A cognitive approach for modelling and reasoning
on common sense knowledge in computational
ontologies

Antonio Lieto
Univ...
Work in collaboration with
• Marcello Frixione

(University of Genova, Italy)

Daniele Radicioni

(University of Torino, I...
Outline
• Brief introduction to the contact points between Cognitive Science
(CS) and AI on the theme of Concept Represent...
Concept Representation (CR)

In Cognitive Science there were different contrasting
theories about “how humans represent an...
Classical Theory – Ex.

TRIANGLE = Polygon with 3 corners and sides

07 March 2014, Department of Computer Science, Univer...
But…

Family Resemblance
(Wittgenstein, 1953)

07 March 2014, Department of Computer Science, University of Bremen, German...
Ex.

No one of these faces share the same (necessary and
sufficient) traits with each other.
Each face shares some traits ...
Prototype Theory
Category membership is not based on
necessary and sufficient conditions but on
typicality traits.

There ...
Multiple Typicality Theories
Prototype theory: prototypes (an approximate, statistically relevant,
representation of a cat...
In AI
There is a similar contraposition between two conflicting
requirements.
Compositionality vs Representing typical inf...
Early KR Systems in AI
- cognitively inspired
- (Pros +): Allowed to represent and reasoning on
tipicality.
- (Cons -): La...
Ex. Frames
Frame 1
Concept 1

Attribute 1
Attribute 2

Value 2

Attribute 3

Value 3

…

Frames, (Minsky M., 1975)

Value ...
KRs Evolution Systems in AI
Not cognitively inspired: e.g. KL-ONE systems (Brachman
and Schmoltze, 1985) and their descend...
Contextualization to the Ontologies

14
Contextualization to the Ontologies
Ontologies are from a representational point of view:
‘’Explicit and formal specificati...
Contextualization to the Ontologies
Ontological Languages (e.g. OWL and OWL2) and
Representations are based on Description...
Ontology Reasoning
Categorization: class assignement to an
individual
e.g. SUPERHERO ≡ BravePERSON ˄
HasSuperpowers ˄ Figh...
Ontology Reasoning/2
Classification: identification of subsumption relation between
classes (IS-A relation).
DOMESTIC DOG ...
Open Problems in Ontologies
Ontologies are expected to represent common sense or
non-classical concepts.
But OWL and OWL 2...
What about non monotonic Categorization ?

Example:
X {hasFur, WagTail, Woof}

???

07 March 2014, Department of Computer ...
Ex. Non Monotonic Categorization

An element X is categorized as a DOG because:
X {hasFur, WagTail, Woof}

No one of these...
Related works
Fuzzy and non monotonic approaches and extensions of DLs
The different proposals that have been advanced can...
Fuzzy Logic and Typicality Effects
(1) polka_dot_zebra(Pina) = .97
(2) zebra(Pina) = .2
x (polka_dot_zebra(x) ↔ zebra(x) ...
General Hints for a Cognitive Proposal
-

Heterogeneous hypothesis on concepts
(Machery, 2010)

-

Dual Process Theory of ...
Heterogeneous hypothesis
Concepts do not constitute a unitary phenomenon.

Different studies (ex. Malt, 1989; Smith et al....
Dual Process Theory
According to the dual process theories two different types of
cognitive processes and systems exist wh...
Systems 1/Systems 2 features
Systems 1 (Implicit)

Systems 2 (Explicit)

Unconscius

Conscious

Automatic

Controllable

E...
Dual Theories and Conceptual Representations
There are some crucial conceptual abilities that can be seen in
terms of syst...
Cognitive Proposal for Concept Reprentation
According to the heterogeneous hypothesis concepts can be
characterized as com...
Conceptual Architecture

The different proposals that have been advanced can be grouped in three main classes: a) fuzzy ap...
Conceptual Frameworks
In order to extend the representational and reasoning
capabilities of computational ontologies the d...
Conceptual Spaces
Conceptual Spaces (Gärdenfors, 2000; 2014) have been proposed
as a «cognitive representational framework...
Domains and Quality Dimensions
Each quality dimension is endowed with a particular
geometrical structure.

Ex: dimension o...
The color spindle

Brightness

Yellow
Green
Intensity

Blue

Red
Hue

07 March 2014, Department of Computer Science, Unive...
Conceptual Spaces - Concepts
Concepts correspond to regions and regions with
different characteristics correspond to diffe...
Prototypes and Operations
The convexity of conceptual regions allows one to
describe points in the regions as having degre...
System and Evaluation
System
A system has been built and equipped with the proposed hybrid
conceptual architecture based on a classical ontologi...
System at work
The whole categorization process regarding our system can be
summarized as follows.
The system takes in inp...
Overview
NL Description

- The big carnivore with yellow and black stripes
- The animal that eats bananas
- The big fish e...
Overview
NL Description
Mapping with
NLP techniques

Typical
Representation

- The big carnivore with yellow and black str...
Preliminary results
The system tested for queries based on common sense descriptions.
The number of tested descriptions is...
Future work
Extending the typical representation of concepts by extracting in a
semi-automatic way the typical features us...
Thanks for your attention  !!!
Antonio Lieto
University of Torino, Dept. of Computer Science
lieto@di.unito.it – lieto.an...
References
Baader, F., and B. Hollunder, 1995, “Embedding defaults into terminologicalknowledge
representation formalisms”...
References
Kahneman, D. (2011). Thinking, fast and slow. New York, NY:Macmillan.
Machery, 2010, “Doing without concepts”. ...
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A cognitive approach for Modelling and Reasoning on Commonsense Knowledge in Computational Ontologies

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

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A cognitive approach for Modelling and Reasoning on Commonsense Knowledge in Computational Ontologies

  1. 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. 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. 2
  3. 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. 3
  4. 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. 4
  5. 5. Classical Theory – Ex. TRIANGLE = Polygon with 3 corners and sides 07 March 2014, Department of Computer Science, University of Bremen, Germany. 5
  6. 6. But… Family Resemblance (Wittgenstein, 1953) 07 March 2014, Department of Computer Science, University of Bremen, Germany. 6
  7. 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. 7
  8. 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. 8
  9. 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. 9
  10. 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. 10
  11. 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. 11
  12. 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. 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. 13
  14. 14. Contextualization to the Ontologies 14
  15. 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. 15
  16. 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. 16
  17. 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. 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. 18
  19. 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. 19
  20. 20. What about non monotonic Categorization ? Example: X {hasFur, WagTail, Woof} ??? 07 March 2014, Department of Computer Science, University of Bremen, Germany. 20
  21. 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. 21
  22. 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. 22
  23. 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. 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. 24
  25. 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. 25
  26. 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. 26
  27. 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. 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. 28
  29. 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. 29
  30. 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. 30
  31. 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. 31
  32. 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. 32
  33. 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. 34. The color spindle Brightness Yellow Green Intensity Blue Red Hue 07 March 2014, Department of Computer Science, University of Bremen, Germany.
  35. 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. 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. 37. System and Evaluation
  38. 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. 38
  39. 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. 39
  40. 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. 40
  41. 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. 41
  42. 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. 42
  43. 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. 43
  44. 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. 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. 45
  46. 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). 46

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