A cognitive approach to concept representation and reasoning and its application to computational ontologies.

1. A cognitive approach for modelling and reasoning
on common sense knowledge in computational
ontologies
Antonio Lieto
University of Torino, Dept. of Computer Science
lieto@di.unito.it – lieto.antonio@gmail.com
07 March 2014, Department of Computer Science, University of Bremen, Germany.

2. Work in collaboration with
• Marcello Frixione
(University of Genova, Italy)
Daniele Radicioni
(University of Torino, Italy)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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3. Outline
• Brief introduction to the contact points between Cognitive Science
(CS) and AI on the theme of Concept Representation.
• Contextualization of the problem of non-classical concept
representation and reasoning in the field of computational
ontologies.
• Presentation of a cognitive approach to Concept Representation
and application to computational ontologies.
• Preliminary results in a QA setting and future work.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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4. Concept Representation (CR)
In Cognitive Science there were different contrasting
theories about “how humans represent and organize the
information in their mind”.
These theories influenced the realization of the early
knowledge representation systems in AI.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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5. Classical Theory – Ex.
TRIANGLE = Polygon with 3 corners and sides
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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6. But…
Family Resemblance
(Wittgenstein, 1953)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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7. Ex.
No one of these faces share the same (necessary and
sufficient) traits with each other.
Each face shares some traits of other faces of the series.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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8. Prototype Theory
Category membership is not based on
necessary and sufficient conditions but on
typicality traits.
There are members of a category that are
more typical and cognitively relevant w.r.t.
others.
(Rosh E., 1975)
Ex: BIRD, {Robin, Toucan, Penguin…}
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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9. Multiple Typicality Theories
Prototype theory: prototypes (an approximate, statistically relevant,
representation of a category). A “central” representation of a
category.
The different proposals that have been advanced can be grouped in three main classes: a) fuzzy approaches, b) probabilistic and Bayesan approaches, c) approaches based
on non-monotonic formalisms.
Exemplar theory: the mental representation of a concept is the set of
the representations of (some of) the exemplars of that category
that we encountered during our lifetime.
Theory theory: concepts are analogous to theoretical terms in a
scientific theory. For example, the concept CAT is individuated by
the role it plays in our mental theory of zoology.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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10. In AI
There is a similar contraposition between two conflicting
requirements.
Compositionality vs Representing typical information
Frege’s Principle “The meaning of a complex symbol s functionally depends on the
syntactic structure of s and from the meaning of primitive symbols in it.”
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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11. Early KR Systems in AI
- cognitively inspired
- (Pros +): Allowed to represent and reasoning on
tipicality.
- (Cons -): Lack of a formal characterization and a clear
semantics (Cons -).
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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12. Ex. Frames
Frame 1
Concept 1
Attribute 1
Attribute 2
Value 2
Attribute 3
Value 3
…
Frames, (Minsky M., 1975)
Value 1
…
….
07 March 2014, Department of Computer Science, University of Bremen, Germany.

13. KRs Evolution Systems in AI
Not cognitively inspired: e.g. KL-ONE systems (Brachman
and Schmoltze, 1985) and their descendants (e.g.
Description Logics based representations and formalisms).
- (Pros +): Formal characterization and semantics.
- (Cons -): It is not possible to represent and to reason on
non-classical concepts. Revival of the classical theory.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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14. Contextualization to the Ontologies
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15. Contextualization to the Ontologies
Ontologies are from a representational point of view:
‘’Explicit and formal specifications of conceptualization”
(Gruber, 1995).
From a logical point of view (reasoning) can be seen as
collections of axioms used as constraints about the
possible models of interpretation about a given domain.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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16. Contextualization to the Ontologies
Ontological Languages (e.g. OWL and OWL2) and
Representations are based on Description Logics
formalisms.
Allow to represent information on concepts and
properties by using logical axioms and according to
standard Tarskian-like DLs formalisms.
Support forms of automatic reasoning (WHICH ONE ?).
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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17. Ontology Reasoning
Categorization: class assignement to an
individual
e.g. SUPERHERO ≡ BravePERSON ˄
HasSuperpowers ˄ FightForJustice
SUPERHERO {….
,}
07 March 2014, Department of Computer Science, University of Bremen, Germany.

