In this paper we present a cognitively inspired system for the representation of conceptual information in an ontology-based environment. It builds on the heterogeneous notion of concepts in Cognitive Science and on the so-called dual process theories of reasoning and rationality, and it provides a twofold view on the same arti cial concept, combining a classical symbolic component (grounded on a formal ontology) with a typicality-based one (grounded on the conceptual spaces framework). The implemented system has been tested in a pilot experimentation regarding the classi cation task of linguistic stimuli. The results show that this modeling solution extends the representational and reasoning \conceptual" capabilities of standard ontology-based systems.
Representing and reasoning on common sense concepts is still an open issue in
the eld of knowledge engineering and, more speci cally, in that of formal
ontologies. In Cognitive Science evidences exist in favor of prototypical concepts,
and typicality-based conceptual reasoning has been widely studied. Conversely,
in the eld of computational models of cognition, most contemporary concept
oriented knowledge representation (KR) systems, including formal ontologies, do
not allow {for technical convenience{ neither the representation of concepts in
prototypical terms nor forms of approximate, non monotonic, conceptual
reasoning. In this paper we focus on the problem of concept representation in the eld
of formal ontologies and we introduce, following the approach proposed in [
The study of concept representation concerns di erent research areas, such
as Arti cial Intelligence, Cognitive Science, Philosophy, etc.. In the eld of
Cognitive Science, the early work of Rosch [
However, these systems lacked in clear formal semantics, and were later
sacri ced in favor of a class of formalisms stemmed from structured inheritance
semantic networks: the rst system in this line of research was the KL-ONE
system [
As a possible way out, we follow the proposal presented in [
The paper is structured as follows: in Section 2 we illustrate the general architecture and the main features of the implemented system. In Section 3 we provide the results of a preliminary experimentation to test inference in the proposed approach, and, nally, we conclude by presenting the related work (Section 4) and by outlining future work (Section 5). 2
A system has been implemented to explore the hypothesis of the hybrid
conceptual architecture. To test it, we have been considering a basic inference task:
given an input description in natural language, the system should be able to nd,
1 This is the case, for example, of exceptions to the inheritance mechanism.
2 For the Web Ontology Language, see http://www.w3.org/TR/owl-features/ and
http://www.w3.org/TR/owl2-overview/, respectively.
even for typicality based description (that is, most of common sense
descriptions), the corresponding concept category by combining ontological inference
and typicality based one. To these ends, we developed a domain ontology (the
naive animal ontology, illustrated below) and a parallel typicality description as
a set of domains in a conceptual space framework [
In the following, i) we rst outline the design principles that drove the development of the system; ii) we then provide an overview of the system architecture and of its components and features; iii) we elaborate on the inference task, providing the detailed control strategy; and nally iv) we introduce the domain ontology and the conceptual space used as case study applied over the restricted domain of animals. 2.1
The theoretical framework known as dual process theory postulates the
coexistence of two di erent types of cognitive systems. The systems3 of the rst
type (type 1) are phylogenetically older, unconscious, automatic, associative,
parallel and fast. The systems of the second type (type 2) are more recent,
conscious, sequential and slow, and featured by explicit rule following [
Another theoretical framework inspiring our system regards the
heterogeneous approach to the concepts in Cognitive Science, according to which
concepts do not constitute a unitary element (see [
Our system is equipped, then, with a hybrid conceptual architecture based on a classical component and on a typical component, each encoding a speci c reasoning mechanism as in the dual process perspective. Figure 1 shows the general architecture of the hybrid conceptual representation.
The ontological component is based on a classical representation grounded on a DL formalism, and it allows specifying the necessary and/or su cient conditions for concept de nition. For example, if we consider the concept water, the classical component will contain the information that water is exactly the chemical substance whose formula is H2O, i.e., the substance whose molecules have two hydrogen atoms with a covalent bond to the single oxygen atom. On the other hand, the prototypical facet of the concept will grasp its prototypical traits, such as the fact that water occurring in liquid state is usually a colorless, odorless and tasteless uid. 3 We assume that each system type can be composed by many sub-systems and processes.
