Similarity and Categorization : Taxonomic and Meronomic parts of Similes

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1 Similarity and Categorization : Taxonomic and Meronomic parts of Similes Charles Tijus Cognition & Usages 2 rue de la Liberté Saint-Denis tijus@univ-paris8.fr Sébastien Poitrenaud Cognition & Usages 2 rue de la Liberté Saint-Denis poitrenaud@univ-paris8.fr Denis Chene Cognition & Usages 2 rue de la Liberté Saint-Denis chene@francetelecom.com Abstract What is a category made of? What are a category's different parts? We propose that the parts of a category are the properties of this category, which is to say that parts of the definition of a category are the properties listed to describe this category. Thus, the color "gray", which is not a physical part of a mouse, is a part of the description of the "mouse category", whilst "whiskers" that is a physical part of a given mouse and is also a part of the description of the "mouse category". We shall define partonomy as the decomposition of an object into its physical parts and meronomy as the decomposition of a category description into its cognitive parts and show how this approach helps to solve some of problems of computing similarity by first building a hierarchy of contextual categories that provides a way to measure similarity. Keywords: Similarity, Categorization, Galois Lattice. 1 How similar is mouse to elephant? Measuring similarity is a key problem in A.I. and in Cognitive science and finding out how similar something (an object, an image, an idea, a text, a situation, a discovery) is to something else would be helpful for the purposes of detection, identification, analogy, thinking, reasoning and problem solving [5, 15]. The usual problem involves decision making: given some knowledge about x, to measure how similar y is to x and, then to accept or reject y as being of the same kind than x. Thus, the decision-making problem is to provide as output a categorization decision about y, given a similarity value between x and y as input. People are supposed to daily solve this kind of decision-making problem. Surprisingly, studies in cognitive psychology show, first, that similarity is not necessarily transitive: For instance, if similarity (Russia, Cuba) = 7 and similarity (Cuba, Jamaica) = 8, then, one should expect similarity (Russia, Jamaica) to be around 7, but the similarity score quoted is 1! Second, similarity is not necessarily asymmetric [17]: x can be quoted as more similar to y, than y to x. The letter «F» is more similar to «E», than «E» to «F». Third, people put things that they have evaluated to be very similar into different categories: similarity does not fit with categorization [5, 8, 13]. A first solution proposed by nonmetric multidimensional scaling (MDS) models, based on Richardson s ideas, could be that the dimensions for comparison differ. A second solution is that natural categorization is guided by similarity, but that people do optimize categorization performance by paying attention to some core properties that are weighted more in similarity than in categorization [10]. However, the problem remains to identify what are the right properties to consider for computing similarity.

2 For instance, Signal Detection Theory is useful for the evaluation of how good a detection system is, if it is possible to define precisely what x and y are and what x and y are not. However, contrary to the Ideal Receiver of the Signal Detection Theory, we usually do not know what x and y are, and are not for computing similarity between x and y. In short, we don t know along which dimensions x and y have to be compared? Thus an initial problem, - the definition problem-, is to find the right dimensions along which x and y can be compared, which means having the right description of x and y. As another solution, we advocate that human categorization is not guided by similarity. That is similarity that is based on categorization. We argue that similarity is the product of categorization and not the reverse. Thus the problem at hand would be how categories are constructed in such a way similar objects could belong to different categories and dissimilar objects could belong to a same category. We present the contextual reciprocal effect theory of categorization [12, 15] and discuss how it may help to solve some of these similarity-categorization problems, to better understand how people process but also for automatic categorization. 2 /Mammal/ is part of both /Elephant/ and /Mouse/ The physical and ecological world is composed of objects. Any object has a number of parts and an arrangement of these parts that defines its structure. Any object also has features along physical dimensions (what it is made of, its shape, color, brightness, ). For people, physical objects do have the physical properties they perceive and the unseen physical properties they know as being those of the objects, but also the cognitive (non-physical) dimensions (functionality and usability) of the object. Note that function and the how-to-use it (cognitive properties) should be more crucial dimensions for people and should be important criteria for categorization, but that parts and arrangements of parts (physical dimensions) justify why an object can be used for a function and why it should be used that way. Verbal descriptors of an object by people can include words that designate parts, and the way parts are arranged, as well as physical and cognitive features. Unlike physical objects, categories are cognitive (or mental) entities. They are representations of groups of objects for cognitive purposes: identification (this is a cat), inference making (it should like