18. Ontology Reasoning/2
Classification: identification of subsumption relation between
classes (IS-A relation).
DOMESTIC DOG ⊆ DOG
SAUSAGE DOG ⊆ DOG
DOMESTIC DOG ≡ DOG ˄ LivesinHouse
DOMESTIC SAUSAGE DOG ⊆ SAUSAGE DOG and
DOMESTIC SAUSAGE DOG LivesinHouse
It is possible to infer:
DOMESTIC SAUSAGE DOG ⊆ DOMESTIC DOG
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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19. Open Problems in Ontologies
Ontologies are expected to represent common sense or
non-classical concepts.
But OWL and OWL 2 semantics does not allow to
represent “non classical concepts”.
Furthermore common sense reasoning is often non
monotonic.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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20. What about non monotonic Categorization ?
Example:
X {hasFur, WagTail, Woof}
???
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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21. Ex. Non Monotonic Categorization
An element X is categorized as a DOG because:
X {hasFur, WagTail, Woof}
No one of these traits is definitory of DOG
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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22. Related works
Fuzzy and non monotonic approaches and extensions of DLs
The different proposals that have been advanced can be grouped in three main classes: a) fuzzy approaches, b) probabilistic and Bayesan approaches, c) approaches based
on non-monotonic formalisms.
Problems:
- fuzzy approaches to prototypical effects encounter some
difficulty with compositionality (Osherson and Smith 1981).
- Computational difficulties (Baader and Hollunder1995) and
extremely complicated semantics.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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23. Fuzzy Logic and Typicality Effects
(1) polka_dot_zebra(Pina) = .97
(2) zebra(Pina) = .2
x (polka_dot_zebra(x) ↔ zebra(x)  polka_dot_thing(x))
the problem is that if we adopt the simplest and more widespread
form of fuzzy logic, the value of a conjunction is calculated as the
minimum of the values of its conjuncts.
This makes it impossible that at the same time the value of
zebra(Pina) is .2 and that of polka_dot_zebra(Pina) is .97.

24. General Hints for a Cognitive Proposal
-
Heterogeneous hypothesis on concepts
(Machery, 2010)
-
Dual Process Theory of Reasoning (Stanovitch
and West, 2000; Evans and Frankish, 2008;
Kahnemann 2011)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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25. Heterogeneous hypothesis
Concepts do not constitute a unitary phenomenon.
Different studies (ex. Malt, 1989; Smith et al. 97-98)
show that people use different conceptual
representations (of the same element) for dealing
with different type of typicality based processes.
This aspect represents a symptom suggesting that
concepts have an heterogeneous nature.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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26. Dual Process Theory
According to the dual process theories two different types of
cognitive processes and systems exist which have been called
respectively system 1 and system 2.
Originally proposed in the psychology of reasoning to account for
systematic errors in reasoning tasks (e.g. conjunction fallacy,
Tversky and Kahnemann, 1983).
Systematic reasoning errors should be ascribed to fast,
associative and automatic system 1 processes, while system 2 is
responsible for the slow and cognitively demanding tasks and
logical activity.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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27. Systems 1/Systems 2 features
Systems 1 (Implicit)
Systems 2 (Explicit)
Unconscius
Conscious
Automatic
Controllable
Evolved early
Evolved late
Parallel, Fast
Sequential, Slow
Pragmatic/contextualized
Logical/Abstract
07 March 2014, Department of Computer Science, University of Bremen, Germany.

