<?xml version="1.0" standalone="yes"?>
<Paper uid="W98-1225">
  <Title>I Natural Language Concept Analysis</Title>
  <Section position="4" start_page="0" end_page="0" type="metho">
    <SectionTitle>
2 A supporting theory
</SectionTitle>
    <Paragraph position="0"> Natural language modelling usually assumes some form of hierarchical structure as given. Experience shows that practical application of such an approach to a non-trivial subset of the language can be a highly complex task (Aarts, 1991). In our search for a more flexible basis we arrived at the question: How does phrase and clause structure emerge in natural language? It appeared that this question is related to a more general one: How can knowledge about real world be structured? We found a philosophical background in C.S.</Paragraph>
    <Paragraph position="1"> Peirce's pragmatism (Peirce, 1931) and a mathematical formalisation of Peirce's ideas in R. Wille's theory on Formal Concept Analysis (FCA) Wille, 1982). Relatedness, for example, relies on Peirce's epistemological argument saying that &amp;quot;... there is no judgment of pure observation without reasoning ' (Houser and Kloesel, 1992). This means that an observation is always tied to &amp;quot;judgment&amp;quot;; in other words, in our case, observation of an object always implies the presence of an attribute, and some interpretation of their relation.</Paragraph>
    <Paragraph position="2"> In the FCA framework, observable world is described by a binary relation between the sets of objects and attributes. These sets give a dichotomous characterisation of observable entities, and together with their relation formalise Peirce's universal categories: firstness, secondness and thirdness. These are defined as follows: &amp;quot;The first is that whose behag is simply in itself, not referring to anything nor lying behind anything. The second is that which is what it is by force of something to which it is second. The third is that which is what it is owing to things between which it mediates and which it brings into relation to each other&amp;quot; (Houser and Kloesel, 1992). For the time being we adopt the interpretation of Lehmann and Wille (Lehmann and Wille, 1995) who state that &amp;quot;the object g is a \[f\]irst ... to which the attribute m is a \[s\]econd...&amp;quot;. According to Lehmann and Wille, this interpretation is compatible with Peirce's general understanding of firstness and secondness.</Paragraph>
    <Paragraph position="3"> In FCA, observations, or concepts, are mathematically formalised. Traditionally, the philosophical notion of a concept is determined by its extension and its intension. The extension consists of all elements (set of objects) belonging to the concept while the intension covers all properties (set of attributes) valid for all those elements.</Paragraph>
    <Paragraph position="4"> In the mathematical model, the triple consisting of the sets, objects (G; Gegenst~tnde) and attributes (M; Merkmale), and the relation between them (R), is called the context (we assume that G and M are finite sets). We say, for g E G, m E M, (g, m) E R or equivalently, (gRin), iff the object g has the attribute m.</Paragraph>
    <Paragraph position="5"> For a context the following mappings are defined: A' = {m e M I gRrn for all g e A} for A C_ G; and B' = {ge G I gRrnforallme B} forB C M.</Paragraph>
    <Paragraph position="6"> A (formal) concept of a context (G, M, R) is a pair (A,B) with A C G, B C M, which satisfies the conditions (i) A' = B and (ii) A = B'.</Paragraph>
    <Paragraph position="7"> Informally, A ~ is calculated from A by considering the elements of A and accumulating the properties common to them all. B' is calculated dually. We say (A, B) is a concept if, by the above calculation, A and B mutually determine each other.</Paragraph>
    <Paragraph position="8"> For any concepts (A1,Bt) and (A2,B2) of a con- null tex~ the hierarchy of concepts is captured by the definition: (A1,B1) &lt; (A2,B2) iffA1 C A2 (or equivalently, iff B1 _D B2). When the above order relation holds, (A1,A~) is called the subconcept of (A2, A~), and (Ae,A'~) the superconcept of (A1,A'I). The set of all concepts of a context with this order relation is called the concept lattice.</Paragraph>
  </Section>
  <Section position="5" start_page="0" end_page="0" type="metho">
    <SectionTitle>
3 Linguistic relations
</SectionTitle>
    <Paragraph position="0"> NLCA applies Wille's theory to natural language by the equivalence: attributes are functors, and objects are arguments. Functor-argument relations, the manifestations of the (combinatorial) properties of lexical items, have various realizations on the linguistic level. For example, the verb-complement relation is not the same as the relation of modification. This becomes clear when we look at the optionality of modifiers. In English, we cannot say, on the basis of encountering a noun, that it needs an adjectival modifier; however, when we encounter an adjective, we do know that at some level it needs a noun because it is a semantic predicate (functor) taking an argument of which it is predicated. In this case, then, there is an asymmetrical relation between functor and argument. On the other hand, the relation between a verb and its complementation is a symmetrical one.</Paragraph>
    <Paragraph position="1"> In NLCA, we distinguish between two kinds of relations: major and minor. These types of relations can be recursively nested, and their sum uniquely characterises the input. The first type of relation, the major relation, or predication, is a pair (p,a), where a functions as an argument to the predicate p. A major relation may involve the distinction between an action/state and its participants (symmetrical relation: each requires the presence of the other) and between an action/state or participant on the one hand and its properties on the other (asymmetrical relation, or modification: the predicate requires the argument of which it is predicated, but the reverse does not hold). We call predicates of the first type major predicates, and predicates of the second type minor predicates.</Paragraph>
    <Paragraph position="2"> It is interesting to note that this distinction reflects the difference between constituency on the one hand, and dependency on the other. In linguistics, these two relations are often treated as (formally) equivalent alternatives. ~ In the current view, they entail a difference in status of the units that are involved in the relation. The nature of the relation in both cases is that of predication; however, in the 1However, see (Fraser, 1996) for some qualifying remarks on this topic.</Paragraph>