drinking milk), and so on. Thus, a category is a three terms "concept": the category itself as a group of objects and a group of shared properties, its extension (the objects it groups: cats) and its intension (the criteria for grouping: eg. having a cat s shape, having hairs, it hums, it scratches, ). Moreover, for cognitive purposes, categories entail categories (cats are mammals, mammals are animals, animals are living beings, ). As entailment of categories forms a hierarchy of categories, we shall use the term taxonomy with a is a kind of link between categories (a cat is a kind of animal, an animal is a kind of living thing). The classical and implicit view of categorization is that one object is to belong to one category, and to one hierarchy of categories. It has been shown [2] that categories are created for goal purpose (objects saved from the fire are objects from a burning house). Our proposal is that people create any kind of categories and of hierarchies of categories along inclusive dimensions (e.g. the objects that are on the table, are objects in the room, are objects in the building, and so on) and that any kind of properties of the objects can be used to build categories. That is what we name contextual categorization. For instance, a book and a newspaper can be categorized as things to read. Adding garbage, the book, the newspaper and the bottle can then be category of things to put in the garbage, and the book an object to save from garbage, while adding Mary s bag can made the book, the newspaper and the bottle

3 being things Mary is going to transport, and the bottle things to be first filled with water. These are examples of on-line categories that people should build in situation in order to understand what happens around them. What is determining the properties are the goal at hand and the way objects can be aligned in order to build categories that differentiate the objects. Thus, categories are not only the well formed dictionary categories, but also contextual categories, each object being categorized relative to the others objects. It follows that two objects (let s say the cat and the dog of Mary) that could be in some circumstances in a same category in a context (Mary feeding her pets), would be in different categories in another context (things Mary is going to bring to the Park), while objects that are quite dissimilar (the cat and the book of Mary) can be put in the same category (things Mary is going to bring to the Park). Given the current situation, we can predict intransitivity, why Mary s dog and cat could have a high similarity score, why Mary s dog and book could have a high similarity score and why Mary s cat and book would have a low similarity score. We can also predict asymmetry in similarity: Mary s dog is more similar than Mary s cat because the dog is a pet as the cat, although the cat is not a pet as the dog that Mary is going to bring to the Park (see figure 2). The main proposal is that categories are built in context: the objects at hand are categorized in one hierarchy of categories. This cognitive flexibility that is responsible for creating categories from properties in context allows metonymy (a Mary s friend in the park: the book and the dog are coming to be understood as the coming of Mary in the Park), and metaphor construction [15]. We formalize this flexibility by what we call meronomy. Meronomy is the whole-to-part decomposition of a category. Meronomy has to be differentiated from partonomy that is the decomposition of an object into its physical parts. The color " gray", which is not a physical part of a mouse, is a part of the description of the mouse category, whilst whiskers which is a physical part, is also a part of the description of the "mouse category". Based on this theoretical distinction, we argue first, that taxonomy (is a kind of) and meronomy (is part of) are two sides of the same coin, X is a kind of Y and Y a part of X, - what Rips and Conrad [13, 14] named the reciprocal effect -, and second, that this approach is helpful for the similarity-categorization problem. 3 Reciprocal effect of categorization Categorization is the ability to group objects within a hierarchy of categories. We focus on categorization instead of category because the cognitive purpose of a category is not primarily to group, but to differentiate between objects. Differentiating between objects is achieved by creating subcategories and, in doing so, hierarchies of categories. Hierarchies of categories have a mathematical formalism labeled Galois Lattices [1, 11]. The On x Pm boolean matrix, which indicates whether each of n objects has or not each of m properties, enables the creation of one hierarchy of categories with transitivity, asymmetry and reflexivity. The maximum number of categories is either 2 n-1, or m if m < 2 n-1, in a lattice whose complexity depends on the way properties are distributed over objects (figure 1). Hierarchies of categories have the inheritance principle of taxonomies (if birds are animals, birds have animal properties in addition to their own properties). For instance in figure 1b, object O 1 is an object of category P3,P5 which has category P1,P2 as superordinate. If P1 is "on the table", P2 "red", P3 "large" and P5 "square", O 1 here would be a kind of "large square" that is a kind of "red thing on the table"; O 2 and O 3 being, for instance, small (P4) triangle (P6) and rectangle (P7). In Figure 1b (bottom), let us label X the category made of P1,P2 and Y the category made of P3,P5. Y is a kind of X. Due to the inheritance principle, category Y includes P1,P2, the properties of category X. This can be seen in the boolean table of figure 1b.

