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.
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A cognitive approach for Modelling and Reasoning on Commonsense Knowledge in Computational Ontologies
A cognitive approach to concept representation and reasoning and its application to computational ontologies.
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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)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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.”
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
Frame 1
Concept 1
Attribute 1 Value 1
Attribute 2 Value 2
Attribute 3 Value 3
… …
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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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
Contextualization to the Ontologies
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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.
Contextualization to the Ontologies
16 07 March 2014, Department of Computer Science, University of Bremen, Germany.
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 {…. , }
07 March 2014, Department of Computer Science, University of Bremen, Germany.
Ontology Reasoning/2 Classification: identification of subsumption relation between
classes (IS-A relation).
It is possible to infer:
DOMESTIC SAUSAGE DOG ⊆ DOMESTIC DOG
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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.
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What about non monotonic Categorization ?
Example:
X {hasFur, WagTail, Woof}
???
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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
21 07 March 2014, Department of Computer Science, University of Bremen, Germany.
Related works
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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.
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.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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)
24 07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
25 07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
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)
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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).
07 March 2014, Department of Computer Science, University of Bremen, Germany.
Conceptual Architecture
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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.
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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).
31 07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
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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.
The color spindle
Intensity
Hue
Brightness
Green
Red
Yellow
Blue
07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
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.
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.
38 07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
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Overview
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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
41 07 March 2014, Department of Computer Science, University of Bremen, Germany.
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.
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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.
43 07 March 2014, Department of Computer Science, University of Bremen, Germany.