Representation of
Concept X hasComponent hasComponent system 2 Monotonic
Reasoning represCelnatsasticioanl of X Ontology-based categorization system 1 Non Monotonic Reasoning
Typical representation of X Exemplar and prototype-based categorization
By adopting the \dual process" notation, in our system the representational
and reasoning functions are assigned to the system 1 (executing processes of
type 1), and they are associated to the Conceptual Spaces framework [
We now brie y introduce the representational frameworks upon which system 1 (henceforth S1) and system 2 (henceforth S2) have been designed.
As mentioned, the aspects related to the typical conceptual component S1
are modeled through Conceptual Spaces [
On the other hand, the representation of the classical component S2 has been implemented based on a formal ontology. As already pointed out, the standard ontological formalisms leave unsolved the problem of representing prototypical information. Furthermore, it is not possible to execute non monotonic inference, since classical ontology-based reasoning mechanisms simply contemplate deductive processes. 2.2
Categorization (i.e., to classify a given data instance into a prede ned set of categories) is one of the classical processes automatically performed both by symbolic and sub-symbolic arti cial systems. In our system categorization is based on a two-step process involving both the typical and the classical component of the conceptual representation. These components account for di erent types of categorization: approximate or non monotonic (performed on the conceptual spaces), and classical or monotonic (performed on the ontology). Di erent from classical ontological inference, in fact, categorization in conceptual spaces proceeds from prototypical values. In turn, prototypical values need not be speci ed for all class individuals, that vice versa can overwrite them: one typical example is the case of birds that (by default) y, except for special birds, like penguins, that do not y.
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 hc0; cci, 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 = fc1; c2; : : : ; cng. This set of results is then checked against cc, the output of S2 (Algorithm 1, line 3): the step is performed by adding to the ontology an individual from the class ci 2 C, modi ed by the information extracted from d, and by checking the consistency of the newly added element with a DL reasoner.
If the S2 system classi es it as consistent with the ontology, then the
classication succeeded and the category provided by S2 (cc) is returned along with
c0, the top scoring class returned by S1 (Algorithm 1: line 8). If cc {the class
computed by S2{ is a superclass or a subclass of one of those identi ed by S1
(ci), both cc and c0 are returned (Algorithm 1: line 11). Thus, if S2 provides
more speci c output, we follow a speci city heuristics; otherwise, the output of
S2 is returned, following the rationale that it is safer.4 If all results in C are
4 The output of S2 cannot be wrong on a purely logical perspective, in that it is
the result of a deductive process. The control strategy tries to implement a tradeo
between ontological inference and the output of S1, which is more informative but
also less reliable from a formal point of view. However, in next future we plan to
explore di erent conciliation mechanisms to ground the overall control strategy.
inconsistent with those computed by S2, a pair of classes is returned including
c0 and the output of S2 having for actual parameters d and Thing, the meta
class of all the classes in the ontological formalism.
A formal ontology has been developed describing the animal kingdom. It has
been devised to meet common sense intuitions, rather than re ecting the
precise taxonomic knowledge of ethologists, so we denote it as nave animal
ontology.5 In particular, the ontology contains the taxonomic distinctions that have
an intuitive counterpart in the way human beings categorize the
corresponding concepts. Classes are collapsed at a granularity level such that they can be
naturally grouped together also based on their accessibility [
The ontology is linked to DOLCE's Lite version;6 in particular, the tree containing our taxonomy is rooted in the agentive-physical-object class, while the body components are set under biological-physical-object, and partitioned between the two disjunct classes head-part (e.g., for framing horns, antennas, fang, etc.) and body-part (e.g., for paws, tails, etc.). The biological-object class in5 The ontology is available at the URL http://www.di.unito.it/~radicion/ datasets/aic_13/Naive_animal_ontology.owl 6 http://www.loa-cnr.it/ontologies/DOLCE-Lite.owl cludes di erent sorts of skins (such as fur, plumage, scales), substances produced and eaten by animals (e.g., milk, wool, poison and fruits, leaves and seeds). 2.4
The conceptual space de nes a metric space that can be used to compute the
proximity of the input entities to prototypes. To compute the distance between
two points p1; p2 we apply a distance metrics based on the combination of the
Euclidean distance and the angular distance intervening between the points.