4 Figure 1: Binary descriptions and corresponding Galois Lattices. Figure 1a (top) and 1b (bottom) show that graph complexity does not depend on the number of objects (O) or of properties (P) but on the way properties are distributed over objects. As Rips & Conrad [1], footnote 3, reported, the property hypothesis of the reciprocal effect states: "If Y is a kind of Y, then Y must have all X's defining properties (as in traditional property models of classification, see [6, 8, 9]. As a consequence, Galois lattice formalism, as well as the property hypothesis, advocates that "mammals are parts of elephants, tools are parts of hammers" in the meronomic sense that "all of the descriptions of mammals are part of the description of elephants and all of the descriptions of tools are part of the description of hammers". This contrasts with the views of [1], p. 201, who wrote "More general classes of objects don't seem to be parts of more specific ones -mammals are not parts of elephants, tools are not parts of hammers, and so on.-" The meaning of the sentence mammals are part of elephants is not that all objects that are mammals are part-of all objects that are elephants. This is evidently false. It means : what one can say about mammals is part-of what one can say about elephants. This can be experimentally verified with participants. To do so, we advocate for a clear distinction between objects in the physical world and the categories used to represent them and to think, talk and communicate about them. Unlike objects, which have a physical counterpart, categories are cognitive. We propose that all the cognitive facts that are related to categories must be studied as cognitive, not physical, entities and require, as such, verbal responses from participants about symbols. Are elephants mammals? should be reformulated as such. Are elephants said to be mammals? which is a better proposal. This provides a way of distinguishing between what the object "elephant" is and what the category ELEPHANT is, since there is nothing in the world that would have only the properties of the category ELEPHANT (being asked to draw an elephant does not tell which real elephant you should draw ). The abstraction of properties from objects in order to form categories is a cognitive operation and has to be treated as such. The meronomic Galois lattice is just the reverse of the taxonomic Galois lattice. The corresponding part-of graph of the kind-of graph of figure 1-bottom is just the reverse, top-down, graph. So, Figure 1-bottom can also be read as a part-of graph. Suppose that O1 is ELEPHANT having nails (p3), defenses (p5), but also having mammals (p1) and four legs (p2) as other ANIMALS which have fur (p4), such as O2-MONKEY with a long tail (p6) and O3-CAT with whiskers (p7). In figure 1-bottom, mammals (p1) and four legs (p2) are common parts of ELEPHANT (O1), MONKEY (O2) and CAT (O3), while fur (p4) is part of MONKEY (O2) and CAT (O3). All of the properties of a category are a subset of all of the properties of a subordinate category: all the parts of the description of MAMMAL (such as having a head, a body, mammals, and so on) are parts of the description of ELEPHANT, the reverse not being true (eg. has tusks). Thus, the meronomic relation is the part-of relation between descriptions, including descriptions of physical parts, while the partonomic relation is the part-of relation between physical parts From our knowledge, the Galois Lattice formalism has never been used to simulate how a given situation can be analyzed through categorization.