28. Dual Theories and Conceptual Representations
There are some crucial conceptual abilities that can be seen in
terms of systems 1/ systems 2 distinction.
For example:
Systems 1
Systems 2
Most Non Monotonic
Categorization
(Use of Typical Knowledge)
Monotonic Categorization
(based on slow, sequential,
deliberative processes)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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29. Cognitive Proposal for Concept Reprentation
According to the heterogeneous hypothesis concepts can be
characterized as composed by different body of knowledge
representing different types of information (representational
problem).
The distinction between system 1 and system 2 processes can
be plausibly applied also to the problem of conceptual
representations. (reasoning problem).
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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30. Conceptual Architecture
The different proposals that have been advanced can be grouped in three main classes: a) fuzzy approaches, b) probabilistic and Bayesan approaches, c) approaches based
on non-monotonic formalisms.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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31. Conceptual Frameworks
In order to extend the representational and reasoning
capabilities of computational ontologies the different
conceptual components can be represented by using different
representational frameworks each allowing a particular form
of reasoning (Frixione and Lieto, 2013).
Conceptual Spaces (System 1 processes and typical
representations).
Ontologies (System 2 processes and classical representations).
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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32. Conceptual Spaces
Conceptual Spaces (Gärdenfors, 2000; 2014) have been proposed
as a «cognitive representational framework» for dealing with
prototypical representation of concepts and the similarity (seen
as a crucial feature of human cognition).
Geometrical representational framework where the information is
organized by quality dimensions are sorted into domains.
The chief idea is that knowledge representation can benefit from the
geometrical structure of conceptual spaces: instances are
represented as points in a space, and their similarity can be
calculated in the terms of their distance according to some suitable
distance measure.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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33. Domains and Quality Dimensions
Each quality dimension is endowed with a particular
geometrical structure.
Ex: dimension of COLOR
Hue- the particular shade of colour
Geometric structure: circle
Value: polar coordinate
Chromaticity- the saturation of the colour; from grey to higher intensities
Geometric structure: segment of reals
Value: real number
Brightness: black to white
Geometric structure: reals in [0,1]
Value: real number
07 March 2014, Department of Computer Science, University of Bremen, Germany.

34. The color spindle
Brightness
Yellow
Green
Intensity
Blue
Red
Hue
07 March 2014, Department of Computer Science, University of Bremen, Germany.

35. Conceptual Spaces - Concepts
Concepts correspond to regions and regions with
different characteristics correspond to different type of
concepts.
Concepts are represented as sets of convex regions
spanning one or more domains. Each domain is made
up of a set of integral quality dimensions.
07 March 2014, Department of Computer Science, University of Bremen, Germany.

36. Prototypes and Operations
The convexity of conceptual regions allows one to
describe points in the regions as having degrees of
centrality, which aligns this representational
framework with prototype theory.
Conceptual space theory describes query operations
that can be applied to the concepts represented in
a conceptual space, including semantic similarity
07 March 2014, Department of Computer Science, University of Bremen, Germany.

