keisthai echein poiein paschein
substance quality quantity relation place time posture possess action passion
ion
secondary virtue discrete equal/un attitudes
equal
genus – equal – degree; degree;
species unequal; contrary contrary
heirarchy no contrary
prôtai ousiai
primary disposition continuous superior
Logical Relation –
capacity 1. inhering ‘in’ (‘accidents inhere in substance’)
2. being ‘said of’ (genus-species)
affections similar
shape
knowledge contrary

7. Vaiśes Categories (padārtha-s)
ika
dravya a
gun karma sāmānya viśes
a samavāya abhāva
substance quality action universal differentiator inherence absence
<9> <24> <5> <2> <infinite> <1> <4>
pr thvī gandha utks a
epan para prāgābhāva
earth smell rising wide prior absence
<infinite> <1>
ap rasa apaks a
epan ^ pradhvam sābhāva
water Taste falling hierarchy posterior absence
<infinite> structure 
tejas rūpa ākuñcana apara anyonyābhāva
fire Color contracting narrow reciprocal absence
<infinite> <indefinite>
vāyu sparśa prasāran
a atayantābhāva
wind Touch expanding absolute absence
<infinite>
ākāśa śabda gamana
medium Sound locomotion
<1> mobile & atomic
kāla khyā
sam non-mobile
time number special qualities
<1> general qualities
dik parimāna special qualities of self Logical Relation –
expanse magnitude quality of self & mobile 1. attribute | attributee
<1> 2. locus | located
ātman pr
thaktva
self otherness
<infinite>
manas samyoga <#/infinite/indefinite> indicates number of sub-categories or number of entities in each substance
mind conjunct
<infinite>
vibhāga
disjunct qualities grasped by one sense organ and their corresponding material substrates
paratva entities not explicitly listed by Kan but accepted as consistent with system
āda
remoteness
aparatva
proximity
buddhi Sukha duhkha icchā dvesa prayatna
cognition happiness misery desire aversion volition  psychic qualities
dharma adharma samskāra gurutva dravatva sneha  dispositional
merit demerit tendency weight fluidity viscosity qualities

8. Foundational Ontology and Automation
Expressibility
Open vocabulary Open grammar
FOUNDATIONAL ONTOLOGY vocabulary
FORMAL NATURAL
ONTOLOG SEMANTIC
Y
ARTIFICIAL LANGUAGE DOMAIN ONTOLOGIES
Controlled grammar Controlled vocabulary
vocabulary
Demand of ontological engineering is to render
comprehensive foundational ontology as formal ontology
instead of natural semantics,
robotic agent requires formal ontology capable of handling impress-meanings

9. Development of Formal Ontology
Formal ontology is not application of formal logic to ontology
ratiocination among entities ratiocination among propositions
•Brentano (1890s) revived formal study of Aristotle.
Concepts of PUNCTIFORM; PLEROSIS; TELEIOSIS
•Husserl (1910s) coined a phrase FORMAL ONTOLOGY
•Smith (1982) revived FO in anthology Parts and Moments
•Mormann (1995) ), “Trope Sheaves: a Topological Ontology of Tropes,” Logic and
Logical Philosophy 3: 129-150
•Smith & Varzi (2000), “Bona Fide and Fiat Boundaries,” Philosophy and
Phenomenological Research 60, 401-420
Use of topological methods and category theory

10. Formal Ontology becomes study of envelopes, boundaries,
terminals, edges, joints, wholes, holes, clusters, mixtures etc.
It does not matter what the stuff is – Forms that shape the stuff
adequately characterize composition and behavior of stuff
These studies can be described as DEPICTIVE Formal Ontologies
They do not disclose formal necessity that generates categories of reality
In Contrast
GENERATIVE Formal Ontology is a
quest to formally derive Categories of Reality

11. GENERATIVE Ontology is possible if boundaries, edges,
joints, terminals etc. are conceived as instances of a
SINGLE, SIMPLE FORM OF CONTIGUITY
which is Recursive