5 The Galois Lattice formalism provides a similarity measure. Consider figure 2. The top graph is the Galois Lattice of 3 objects, a cat and a dog that are pets, the dog being brought to the park as the book to be read. (top graph). In this situation, and only in this context, Dog is a kindof (feeding, pet) as CAT, but also a kind-of (topark) as BOOK. Similarity can be computed as the number of valued arcs to join two objects: 1 in the kind-of relation, 2 in the opposite direction. Thus DOG-CAT similarity value would be of 1, while the CAT-DOC similarity value would be of 2 (asymmetry). The DOG- BOOK (or the BOOK-DOG) similarity value would be of 3, while the CAT-BOOK similarity value would be of 5 (no-transitivity). Thus, DOG would be evaluated as more similar than CAT than CAT is similar to DOG. The same phenomenon occurs in the Russia-Cuba-Jamaica case: CUBA is more similar to RUSSIA than RUSSIA to CUBA. Figure 2: The Galois Lattice of 3 objects with properties (f: feature), a cat and a dog that are pets, the dog being brought to the park as the book to be read (top graph), and the Galois lattice of Russia Cuba - Jamaica case. (bottom graph). The cognitive flexibility of creating contextual categories is possible only if any of the properties can be used for categorization. This is why the reciprocal effect in the merononic relation is important in the contextual categorization theory: if X is a part of Y, then Y is a kind of X. This means than any property that belongs to the description of a category can be used to form a superordinate category. For instance, to bring to the park which is one of the properties of Mary s dog (figure 2, top) can be used if necessary to form a category; for instance the category of the things Mary takes along to the Park. The cognitive flexibility underlying contextual categorization would be based on the meronomic reciprocal effect. The meronomic reciprocal effect appears to be a complex process when building a hierarchy of categories. Let s consider, to bring to the veterinarian as being a property of Mary s cat. Since the category things bring to the veterinarian is built, let s say by Mary s friend after Mary, - who is going to the park with her dog and book-, said I will also bring the cat to the veterinarian, a hierarchy of categories is to be built with to bring to the park a property of the Mary s dog and book and with to bring outside the house that is a property of Mary s cat, dog and book. Building the hierarchy of categories for a set of objects in a given context is to find the shared and unshared properties with lines of properties [12]: to bring to the park and to bring to the veterinarian are values of to bring outside the house, the reverse being not true. If people do make contextual hierarchies of categories, they should agree that if p i is a property of category C i, then C i is a kind-of category Cp i and if p jj is a property of category Cp i, then Cp i is a kind-of category Cp ij and so on. They also should disagree that p i is a part-of the description of Cp ij (we don t know). We report below experiments we run in order to check if the reciprocal effect in hierarchy of categories is a human ability. If so, results would indicate that people could make categories, and categories of categories, from features.

