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

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.

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.

“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

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).

Problemno 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.

Proposal

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

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.

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.

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

Ex. CS for “Color”

Intensity

Hue

Brightness

Green

Red

Yellow

Blue

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).

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.

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.

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.

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).

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.

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.

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.

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.

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/

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.

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

Classical Theory – Ex.

22

TRIANGLE = Polygon with 3 corners and sides

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

atypical

typical

P

Exemplars and Exemplar-based Reasoning• Categories as composed by a list of exemplars. New

percepts are compared to known exemplars (not to Prototypes).

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).

System Conceptual Structure

28

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 termsof frames [Minsky, 1975] or semantic networks [Quillian,1968]; ii) from a conceptual space perspective, prototypes canbe 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, onthe other hand, be represented as reinforced patterns of con-nections in Artificial Neural Networks (ANNs). Similarly,for the exemplars-based body of knowledge, both symbolicand conceptual space representations can be used, as well asthe sub-symbolic paradigm. In particular, exemplars can berepresented 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 forthe classical body of knowledge it is –at least in principle–,possible to use the same frameworks. However, this seemsto be a case where symbolic and conceptual levels are moreappropriate w.r.t. the sub-symbolic one.

Summing up, all the different types of conceptual repre-sentations can be implemented in cognitive artificial systemsand architectures. In addition, different computational mech-anisms for “proxyfying” conceptual representations can beapplied. In the next Section we illustrate and discuss the rep-resentational levels and the associated computational frame-works we adopted for each type of body of knowledge.

3 The DUAL-PECCS SystemAs mentioned, the DUAL-PECCS relies on the heteroge-neous proxytypes approach and on the dual process theory.It is equipped with a hybrid knowledge base composed ofheterogeneous representations of the same conceptual enti-ties: that is, the hybrid knowledge base includes prototypes,exemplars and classical representations for the same concept.Both prototypes and exemplars are represented at the con-ceptual level (see Section 3.1), while classical information isrepresented through standard symbolic formalisms (i.e., bymeans of a formal ontology).

The retrieval of such representations is driven by differentprocess types. In particular, prototype and exemplar-based re-trieval is based on a fast and approximate kind of categoriza-tion, and benefits from common-sense information associatedto concepts. On the other hand, the retrieval of the classicalrepresentation of concepts is featured by explicit rule follow-ing, and makes no use of common-sense information. Thesetwo differing categorization strategies have been widely stud-ied in psychology of reasoning in the frame of the dual pro-cess theory, that postulates the co-existence of two differ-ent types of cognitive systems [Evans and Frankish, 2009;Kahneman, 2011]. The systems of the first type (type 1) arephylogenetically older, unconscious, automatic, associative,parallel and fast. The systems of the second type (type 2) aremore recent, conscious, sequential and slow, and featured byexplicit rule following. We assume that both systems can becomposed in their turn by many sub-systems and processes.According to the hypotheses in [Frixione and Lieto, 2012;Frixione and Lieto, 2014], the conceptual representation of

is-a: felinecolor: yellowhasPart: furhasPart: tailhasPart: stripes

...

conceptual space representation

concept Tiger

Kingdom: AnimaliaClass: MammaliaOrder: CarnivoraGenus: PantheraSpecies: P. tigris

prototype of Tiger exemplars of Tiger

white-tigeris-a: felinecolor: whitehasPart: furhasPart: tailhasPart: stripes...

...

ontological representation

classical information

Typicality-based knowledge

Classical knowledge

Hybrid Knowledge Base

Figure 1: Heterogeneous representation of the tiger concept

our system includes two main sorts of components, based onthese two sorts of processes. Type 1 processes have been de-signed to deal with prototypes- and exemplar-based retrieval,while Type 2 processes have been designed to deal with de-ductive inference.

The two sorts of system processes interact (Algorithm 1),since Type 1 processes are executed first and their results arethen refined by Type 2 processes. In the implemented sys-tem the typical representational and reasoning functions areassigned to the System 1 (hereafter S1), which executes pro-cesses of Type 1, and are associated to the Conceptual Spacesframework [Gardenfors, 2000; Gardenfors, 2014]. On theother hand, the classical representational and reasoning func-tions are assigned to the System 2 (hereafter S2) to executeprocesses of Type 2, and are associated to a standard ontolog-ical representation.

Figure 1 shows the heterogeneous representation for theconcept tiger, with prototypical and exemplar-based repre-sentations semantically pointing to the same conceptual en-tity. In this example, the exemplar and prototype-based rep-resentations make use of non classical information. Namely,the prototypical representation grasps information such asthat tigers are wild animals, their fur has yellow and blackstripes, etc.; the exemplar-based representations grasp infor-mation on individuals (such as white-tiger, which is a partic-ular tiger with white fur). Both sorts of representations acti-vate Type 1 processes. On the other hand, the classical bodyof knowledge is filled with necessary and sufficient informa-tion to characterize the concept (representing, for example,the taxonomic information that a tiger is a mammal and acarnivore), and activates Type 2 processes.

