a cognitive approach for modelling and reasoning on commonsense knowledge in computational...

A cognitive approach for modelling and reasoning

on common sense knowledge in computational

ontologies

Antonio Lieto

University of Torino, Dept. of Computer Science

[email protected] – [email protected]

07 March 2014, Department of Computer Science, University of Bremen, Germany.

Work in collaboration with

• Marcello Frixione Daniele Radicioni

(University of Genova, Italy) (University of Torino, Italy)


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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.


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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.


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Classical Theory – Ex.


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TRIANGLE = Polygon with 3 corners and sides

But…


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Family Resemblance (Wittgenstein, 1953)

Ex.


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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.

Prototype Theory


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(Rosh E., 1975)

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. Ex: BIRD, {Robin, Toucan, Penguin…}

Multiple Typicality Theories

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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.

Prototype theory: prototypes (an approximate, statistically relevant, representation of a category). A “central” representation of a category.

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.



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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.”


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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 -).

Ex. Frames

…. Frames, (Minsky M., 1975)


Frame 1

Concept 1

Attribute 1 Value 1

Attribute 2 Value 2

Attribute 3 Value 3

… …


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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.

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Contextualization to the Ontologies


15 07 March 2014, Department of Computer Science, University of Bremen, Germany.

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.



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 ?).

Ontology Reasoning

Categorization: class assignement to an

individual

e.g. SUPERHERO ≡ BravePERSON ˄

HasSuperpowers ˄ FightForJustice

SUPERHERO {…. , }


Ontology Reasoning/2 Classification: identification of subsumption relation between

classes (IS-A relation).

It is possible to infer:

DOMESTIC SAUSAGE DOG ⊆ DOMESTIC DOG


DOMESTIC DOG ⊆ DOG

SAUSAGE DOG ⊆ DOG

DOMESTIC DOG ≡ DOG ˄ LivesinHouse

DOMESTIC SAUSAGE DOG ⊆ SAUSAGE DOG and

DOMESTIC SAUSAGE DOG LivesinHouse

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.


What about non monotonic Categorization ?

Example:

X {hasFur, WagTail, Woof}

???


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


Related works

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Fuzzy and non monotonic approaches and extensions of DLs

Problems:

- fuzzy approaches to prototypical effects encounter some

difficulty with compositionality (Osherson and Smith 1981).

- Computational difficulties (Baader and Hollunder1995) and

extremely complicated semantics.


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.

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)


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.


Dual Process Theory

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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.


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


Dual Theories and Conceptual Representations

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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)


Cognitive Proposal for Concept Reprentation

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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).


Conceptual Architecture

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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).


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.


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


The color spindle

Intensity

Hue

Brightness

Green

Red

Yellow

Blue


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.


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


System and Evaluation

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.


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.


Overview


NL Description - The big carnivore with yellow and black stripes

- The animal that eats bananas

- The big fish eating plankton

Typical Representation

Mapping with NLP techniques

List of Concepts : - Whale 1.0 - Shark 0.5 - …

Output S1 Check on S2

Ontological Repr. - Whale NOT Fish - Whale Shark OK

Output S2

Output S1 + S2 Whale Whale Shark

Overview


NL Description - The big carnivore with yellow and black stripes

- The animal that eats bananas

- The big fish eating plankton

Typical Representation

Mapping with NLP techniques

List of Concepts : - Whale 1.0 - Shark 0.5 - …

Output S1

Check on S2

Ontological Repr - Whale NOT Fish - Whale Shark OK

Output S2

Concept Whale

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.


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.


Thanks for your attention !!!

Antonio Lieto

University of Torino, Dept. of Computer Science

[email protected] – [email protected]


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

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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