6 4 Testing the reciprocal effect of categorization For two categories X (e.g. elephant) and Y (e.g. Animal) testing an X-to-Y reciprocal effect is a three parts question: 1. Does X is kind-of Y imply Y is part-of X? 2. Does Y is part-of X imply X is kind-of Y? 3. Does Y is kind-of X imply X is part-of Y? 4. Does X is part-of Y imply Y is kind-of X? A kind-of-to-part-of oriented reciprocal effect can be observed (figure 3): - If X kind-of Y implies Y part-of X while X partof Y is not observed and when Y part-of X implies X kind-of Y while Y kind-of X is not observed, or - If Y kind-of X implies X part-of Y while Y partof X is not observed and when X part-of Y implies Y kind-of X while X kind-of Y is not observed. Note that there is usually a high degree of variability and instability in category representations, in tasks of both property generation and judgment of typicality (Barsalou, 1989). There was no significant difference between taxonomy and meronomy and between the two orders of presentation (X-to-Y vs. Y-to-X). In contrast, the predicted interaction, (taxonomy vs. meronomy) x (X-to-Y vs. Y-to-X), was found across all experiments (Table 1). Table 1: The reciprocal effect was found across the whole set of experiments both for categories (top table) and for parts (bottom table): no X-to- Y order effect, no difference between kind-of and part-of relations, but a strong order-relation interaction effect. (X-to-Y vs Y-to-X) parrot bird animal living being cacatoes 0.3 (p=.6) 0.1 (p=.81) (p=.74) parrot 0 2 (p=.16) 1 (p=.32) bird 0.1 (p=.79) 1.4 (p=.24) animal 0.1 (p=.77) oack tree plant natural thing cork oack 0.9 (p=.76) 0.1 (p=.75) 0.26 (p=.61) 0.1 (p=.79) oack 11.1 (p=.002) 0.7 (p=.4) 0.1 (p=.79) tree 1.5 (p=.22) 0 plant 0 (Taxonomy vs Meronomy) parrot bird animal living being cacatoes 1.4 (p=.25) 2.6 (p=.12) 1.4 (p=.25) 0.9 (p=.36) parrot (p=.74) 0.1 (p=.71) bird 0.6 (p=.43) 0 animal 0.12 (p=.73) oack tree plant natural thing cork oack 0.4 (p=.53) 0.1 (p=.73) 2.4 (p=.13) 2.9 (p=.1) oack 6.2 (p=.02) 0.1 (p=.77) 1 (p=.32) tree 0.4 (p=.56) 4.6 (p=.04) plant 0 (Taxonomy vs Meronomy) x (X-to-Y vs Y-to-X) parrot bird animal living being cacatoes 48.9 (p<.0001) 54.9 (p<.0001) 48.9 (p<.0001) 81.9 (p<.0001) parrot (p<.0001) 79.1 (p<.0001) (p<.0001) bird 37.1 (p<.0001) 57.8 (p<.0001) animal (p<.0001) oack tree plant natural thing cork oack 12.7 (p<.001) (p<.0001) 14.4 (p<.005) 57.8 (p<.0001) oack (p<.0001) 18.8 (p<.0001) 81.0 (p<.0001) tree 3.1 (p<.08) 99.3 (p<.0001) plant 57.8 (p<.0001) Figure 3: Expected data from the reciprocal effect of categorization: if Y is a kind of X (high YES score), then X is not a kind of Y (low YES score), X is a part of Y (high YES score) and Y is not a part of X (low YES score). Running four experiments, with forty participants for each experiment, we tested the reciprocal effect of categorization using animals and plants (experiment 1), parts of animals and parts of plants (experiment 2), verbs of displacement (experiment 3), and the set of verbs of mental activities used by [13, 14] and verbs provided by [4] (experiment 4). (X-to-Y vs Y-to-X) feather wing bird's body bird feather's point 0.8 (p=.37) 2.8 (p=.1) 1.3 (p=.27) 6.3 (p=.017) feather 1 (p=.34) 3 (p=.09) 1.4 (p=.25) wing 0.2 (p=.66) 0.2 (p=.63) bird's body 9.6 (p=.004) leaf branch tree forest leaf nerve 1.3 (p=.3) (p=.1) 3 (p=.1) leaf 0.8 (p=.4) 0.1 (p=.8) 2.7 (p=.1) branch 3.9 (p=.1) 7.3 (p=.01) tree 18.8 (p=.0001) (Partonomy vstaxonomy) feather wing bird's body bird feather's point 0.3 (p=.6) 0.6 (p=.44) 3.2 (p=.08) 2.5 (p=.12) feather 1.3 (p=.26) 4.8 (p=.04) 9.6 (p=.004) wing 7.5 (p=.009) 3.2 (p=.08) bird's body 5.3 (p=.03) leaf branch tree forest leaf nerve 0.3 (p=.6) 2.3 (p=.1) 4.9 (p=.03) 0.7 (p=.4) leaf 0.8 (p=.4) 6.8 (p=.01) 0.1 (p=.8) branch 0.5 (p=.47) 1.3 (p=.26) tree 0.1 (p=.8) (Partonomy vstaxonomy) x (X-to-Y vs Y-to-X) feather wing bird's body bird feather's point 4.2 (p<.05) 1.7 (p=.20) 7.3 (p<.01) 4.5 (p<.05) feather 32.7 (p<.0001) 10.7 (p<.003) 16.0 (p<.0003) wing 14.7 (p<.0005) 7.3 (p<.01) bird's body 3.4 (p<.07) leaf branch tree forest leaf nerve.98 (p=.33) 1.0 (p=.31).89 (p=.35) 23.8 (p<.0001) leaf 0.08 (p=.77) 18.8 (p<.0001) 20.0 (p<.0001) branch 21.8 (p<.0001) 39.9 (p<.0001) tree 35.0 (p<.0001)

