Extending the knowledge level of cognitive architectures with Conceptual Spaces (+ a case study with Dual-PECCS: a hybrid knowledge representation system for common sense reasoning). Talk given at Stockholm, September 2016.

1. Extending the Knowledge Level of General Cognitive Architectures with
Conceptual Spaces
Antonio Lieto
University of Turin, Dept. of Computer Science, Italy
ICAR-CNR, Palermo, Italy
http://www.antoniolieto.net
Conceptual Spaces Workshop 2016, Stockholm, 25-27 July 2016

2. Outline
– (General) Cognitive Architectures (CAs)
– Knowledge Level in CAs: Open problems
– Role of Conceptual Spaces in CAs
– Case Study: a system employing Conceptual Spaces
and Ontologies able to categorize simple common
sense linguistic descriptions (e.g. riddles) by mixing
different types of common sense knowledge and
reasoning.

3. Cognitive Architectures
3
Allen Newell (1990)
Unified Theory of Cognition
A cognitive architecture (Newell, 1990) implements the
invariant structure of the cognitive system.
It captures the underlying commonality between different
intelligent agents and provides a framework from which
intelligent behavior arises.
Aim at reaching human level intelligence in a general
setting, by means of the realization of artificial artifacts
built upon them.

4. “Natural/Cognitive” Inspiration and AI
Early AI
Cognitive Inspiration
for the Design of “Intelligent Systems”
M. Minsky
R. Shank
Modern AI
“Intelligence” in terms of
optimality of a performance
(narrow tasks)
mid‘80s
A. Newell
H. Simon
e.g. IBM Watson…
N. Wiener

5. Representations in CAs
There are different representational assumptions available in
current Cognitive Architectures (CAs)
- Ex: Fully Connectionist Architectures: LEABRA (O’Reilly and
Munakata, 2000)
- Ex: Hybrid Architectures: ACT-R (Anderson et al. 2004), CLARION
(Sun, 2006)
- Ex. Fully Symbolic Architectures: SOAR (Laird 2012)
- Ex. Architectures integrating Diagrammatic Representations (e.g.
bi-SOAR (Kurup and Chandrasekaran, 2008).

6. Problem
no one of these representation can account for all aspects of cognition.
- Symbolic representations —-> COMPOSITIONALITY, an irrevocable
trait of human cognition (Fodor and Pylyshyn, 88).
- Sub-symbolic representations (including deep nets) —-> LEARNING,
PERCEPTION, CATEGORIZATION.
- Diagrammatic representations —> VISUAL IMAGERY, SPATIAL
REASONING.
We need, in computational systems, different levels of representation to
cover the full aspect of cognitive phenomena.

7. Proposal
A way to unify these aspects is with Conceptual Spaces used as a Lingua
Franca (Lieto, Chella and Frixione, forthcoming in BICA Journal).

8. Conceptual Spaces (CS)
Conceptual Spaces (Gärdenfors, 2000), are geometrical
representational framework where the information is
organized by quality dimensions 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.

9. Conceptual Spaces - Concepts
Concepts corresponds 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.

10. Domains and Quality Dimensions
Each quality dimension is endowed with a particular
geometrical structure.
Ex: dimensions 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

11. Ex. CS for “Color”
Intensity
Hue
Brightness
Green
Red
Yellow
Blue

12. 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 (Rosch, ’75).

13. CS Advantages
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.
W.r.t. Symbolic Representations (SR) => allow to deal with the
problem of compositionality with common-sense concepts.
W.r.t. Sub-symbolic Representations => alleviate the opacity
problem in neural networks (this problems explodes with
deep nets). An interpretation on neural nets in terms of
Conceptual Spaces can offer a more abstract and
transparent view of the underlying neural representations
and processes (compliance the Semantic Pointer Perspective
in SPAUN, Eliasmith 2012).
W.r.t. Diagrammatical/Analogical Representations =>
Conceptual Spaces can offer an unified framework for this
different families of representations.