In the following we introduce the two representational andreasoning frameworks used in our system, by focusing i) onhow typicality information (including both prototypes and ex-emplars) and their corresponding non monotonic reasoningprocedures can be encoded through conceptual spaces; andii) on how classical information can be naturally encoded interms of formal ontologies.

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.

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

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 termsof frames [Minsky, 1975] or semantic networks [Quillian,1968]; ii) from a conceptual space perspective, prototypes canbe 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, onthe other hand, be represented as reinforced patterns of con-nections in Artificial Neural Networks (ANNs). Similarly,for the exemplars-based body of knowledge, both symbolicand conceptual space representations can be used, as well asthe sub-symbolic paradigm. In particular, exemplars can berepresented 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 forthe classical body of knowledge it is –at least in principle–,possible to use the same frameworks. However, this seemsto be a case where symbolic and conceptual levels are moreappropriate w.r.t. the sub-symbolic one.

Summing up, all the different types of conceptual repre-sentations can be implemented in cognitive artificial systemsand architectures. In addition, different computational mech-anisms for “proxyfying” conceptual representations can beapplied. In the next Section we illustrate and discuss the rep-resentational levels and the associated computational frame-works we adopted for each type of body of knowledge.

3 The DUAL-PECCS SystemAs mentioned, the DUAL-PECCS relies on the heteroge-neous proxytypes approach and on the dual process theory.It is equipped with a hybrid knowledge base composed ofheterogeneous representations of the same conceptual enti-ties: that is, the hybrid knowledge base includes prototypes,exemplars and classical representations for the same concept.Both prototypes and exemplars are represented at the con-ceptual level (see Section 3.1), while classical information isrepresented through standard symbolic formalisms (i.e., bymeans of a formal ontology).

The retrieval of such representations is driven by differentprocess types. In particular, prototype and exemplar-based re-trieval is based on a fast and approximate kind of categoriza-tion, and benefits from common-sense information associatedto concepts. On the other hand, the retrieval of the classicalrepresentation of concepts is featured by explicit rule follow-ing, and makes no use of common-sense information. Thesetwo differing categorization strategies have been widely stud-ied in psychology of reasoning in the frame of the dual pro-cess theory, that postulates the co-existence of two differ-ent types of cognitive systems [Evans and Frankish, 2009;Kahneman, 2011]. The systems of the first type (type 1) arephylogenetically older, unconscious, automatic, associative,parallel and fast. The systems of the second type (type 2) aremore recent, conscious, sequential and slow, and featured byexplicit rule following. We assume that both systems can becomposed in their turn by many sub-systems and processes.According to the hypotheses in [Frixione and Lieto, 2012;Frixione and Lieto, 2014], the conceptual representation of

is-a: felinecolor: yellowhasPart: furhasPart: tailhasPart: stripes

...

conceptual space representation

concept Tiger

Kingdom: AnimaliaClass: MammaliaOrder: CarnivoraGenus: PantheraSpecies: P. tigris

prototype of Tiger exemplars of Tiger

white-tigeris-a: felinecolor: whitehasPart: furhasPart: tailhasPart: stripes...

...

ontological representation

classical information

Typicality-based knowledge

Classical knowledge

Hybrid Knowledge Base

Figure 1: Heterogeneous representation of the tiger concept

our system includes two main sorts of components, based onthese two sorts of processes. Type 1 processes have been de-signed to deal with prototypes- and exemplar-based retrieval,while Type 2 processes have been designed to deal with de-ductive inference.

The two sorts of system processes interact (Algorithm 1),since Type 1 processes are executed first and their results arethen refined by Type 2 processes. In the implemented sys-tem the typical representational and reasoning functions areassigned to the System 1 (hereafter S1), which executes pro-cesses of Type 1, and are associated to the Conceptual Spacesframework [Gardenfors, 2000; Gardenfors, 2014]. On theother hand, the classical representational and reasoning func-tions are assigned to the System 2 (hereafter S2) to executeprocesses of Type 2, and are associated to a standard ontolog-ical representation.

Figure 1 shows the heterogeneous representation for theconcept tiger, with prototypical and exemplar-based repre-sentations semantically pointing to the same conceptual en-tity. In this example, the exemplar and prototype-based rep-resentations make use of non classical information. Namely,the prototypical representation grasps information such asthat tigers are wild animals, their fur has yellow and blackstripes, etc.; the exemplar-based representations grasp infor-mation on individuals (such as white-tiger, which is a partic-ular tiger with white fur). Both sorts of representations acti-vate Type 1 processes. On the other hand, the classical bodyof knowledge is filled with necessary and sufficient informa-tion to characterize the concept (representing, for example,the taxonomic information that a tiger is a mammal and acarnivore), and activates Type 2 processes.