7 Unlike Rips and Conrad, we argue that "MAMMAL is part of ELEPHANT", which is to say that all the description of mammals is a part of the description of elephant. Furthermore, any part of the description of a category can be used to form a superordinate category. This is a reciprocal effect we found with people in our experiments. Our view is to distinguish between words and the categories denoted by words, and between category extension and intension. For instance, [4] write "The entailment relation between nouns must be strictly distinguished from the meronymic relation, which is always independent of, and never included in, the hyponymic relation "a leaf is a part of tree" but it is not the case that "a leaf is a kind of tree." (p.569). First, a "noun" entails nothing per se, but what it refers to, may entail something. The noun "leaf" doesn't entail "is a part of tree" per se. It is a for a certain person, in a certain context that the noun "leaf" will evoke something that is a part of a tree (for instance, in a sentence like "the wind blows the leaves") or will not evoke something that is a part of a tree ("the wind blows the dead leaves"). Second, the "something" which is designated by the word "leaf" may not be an object but a category: "leaf" may refer to "any oak leaf" ("that leaf... is missing from my collection of leaves"). Like [2, 3] and others [7], we think that categories are constructed on line, as ad hoc categories, but also as contextual categories in which real objects can be instantiated in the context of a situation ("look at that leaf"), or of a representation ("the dead leaves of autumn. A. Rimbaud). Thus, if people are able to built hierarchies of categories from properties of objects of the current situation, doing so, they find the right dimensions along which objects can be compared, which means having a description that put the objects in relation. This is a way to solve the problem of dimensions identification for computing similarity. 5 The reciprocal effect of categorization: a key to similarity Similarity judgment is dependent on context [9, 17] and categories are very sensitive to context [15]. This is the case because properties used for similarity or for categorization will be dependent on context. For instance, in the two easily comprehensible sentences "to move the pieces of furniture" and "to polish furniture", furniture does not have the same set of properties and subsequently the same extension: ''made of wood'' would be restricting the furniture to be polished. Taking into account the context is to compute similarity and categorization within the context. For categorization, it is a new approach to consider that categories are built on line within the context, each object being categorized in the context of the other objects. This is different from Barsalou s ad hoc categories (objects are grouped because they participate to an agent s goal). In the contextual categorization theory, objects of the situation at hand are put in relation, grouped and differentiated in a hierarchy of categories. The goal intervenes to filter among properties and objects. The cognitive reciprocal effect means that people can build up categories from parts of the description of the object at hand. This process of extracting properties to build up categories of actual objects and a hierarchy of categories is what we think to be the basic cognitive mechanism of contextual categorization. Contextual categorization approach differs from the classical view that limits categories as being long-term memory entities that intervene to recognize and identify the objects at hand. In the contextual categorization view, categories in memory, dictionaries categories (cats are animals) as well as empirical categories (cats in the garden are Mary s cats) are mixed with contextual properties (to hear mewings) to build up a hierarchy of categories. Thus the contextual categorization theory is mainly a theory about understanding, thinking and reasoning (these are mewings of cats, these are mewings of Mary s cats, these are mewings of Mary s cats because they are hungry, ). What s about similarity? Computing similarity is often processed by starting considering all is known about the objects to be compared, then to decide if yes or no these objects can be put in a same category. More precisely, knowing the category of X, the problem is to decide if Y can be put in the category of X. If such decision-making can be done, then procedures that are applied to X could be adapted to Y.