Namely, we use Euclidean metrics to compute within-domain distance, while for
dimensions from di erent domains we use the Manhattan distance metrics, as
suggested in [
The representation format adopted in conceptual spaces (e.g., for the concept whale) includes information such as:
02062744n,whale,dimension(x=350,y=350,z=2050),color(B=20,H=20,S=60),food=10 that is, the WordNet synset identi er, the lemma of the concept in the description, information about its typical dimensions, color (as the position of the instance on the three-dimensional axes of brightness, hue and saturation) and food. Of course, information about typical traits varies according to the species. Three domains with multiple dimensions have been de ned:7 size, color and habitat. Each quality in a domain is associated to a range of possible values. To avoid that larger ranges a ect too much the distance, we have introduced a damping factor to reduce this e ect; also, the relative strength of each domain can be parametrized.
We represent points as vectors (with as many dimensions as required by the considered domain), whose components correspond to the point coordinates, so that a natural metrics to compute the similarity between them is cosine similarity. Cosine similarity is computed as the cosine of the angle between the considered vectors: two vectors with same orientation have a cosine similarity 1, while two orthogonal vectors have cosine similarity 0. The normalized version of cosine similarity (c^s), also accounting for the above weights wi and context k is computed as c^s(p1; p2; k) = pPn i=1 wi(p1;i)2
Pin=1 wi(p1;i p2;i) pPn i=1 wi(p2;i)2 : 7 We de ned also further domains with one dimension (e.g., whiskers, wings, paws, fang, and so forth), but for our present concerns they are of less interest. The conceptual space is available at the URL http://www.di.unito.it/~radicion/datasets/ aic_13/conceptual_space.txt.
Moreover, to satisfy the triangle inequality is a requirement upon distance in a metric space; unfortunately, cosine similarity does not satisfy triangle inequality, so we adopt a slightly di erent metrics, the angular similarity (a^s), whose values vary over the range [0; 1], and that is de ned as Angular distance allows us to compare the shape of animals disregarding their actual size: for example, it allows us to nd that a python is similar to a viper even though it is much bigger.
In the metric space being de ned, the distance d between individuals ia; ib is
computed with the Manhattan distance, enriched with information about
context k that indicates the set of weights associated to each domain. Additionally,
the relevance of domains with fewer dimensions (that would obtain overly high
weights) is counterbalanced by a normalizing factor (based on the work by [
q d(ia; ib; K) = jDj j distE (pj (ia); pj (ib); kj ) ; (1) where K is the whole context, containing domain weights wj and contexts kj , and jDj j is the number of dimensions in each domain.
In this setting, the distance between each two concepts can be computed as the distance between two regions in a given domain, and then to combining them through the Formula 1. Also, we can compute the distance between any two region prototypes, or the minimal distance between their individuals, or we can apply more sophisticated algorithms: in all cases, we have designed a metric space and procedures that allow characterizing and comparing concepts herein. Although angular distance is currently applied to compute similarity in the size of the considered individuals, it can be generalized to further dimensions. 3
The evaluation consisted of an inferential task aimed at categorizing a set of linguistic descriptions. Such descriptions contain information related to concepts typical features. Some examples of these common-sense descriptions are: \the big carnivore with black and yellow stripes" denoting the concept of tiger, and \the sweet water sh that goes upstream" denoting the concept of salmon, and so on. A dataset of 27 \common-sense" linguistic descriptions was built, containing a list of stimuli and their corresponding category: this is the \prototypically correct" category, and in the following is referred to as the expected result.8 The set of stimuli was devised by a team of neuropsychologists and philosophers in 8 The full list is available at the URL http://www.di.unito.it/~radicion/ datasets/aic_13/stimuli_en.txt.