37. System and Evaluation

38. System
A system has been built and equipped with the proposed hybrid
conceptual architecture based on a classical ontological component
and on a typical component represented in terms of conceptual
spaces (Ghignone, Lieto, Radicioni, 2013).
Each component encodes a specific reasoning mechanism as in the
dual process perspective.
Such system takes as input description in natural language and is
involved in tasks of concept identification and retrieval: i.e. given a
description it must identify the concept corresponding to that
description exploiting the inferential capabilities of the proposed
architecture.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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39. System at work
The whole categorization process regarding our system can be
summarized as follows.
The system takes in input a textual description d and produces in
output a pair of categories : the output of S1 and S2,
respectively.
The S1 component takes in input the information extracted from
the description d, and produces in output a set of classes C =
c1; c2. This set of results is then checked against S2.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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40. Overview
NL Description
- The big carnivore with yellow and black stripes
- The animal that eats bananas
- The big fish eating plankton
Mapping with
NLP techniques
Output S1
Typical
Representation
Output S2
Check on S2
Ontological Repr.
List of Concepts :
- Whale 1.0
- Shark 0.5
- …
-
Whale NOT Fish
Whale Shark OK
Output S1 + S2
Whale
Whale Shark
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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41. Overview
NL Description
Mapping with
NLP techniques
Typical
Representation
- The big carnivore with yellow and black stripes
- The animal that eats bananas
- The big fish eating plankton
Concept Whale
List of Concepts :
- Whale 1.0
- Shark 0.5
- …
Output S1
Check on
S2
Ontological Repr
-
Whale NOT Fish
Whale Shark OK
Output S2
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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42. Preliminary results
The system tested for queries based on common sense descriptions.
The number of tested descriptions is still limited (36) since the proposed
hybrid conceptual structure has been created only for a small set of
concepts.
- It was able to categorize all the descriptions.
- Only 1 of the typical description would have been categorized by using
only the ontological component.
- It was able to categorize even ontologically incoherent descriptions.
- The “correct” description, from a cognitive point of view, is retrieved by the
S1 component in the 92% of the cases.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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43. Future work
Extending the typical representation of concepts by extracting in a
semi-automatic way the typical features using available linguistic
resources such as: Wordnet, Framenet, ConceptNet, DBpedia…
Using a large ontological knowledge base as S2:
- Open Cyc: ~239,000 concepts ~2,093,000 triple, ~22,000
predicates
Extending the evaluation for a large set of common sense queries to
search engines (Bing, Google,…) in terms of Precision.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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44. Thanks for your attention  !!!
Antonio Lieto
University of Torino, Dept. of Computer Science
lieto@di.unito.it – lieto.antonio@gmail.com
07 March 2014, Department of Computer Science, University of Bremen, Germany.

45. References
Baader, F., and B. Hollunder, 1995, “Embedding defaults into terminologicalknowledge
representation formalisms”, J. Autom. Reasoning 14, 1:149–180.
Brachmann, R.J., Schmolze, J.G., 1985, “An overview of the KL-ONE knowledge
representation system”. Cognitive Science 9(2).
Evans, J.S.B., Frankish, K.E., 2008, “In two minds: Dual processes and beyond”.
Oxford University Press.
Frixione, M., Lieto, A., 2013, “Dealing with Concepts: from Cognitive Psychology to
Knowledge Representation”. Frontiers of Psychological and Behavioural Science
2(3) (July 2013).
Gärdenfors, 2000, “Conceptual Spaces: The Geometry of Thought”, MIT Press.
Ghignone L., Lieto A. and Radicioni P., 2013, "Typicality-Based Inference by Plugging
Conceptual Spaces Into Ontologies", Proceedings of AIC'13 Workshop, Torino, 3rd
December 2013. CEUR Workshop Proceedings.
Gruber, 1995, “Toward principles for the design of ontologies used for knowledge
sharing” in International Journal of Human-Computer Studies, Vol. 43, Issues 4-5,
November 1995.
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46. References
Kahneman, D. (2011). Thinking, fast and slow. New York, NY:Macmillan.
Machery, 2010, “Doing without concepts”. Oxford University Press.
Malt, 1989; “An on-line investigation of prototype and exemplar strategies in
classification”. Journal of Experimental Psychology: Learning, Memory, and
Cognition 15(4), 539–555 (1989).
Rosch, E., 1975, Cognitive representations of semantic categories. Journal of
experimental psychology: General 104(3).
Minsky, M., 1975, “A framework for representing knowledge”. In Winston, P., ed.: The
Psychology of Computer Vision. McGraw-Hill, New York (1975).
Stanovitch, K. & West, R. (2000). Individual differences in reasoning: Implications for
the rationality debate?. The Behavioural and Brain Sciences 23, 5: 645- 65.
Tversky, A. & Kahneman, D. (1983). Extension versus intuitive reasoning: The
conjunction fallacy in probability judgment. Psychological Review, 90 (4).
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