14. Compositionality and Typicality (in SR)
(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.

15. Compositionality and Typicality (in CS)
According to the conceptual spaces approach, Pina should presumably turn
out to be very close to the center of polka dot zebra (i.e. to the
intersection between zebra and polka dot thing).
In other words, she should turn out to be a very typical polka dot zebra,
despite being very eccentric on both the concepts zebra and polka dot
thing; that is to say, she is an atypical zebra and an atypical polka dot thing.
This representation better captures our intuitions about typicality.

16. CS and Sub-symbolic Representations
The opacity of this class of representations is difficult to accept in CAs aiming at
providing transparent models of human cognition and that, as such, should be
able not only to predict the behavior of a cognitive artificial agent but also to
explain it.
CS offer a more transparent interpretation of underlying neural networks.
Ex. the operation of each layer may be described as a functional geometric space
where the dimensions are related to the transfer functions of the units of the
layer itself. In this interpretation, the connection weights between layers may be
described in terms of transformation matrices from one space to another.
Different works showing: i) how these transformation operations can be done
(also with convolutional neural networks, Eliasmith et al., 2015) and ii) how it
is possible to interpret Radial Basis Function networks in terms of CS (Balkenius,
1999).

17. More about Analog/Diagrammatic
Representations
A plethora of different kinds of diagrammatic representations (e.g. Mental Models
Johnson-Laird 2006).
Ex. The relation “to be on the right of” is usually transitive:
if A is on the right of B and B is on the right of C then A is on the right of C.
But in a round table situation it can happen that C is on the right of B, B is on the
right of A but A is on the left of C.
Complex to model in
symbolic terms.
Interpretable in terms
of CS.

18. CS for Unifying Analog and Diagrammatical
Representations
Conceptual spaces are useful also in representing non-specifically spatial
domains phenomena.
A typical problem of both symbolic and neural representations regards
the ability to track the identity of individual entities over time.
Conceptual Spaces suggest a way to face the problem: in a dynamic
perspective, objects can be rather seen as trajectories in a suitable
Conceptual Space indexed by time.
As the properties of an object are modified, the point, representing it in
the Conceptual Space, moves according to a certain trajectory (Chella,
Coradeschi, Frixione, Saffiotti, 2004).
Also in this case, crucial aspects of diagrammatic representations find a
more general and unifying interpretation in Conceptual Spaces.

19. CS for Unifying Analog and Diagrammatical
Representations/2
A plethora of different kinds of diagrammatic representations
has been proposed without the development of a unifying
theoretical framework.
Conceptual Spaces, thanks to their geometrical nature, allow
the representation of this sort of information and offer, at
the same time a general, well understood and theoretically
grounded framework that could enable to encompass most of
the existing diagrammatic representations.

20. Still Problem(s)…
CAs are general structures without a corresponding “general”
content, able to cover the different types of knowledge available
to humans and used by them in decision making processes.
The knowledge represented and manipulated by such CAs is usually
ad hoc built and homogeneous in nature (Lieto, Lebiere and
Oltramari, submitted).
It mainly covers, in fact, only the so called “classical” part of
conceptual information (that one representing concepts in terms of
necessary and sufficient conditions).
On the other hand, the so called “common-sense” conceptual
components of our knowledge is largely absent in such
computational frameworks.

21. Case study: Dual-PECCS
DUAL-PECCS (Dual Prototype and Exemplars Based Conceptual
Categorization Systems): A system able to categorize simple common
sense linguistic descriptions (e.g. riddles) by mixing different types
of common sense knowledge and reasoning.
Lieto, Radicioni, Rho (JETAI 2016, IJCAI 2015)
http://www.dualpeccs.di.unito.it/

22. System Novelties
– Representation:
– heterogeneous conceptual structures: compliance
with the computational frameworks of cognitive
architectures (heterogeneous proxytypes).
– Reasoning:
– 2 types of common sense inference (based on
prototypes and exemplars).
– Dual process reasoning (Common sense +
Standard categorization).
– Integration into the ACT-R (Anderson et al. 2004)
and CLARION (Sun, 2006) cognitive architectures.