Test cases categorized
[ 1.] Cases where S1 and S2 returned the same category
[2a.] Cases where S1 returned the expected category
[2b.] Cases where S2 returned the expected category
Cases where S1 OR S2 returned the expected category
the frame of a broader project, aimed at investigating the role of visual load in
concepts involved in inferential and referential tasks. Such input was used for
querying the system as in a typicality based question-answering task. In
Information Retrieval such queries are known to belong to the class of \informational
queries", i.e., queries where the user intends to obtain information regarding a
speci c information need. Since it is characterized by uncertain and/or
incomplete information, this class of queries is by far the most common and complex to
interpret, if compared to queries where users can search for the URL of a given
site (`navigational queries'), or look for sites where some task can be performed,
like buying music les (`transactional queries') [
We devised some metrics to assess the accuracy of the system, and namely we recorded the following information: 1. how often S1 and S2 returned in output the same category; 2. in case di erent outputs were returned, the accuracy obtained by S1 and S2: 2a. the accuracy of S1. This gure is intended to measure how often the top ranked category c0 returned by S1 is the same as that expected. 2b. the accuracy of S2, that is the second category returned in the output pair hc ; cci. This gure is intended to measure how often the cc category is the appropriate one w.r.t. the expected result. We remark that cc has not been necessarily computed by starting from c0: in principle any ci 2 C might have been used (see also Algorithm 1, lines 3 and 15).
The results obtained in this preliminary experimentation are presented in Table 1. All of the stimuli were categorized, although not all of them were correctly categorized. However, the system was able to correctly categorize a vast majority of the input descriptions: in most cases (92:6%) S1 alone produces the correct output, with considerable saving in terms of computation time and resources. Conversely, none of the concepts (except for one) described with typical features would have been classi ed through classical ontological inference. It is in virtue of the former access to conceptual spaces that the whole system is able to categorize such descriptions. Let us consider, e.g., the description \The animal that eats bananas". The ontology encodes knowledge stating that monkeys are omnivore. However, since the information that usually monkeys eat bananas cannot be represented therein, the description would be consistent to all omnivores. The information returned would then be too informative w.r.t. the granularity of the expected answer.
Another interesting result was obtained for the input description \the big herbivore with antlers". In this case, the correct answer is the third element in the list C returned by S1; but thanks to the categorization performed by S2, it is returned in the nal output pair (see Algorithm 1, line 8).
Finally, the system revealed to be able to categorize stimuli with typical, though ontologically incoherent, descriptions. As an example of such a case we will consider the categorization results obtained with the following stimulus: \The big sh that eats plankton". In this case the prototypical answer expected is whale. However, whales properly are mammals, not shes. In our hybrid system, S1 component returns whale by resorting to prototypical knowledge. If further details were added to the input description, the answer would have changed accordingly: in this sense the categorization performed by S1 is non monotonic in nature. When then C (the output of S1) is checked against the ontology as described by the Algorithm 1 at lines 7{13, and an inconsistency is detected,9 the consistency of the second result in C (shark in this example) is tested against the ontology. Since this answer is an ontologically compliant categorization, then this solution is returned by the S2 component. The nal output of the categorization is then the pair hwhale; sharki: the rst element, prototypically relevant for the query, would have not been provided by querying a classical ontological representation. Moreover, if the ontology recorded the information that also other shes do eat plankton, the output of a classical ontological inference would have included them, too, thereby resulting in a too large set of results w.r.t. the intended answer. 4
In the context of a di erent eld of application, a solution similar to the one
adopted here has been proposed in [
In other respects, our system is also akin to that ones developed in the eld of
the computational approach to the above mentioned dual process theories. A rst
example of such \dual based systems" is the mReasoner model [
In this paper we presented a cognitively inspired system to extend the representational and reasoning capabilities of classical ontological representations. We tested it in a pilot study concerning a categorization task involving typicality based queries. The results show that the proposed architecture e ectively extends the reasoning and representational capabilities of formal ontologies towards the domain of prototype theory.
Next steps will be to complete the implementation of current system: rst, we will work to the automatization of the Information Extraction from linguistic descriptions, and then to the automatization of the mapping of the extracted information onto the conceptual representations in S1 and S2. In near future we will also extend the coverage of the implemented system to further domains.
Yet, we are designing a learning setting to modify weights in conceptual spaces according to experience (thereby qualifying the whole system as a supervised learning one). This line of research will require the contribution of theoretical and experimental psychologists, to provide insightful input to the development of the system, and experimental corroboration to its evolving facets, as well. Future work will also include the evaluation of the system on web data, namely to experiment by using search engine web logs, in order to verify whether and to what extent the implemented system matches the actual users' informational needs.