In the following we introduce the two representational andreasoning frameworks used in our system, by focusing i) onhow typicality information (including both prototypes and ex-emplars) and their corresponding non monotonic reasoningprocedures can be encoded through conceptual spaces; andii) on how classical information can be naturally encoded interms of formal ontologies.

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.

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 termsof frames [Minsky, 1975] or semantic networks [Quillian,1968]; ii) from a conceptual space perspective, prototypes canbe 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, onthe other hand, be represented as reinforced patterns of con-nections in Artificial Neural Networks (ANNs). Similarly,for the exemplars-based body of knowledge, both symbolicand conceptual space representations can be used, as well asthe sub-symbolic paradigm. In particular, exemplars can berepresented 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 forthe classical body of knowledge it is –at least in principle–,possible to use the same frameworks. However, this seemsto be a case where symbolic and conceptual levels are moreappropriate w.r.t. the sub-symbolic one.

Summing up, all the different types of conceptual repre-sentations can be implemented in cognitive artificial systemsand architectures. In addition, different computational mech-anisms for “proxyfying” conceptual representations can beapplied. In the next Section we illustrate and discuss the rep-resentational levels and the associated computational frame-works we adopted for each type of body of knowledge.

3 The DUAL-PECCS SystemAs mentioned, the DUAL-PECCS relies on the heteroge-neous proxytypes approach and on the dual process theory.It is equipped with a hybrid knowledge base composed ofheterogeneous representations of the same conceptual enti-ties: that is, the hybrid knowledge base includes prototypes,exemplars and classical representations for the same concept.Both prototypes and exemplars are represented at the con-ceptual level (see Section 3.1), while classical information isrepresented through standard symbolic formalisms (i.e., bymeans of a formal ontology).

The retrieval of such representations is driven by differentprocess types. In particular, prototype and exemplar-based re-trieval is based on a fast and approximate kind of categoriza-tion, and benefits from common-sense information associatedto concepts. On the other hand, the retrieval of the classicalrepresentation of concepts is featured by explicit rule follow-ing, and makes no use of common-sense information. Thesetwo differing categorization strategies have been widely stud-ied in psychology of reasoning in the frame of the dual pro-cess theory, that postulates the co-existence of two differ-ent types of cognitive systems [Evans and Frankish, 2009;Kahneman, 2011]. The systems of the first type (type 1) arephylogenetically older, unconscious, automatic, associative,parallel and fast. The systems of the second type (type 2) aremore recent, conscious, sequential and slow, and featured byexplicit rule following. We assume that both systems can becomposed in their turn by many sub-systems and processes.According to the hypotheses in [Frixione and Lieto, 2012;Frixione and Lieto, 2014], the conceptual representation of

is-a: felinecolor: yellowhasPart: furhasPart: tailhasPart: stripes

...

conceptual space representation

concept Tiger

Kingdom: AnimaliaClass: MammaliaOrder: CarnivoraGenus: PantheraSpecies: P. tigris

prototype of Tiger exemplars of Tiger

white-tigeris-a: felinecolor: whitehasPart: furhasPart: tailhasPart: stripes...

...

ontological representation

classical information

Typicality-based knowledge

Classical knowledge

Hybrid Knowledge Base

Figure 1: Heterogeneous representation of the tiger concept

our system includes two main sorts of components, based onthese two sorts of processes. Type 1 processes have been de-signed to deal with prototypes- and exemplar-based retrieval,while Type 2 processes have been designed to deal with de-ductive inference.

The two sorts of system processes interact (Algorithm 1),since Type 1 processes are executed first and their results arethen refined by Type 2 processes. In the implemented sys-tem the typical representational and reasoning functions areassigned to the System 1 (hereafter S1), which executes pro-cesses of Type 1, and are associated to the Conceptual Spacesframework [Gardenfors, 2000; Gardenfors, 2014]. On theother hand, the classical representational and reasoning func-tions are assigned to the System 2 (hereafter S2) to executeprocesses of Type 2, and are associated to a standard ontolog-ical representation.

Figure 1 shows the heterogeneous representation for theconcept tiger, with prototypical and exemplar-based repre-sentations semantically pointing to the same conceptual en-tity. In this example, the exemplar and prototype-based rep-resentations make use of non classical information. Namely,the prototypical representation grasps information such asthat tigers are wild animals, their fur has yellow and blackstripes, etc.; the exemplar-based representations grasp infor-mation on individuals (such as white-tiger, which is a partic-ular tiger with white fur). Both sorts of representations acti-vate Type 1 processes. On the other hand, the classical bodyof knowledge is filled with necessary and sufficient informa-tion to characterize the concept (representing, for example,the taxonomic information that a tiger is a mammal and acarnivore), and activates Type 2 processes.

In the following we introduce the two representational andreasoning frameworks used in our system, by focusing i) onhow typicality information (including both prototypes and ex-emplars) and their corresponding non monotonic reasoningprocedures can be encoded through conceptual spaces; andii) on how classical information can be naturally encoded interms of formal ontologies.

• 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

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

• 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

• 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

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

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