23. In Cognitive Science there were/are different
contrasting theories about “how humans represent
and organize the information in their mind”…This
research also influenced Artificial Intelligence
23

24. Classical Theory – Ex.
22
TRIANGLE = Polygon with 3 corners and sides

25. Prototypes and Prototypical Reasoning
• Categories based on prototypes (Rosh,1975)
• New items are compared to the prototype
atypical
typical
P

26. Exemplars and Exemplar-based Reasoning
• Categories as composed by a list of exemplars. New
percepts are compared to known exemplars (not to
Prototypes).

27. Heterogeneous Hypothesis
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.
Different representational structures have different accessing procedures
(reasoning) to their content.
Prototypes, Exemplars and other conceptual representations can co-exists
and be activated in different contexts (Malt 1989).

28. System Conceptual Structure
28
differ-
spec-
terms
illian,
es can
egion
spec-
an, on
f con-
ilarly,
mbolic
ell as
an be
tems,
artic-
so for
iple–,
is-a: feline
color: yellow
hasPart: fur
hasPart: tail
hasPart: stripes
...
conceptual space
representation
concept Tiger
Kingdom: Animalia
Class: Mammalia
Order: Carnivora
Genus: Panthera
Species: P. tigris
prototype of Tiger exemplars of Tiger
white-tiger
is-a: feline
color: white
hasPart: fur
hasPart: tail
hasPart: stripes
...
...
ontological
representation
classical information
Typicality-based
knowledge
Classical
knowledge
Hybrid Knowledge Base

29. Related Work
Semantic Pointers
29
(Eliasmith et al. 2012 and 2015). Their focus is on sensory channels. Our focus is
on the heterogeneity regarding the content of the represented information. The
content is cross-channel.

30. Dual Process Reasoning
11
Reasoning Harmonization based on the dual process
(Stanovitch and West, 2000; Kahnemann 2011).
In human cognition, type 1 processes are executed fast
and are not based on logical rules. Then they are checked
against more logical deliberative processes (type 2
processes).
Type 1 Processes Type 2 Processes
Automatic Controllable
Parallel, Fast Sequential, Slow
Pragmatic/contextualized Logical/Abstract

31. ACT-R Integration
• “Extended” Declarative
Memory of ACT-R
• Integration of the dual
process base categorisation
processes in ACT-R
31
for a given concept can be represented by adopting differ-
ent computational frameworks: i) from a symbolic perspec-
tive, prototypical representations can be encoded in terms
of frames [Minsky, 1975] or semantic networks [Quillian,
1968]; ii) from a conceptual space perspective, prototypes can
be geometrically represented as centroids of a convex region
(more on this aspect later); iii) from a sub-symbolic perspec-
tive, the prototypical knowledge concerning a concept can, on
the other hand, be represented as reinforced patterns of con-
nections in Artificial Neural Networks (ANNs). Similarly,
for the exemplars-based body of knowledge, both symbolic
and conceptual space representations can be used, as well as
the sub-symbolic paradigm. In particular, exemplars can be
represented as instances of a concept in symbolic systems,
as points in a geometrical conceptual space, or as a partic-
ular (local) pattern of activation in a ANN. Finally, also for
the classical body of knowledge it is –at least in principle–,
is-a: feline
color: yellow
hasPart: fur
hasPart: tail
hasPart: stripes
...
conceptual space
representation
concept Tiger
Kingdom: Animalia
Class: Mammalia
Order: Carnivora
Genus: Panthera
Species: P. tigris
prototype of Tiger exemplars of Tiger
white-tiger
is-a: feline
color: white
hasPart: fur
hasPart: tail
hasPart: stripes
...
...
ontological
representation
classical information
Typicality-based
knowledge
Classical
knowledge
Hybrid Knowledge Base
ACT-R concepts represented as en “empty
chunk” (chunk having no associated
information, except for its WordNet synset ID
and a human readable name), referred to by
the external bodies of knowledge
(prototypes and exemplars) acting like
semantic pointers.