8 Considering the context is to add the other objects of the current situation in the comparison process. Categorizing the objects using the properties they share and the properties that differentiate the objects limits the number of properties. A number that can be reduce by the goal at hand. Then, similarity merges from the hierarchy of categories. In addition, for a same person, a same object can belong to different dictionary or empirical categories: 0 can be a digit or a letter; - can be minus or a dash. This is the reason why we advocate for a clear distinction between objects in the physical world and the categories used to represent them. And this is why context is important: it helps to state what kind of things the object is while the reciprocal effect helps to take some parts of the description to build categories. Finally, we suggest also that context and contextual categorization are providers of properties. For instance, through the categorization process, two objects that are different from each other could be put together in a same category because they differ from all the other objects that share some properties. For instance, in the set of 9 objects made of 1 A, b, 9, 2, ), K, L,*, although ) and * are very dissimilar, they can be categorized as being different of the others alphanumerical objects. The context determines categorization and categorization determines similarity, not the reverse. References [1] M. Barbut & B. Monjardet (1970). Ordre et classification: algèbre et combinatoire. Paris: Hachette. [2] L.W. Barsalou (1983). Ad hoc categories. Memory and Cognition, 11, [3] L.W. Barsalou (1989). Intraconcept similarity and its implications for interconcept similarity. In S. Vosniadou, & A. Ortony (Eds.) Similarity and Analogical Reasoning. New York: Cambridge University Press (pp ) [4] C. Fellbaum & G.A. Miller (1989). Folk Psychology or semantic entailment. Psychological Review, 97, [5] R.L. Goldstone (1994). The role of similarity in categorization: providing a groundwork. Cognition, 52, [6] R.L. Goldstone & J. Son. (2005). Similarity. In K. Holyoak & R. Morrison (Eds.). Cambridge Handbook of Thinking and Reasoning. Cambridge: Cambridge University Press. (pp ). [7] G. Lakoff (1986). Women, fire and dangerous things: What categories tell us about the nature of thought. Chicago: University of Chicago Press. [8] D.L. Medin (1989). Concepts and conceptual structure. American Psychologist. 44, [9] D.L. Medin, R.L. Golstone & D. Gentner (1993). Respects for similarity. Psychological Review, 100, [10] R.M. Nosofsky (1986). Attention, similarity, and the identificationcategorization relationship. Journal of Experimental Psychology: General, 115, [11] S. Poitrenaud (1995). The Procope Semantic Network: an alternative to action grammars. International. Journal of Human- Computer Studies, 42, [12] S. Poitrenaud, J.-F. Richard & C. Tijus. (2005). Properties, categories and categorization. Thinking and Reasoning, 11, [13] L.J. Rips & Collins, A. (1993). Categories and resemblance. Journal of Experimental Psychology: General, 122, [14] L.J. Rips & F.G. Conrad (1989). Folk Psychology of Mental Activities. Psychological Review, 96, [15] C. Tijus (2001). Contextual Categorization and Cognitive Phenomena, in V. Akman, P. Bouquet, R. Thomason, & R. A. Young, Modeling and Using Context. Berlin: Springer-Verlag, pp [17] A. Tversky (1977). Features of similarity. Psychological Review, 84,