Ontologies,%20Conceptualizations,%20and%20Possible%20Worlds%20Revisiting%20

1
Ontologies, Conceptualizations,and Possible
WorldsRevisiting Formal Ontologies and
Information Systems10 years later

• Nicola Guarino
• CNR Institute for Cognitive Sciences and
  Technologies,
• Laboratory for Applied Ontology, Trento, Italy

www.loa-cnr.it
2
Summary

• Reality, perception, and conceptualizations
• Computational ontologies as logical
  characterizations of conceptualizations
• Differences betwen ontologies kinds of ontology
  change
• Evolution with respect to previous works of mine
• What are possible worlds? What is the domain of
  discourse?
• Clearer distinction between possible worlds and
  logical models
• Explicit role of perception in clarifying the
  notion of conceptualization
• hPossible worlds as sensory states (also in a
  metaphorical sense perception as observation
  perspective focusing on raw data)
• More detailed account of kinds of ontology change

3
Ontology and Ontologies

• Ontology the philosophical discipline
• Study of what there is (being qua being...)
• ...a liberal reinterpretation for computer
  science
• content qua content, independently of the way it
  is represented
• Study of the nature and structure of reality
• ontologies

Specific (theoretical or computational)
artifactsexpressing the intended meaning of a
vocabularyin terms of primitive categories and
relations describingthe nature and structure of
a domain of discourse
...in order to account for the competent use of
vocabulary in real situations!
Gruber Explicit and formal specifications of a
conceptualization
4
What is a conceptualization

• Formal structure of (a piece of) reality as
  perceived and organized by an agent,
  independently of
• the vocabulary used
• the actual occurence of a specific situation
• Different situations involving same objects,
  described by different vocabularies, may share
  the same conceptualization.

5
Example 1 the concept of red
a b
a
b
a,b

6
Example 2 the concept of on
a
lta,b gt
b
b
ltb,a gt
a

b
a
7
Relations vs. Conceptual Relations
ordinary relations are defined on a domain D
conceptual relations are defined on a domain
space ltD, Wgt
But what are possible worlds? What are the
elements of a domain of discourse?
8
What is a conceptualization? A cognitive approach

• Humans isolate relevant invariances from
  physical reality (quality distributions) on the
  basis of
• Perception (as resulting from evolution)
• Cognition and cultural experience (driven by
  actual needs)
• (Language)
• presentation atomic event corresponding to the
  perception of an external phenomenon occurring in
  a certain region of space (the presentation
  space).
• Presentation pattern (or input pattern) a
  pattern of atomic stimuli each associated to an
  atomic region of the presentation space. (Each
  presentation tessellates its presentation space
  in a sum of atomic regions, depending on the
  granularity of the sensory system).
• Each atomic stimulus consists of a bundle of
  sensory quality values (qualia) related to an
  atomic region of timespace (e.g., there is red,
  here it is soft and white, here).
• Domain elements corresponds to invariants within
  and across presentation patterns

9
From experience to conceptualization
Domain of Discourse D
1998
2008
10
Possible worlds as presentation patterns(or
sensory states)

• Presentation pattern unique (maximal) pattern of
  qualia ascribed to a spatiotemporal region
  tessellated at a certain granularity
• ...This corresponds to the notion of state for a
  sensory system (maximal combination of values for
  sensory variables)

Possible worlds are (for our purposes)sensory
states (or if you prefer, sensory situations)
11
Constructing the cognitive domain

• Synchronic level topological/morphological
  invariants within a single presentation pattern
• Unity properties are verified on presentation
  patterns on the basis of pre-existing schemas
  topological and morphological wholes (percepts)
  emerge
• Diachronic level temporal invariants across
  multiple presentation patterns
• Objects equivalence relationships among percepts
  belonging to different presentations are
  established on the basis of pre-existing schemas
• Events unity properties are ascribed to percept
  sequences belonging to different atomic
  presentations

12
The basic ingredients of a conceptualization
(simplified view)

• cognitive objects mappings from presentation
  patterns into their parts
• for every presentation, such parts constitute the
  perceptual reification of the object.
• concepts and conceptual relations functions from
  presentation patterns into sets of (tuples of)
  cognitive objects
• if the value of such function (the concepts
  extension) is not an empty set, the correponding
  perceptual state is a (positive) example of the
  given concept
• Rigid concepts same extension for all
  presentation patterns (possible worlds)

13
Language L
Good
14
Ontology Quality Precision and Coverage
High precision, max coverage
Low precision, max coverage
Max precision, limited coverage
Low precision, limited coverage
15
When precision is not enough
Only one binary predicate in the language
on Only three blocks in the domain a, b,
c. Axioms (for all x,y,z) on(x,y) -gt
on(y,x) on(x,y) -gt ?z (on(x,z) ? on(z,y))
Non-intended models are excluded, but the rules
for the competent usage of on in different
situations are not captured.
16
The reasons for ontology inaccuracy

• In general, a single intended model may not
  discriminate between positive and negative
  examples because of a mismatch between
• Cognitive domain and domain of discourse lack of
  entities
• Conceptual relations and ontology relations lack
  of primitives
• Capturing all intended models is not sufficient
  for a perfect ontology
• Precision non-intended models are excluded
• Accuracy negative examples are excluded

17
Kinds of ontology change(to be suitably encoded
in versioning systems!)

• Reality changes
• Observed phenomena
• Perception system changes
• Observed qualities (different qualia)
• Space/time granularity
• Quality space granularity
• Conceptualization changes
• Changes in cognitive domain
• Changes in conceptual relations
• metaproperties like rigidity contribute to
  characterize them (OntoClean assumptions reflect
  a particular conceptualization)
• Logical characterization changes
• Domain
• Vocabulary
• Axiomatization (Correctness, Coverage, Precision)
• Accuracy

18
Perception as a metaphor for the initial phase of
conceptual modeling

• Is student a rigid concept?
• If you look at possible worlds, in the common
  understanding of this notion, your answer is no
  (it is rather antirigid it is always possible to
  be a non-student)
• If you focus your perception on a restricted
  point of view, then it may turn out to be rigid
  (in terms of the possible worlds you are able
  to perceive)

19

• Kinds of ontology change
• Reality changes
• Focus of attention changes
• Perception system changes
• Conceptualization changes
• Logical characterization changes