32. CLARION Integration
• “Extende
32
for a given concept can be represented by adopting differ-
ent computational frameworks: i) from a symbolic perspec-
tive, prototypical representations can be encoded in terms
of frames [Minsky, 1975] or semantic networks [Quillian,
1968]; ii) from a conceptual space perspective, prototypes can
be geometrically represented as centroids of a convex region
(more on this aspect later); iii) from a sub-symbolic perspec-
tive, the prototypical knowledge concerning a concept can, on
the other hand, be represented as reinforced patterns of con-
nections in Artificial Neural Networks (ANNs). Similarly,
for the exemplars-based body of knowledge, both symbolic
and conceptual space representations can be used, as well as
the sub-symbolic paradigm. In particular, exemplars can be
represented as instances of a concept in symbolic systems,
as points in a geometrical conceptual space, or as a partic-
ular (local) pattern of activation in a ANN. Finally, also for
the classical body of knowledge it is –at least in principle–,
is-a: feline
color: yellow
hasPart: fur
hasPart: tail
hasPart: stripes
...
conceptual space
representation
concept Tiger
Kingdom: Animalia
Class: Mammalia
Order: Carnivora
Genus: Panthera
Species: P. tigris
prototype of Tiger exemplars of Tiger
white-tiger
is-a: feline
color: white
hasPart: fur
hasPart: tail
hasPart: stripes
...
...
ontological
representation
classical information
Typicality-based
knowledge
Classical
knowledge
Hybrid Knowledge Base
• natively “dual process”
• Typicality information (conceptual
spaces) —> implicit NACS layer
• Classical (ontology)—> explicit NACS
The mapping between the sub-symbolic module of
CLARION and the vector-based representations of
the Conceptual Spaces has been favored, since
such architecture also synthesizes the implicit
information in terms of dimensions-values pairs

33. Evaluation
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.
112 common sense linguistic descriptions provided by a team of
linguists, philosophers and neuroscientists interested in the neural
basis of lexical processing (FMRI).
Gold standard: for each description they recorded the human
answers for the categorization task.
Stimulus Expected
Concept
Expected Proxy-
Representation
Type of Proxy-
Representation
… … … …
The primate
with red nose
Monkey Mandrill EX
The feline with
black fur that
hunts mice
Cat Black cat EX
The domestic
feline
Cat Cat PR

34. 34
• Two evaluation metrics have been devised:
- Concept Categorization Accuracy: estimating how often
the correct concept has been retrieved;
- Proxyfication Accuracy: how often the correct concept
has been retrieved AND the expected representation
has been retrieved, as well.
Accuracy Metrics

35. 35
• Three sorts of proxyfication errors were committed:
- Ex-Proto, an exemplar is returned in place of a prototype;
- Proto-Ex, we expected a prototype, but a prototype is
returned;
- Ex-Ex, an exemplar is returned differing from the
expected one.
• Three sorts of proxyfication errors were committed:
- Ex-Proto, an exemplar is returned in place of a prototype;
- Proto-Ex, we expected a prototype, but a prototype is
returned;
- Ex-Ex, an exemplar is returned differing from the
expected one.
Proxyfication Error

36. Upshots
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.
Proposed an extension/integration of the Knowledge Level of
CAs with Conceptual Spaces
Conceptual Spaces provide advantages w.r.t. the symbolic and
sub symbolic representational level in CA and a possibile
unification framework for the diagrammatic
representations
Conceptual Spaces allow to combine common-sense
representation and reasoning and classical representation
and reasoning
Integration of a KR and Reasoning System with 2 Cognitive
Architectures making different assumptions about the
structures and the processes of our cognition

37. Extending the Knowledge Level of General Cognitive Architectures with
Conceptual Spaces
Antonio Lieto
University of Turin, Dept. of Computer Science, Italy
ICAR-CNR, Palermo, Italy
Conceptual Spaces Workshop 2016, Stockholm, 25-27 July 2016