    <Paragraph position="3"> constituency case each part assumes the presence of the other, whereas in the dependency case, the predicate is optional.</Paragraph>
    <Paragraph position="4"> There are Various distinguishing factors between major and minor predicates. In English, major predicates (usually) relate to the noun-verb division; minor predicates do not. Major predicates are typically realized by verbs; minor predicates by adjectives and adverbs. There is never more than one major predicate associated with an argument; there may be several minor predicates related to the same argument.</Paragraph>
    <Paragraph position="5"> (This reflects the possibility of having zero or more modifiers of an action or participant.) Both major and minor predicates can provide semantic roles, but major predicates introduce participant roles for their arguments; minor predicates can introduce additional roles (such as location or manner) or properties of their arguments.</Paragraph>
    <Paragraph position="6"> The second type of relation, the minor relation, or qualification, distinguishes between the core content of a linguistic expression and some qualification of it. At the level of an action and its participants, for example, this qualification may relate to referential status of NPs (e.g. definite vs. indefinite article), or to tense and aspect information at clause level.</Paragraph>
    <Paragraph position="7"> Intensifying adverbs (e.g. very, extremely, deeply) and comparative adverbs (e.g. more and most) also belong to the class of qualifiers. These examples suggest that qualification may also have a symmetrical and asymmetrical variant: article, tense, aspect etc.</Paragraph>
    <Paragraph position="8"> being of the first type, and intensifying and comparative adverbs of the second. However, this is still an object of further study. In this paper we will restrict ourselves to the distinction between qualifier and core in general.</Paragraph>
    <Paragraph position="9"> The difference between a minor predicate and a qualifier is that the latter does not introduce a meaning that is independent of the element it qualifies. 2 The presence of a qualifier of a specific type, therefore, also signals the presence of its counterpart. Furthermore, there can be several modifiers associated with an argument or predicate; typically, however, there will only be a single (possibly composite) quali~er. In the case of referential information, for instance, the qualifier situates the argument or predicate in its referential context of which there will only be one. In some cases different aspects of the 2By contrast, a minor predicate has some aspect of meaning that is independent of the element it combines with. This is illustrated by the fact that minor predicates can be used in different contexts. For example, a prepositional phrase can modify an argument (e.g. noun) but also a predicate (e.g. verb). An adjective phrase can be used as a modifier of a noun, but also in the complemenration of a verb.</Paragraph>
    <Paragraph position="10"> Kamphuis and Sarbo 207 Natural Language Concept Analysis qualifier can be expressed separately (such as tense and aspect); in that case these different aspects must be unifiable but there cannot be more than a single qualifier relating to the same domain.</Paragraph>
    <Paragraph position="11"> The qualifier evokes its COUnterpart; nevertheless, the semantic 'core' is also complete in itself, in that it forms a full account of semantic relationships.</Paragraph>
    <Paragraph position="12"> Therefore it does not require realization of the qualifier as such: cf. the use of such bare relations in captions or telegram style speech (e.g. &amp;quot;Lion attacked woman.t&amp;quot; ).</Paragraph>
    <Paragraph position="13"> Summing up, we distinguish between the following relations:  * major predication * minor predication * qualification.</Paragraph>
    <Paragraph position="14">  A schematic representation of these possibilities is given in Fig. 1.</Paragraph>
    <Paragraph position="15">  It is important to note that this diagram does not represent the hierarchical structure of sentences, or the organisation of conceptual content within the sentence (we will come back to this below); it merely shows the different types of relations that our approach identifies. These relations lie at the heart of structure formation in NL. How phrase structure emerges as a result of their interaction is explained in Sect. 6.</Paragraph>
    <Paragraph position="16"> As mentioned, the different relations can be recursively nested. For example, at the level of argument, a modifying predicate may be added in the form of an adjective phrase, or a qualifier may be present in the form of a determiner. Each element that is added stands in a certain relation to its counterpart, based on the type of relation that was applied.</Paragraph>
    <Paragraph position="17"> There is a potential mapping between the linguistic relations displayed in Fig. 1 and the hierarchical organisation of information structure. For example, it is likely that the major predication relation is the most important information carrier with respect to the semantic content of the sentence, and that the minor predication relation reflects additional information of less importance. This illustrates the relative contribution of the different linguistic relations to information content. In information retrieval this could help to generate a concise representation of retrieved text. It would also be in line with the use, already mentioned, of the major predication relation in captions or telegram style speech; furthermore, it could be a possible explanation for the ability of speed-reading that readers may develop.</Paragraph>
    <Paragraph position="18"> The qualification gives concrete reference to all the items involved in the predication relation, and as such is relevant for all levels. The presence of the qualifier at all levels of representation is a matter of some importance: word order, for instance, may also be classified as part of the qualification relation (e.g. in English, word order is relevant for identifyhag questions, and also in assigning thematic roles to participants). The relationship between qualifiers in NLCA, and operators in the semantically based hierarchy of Role and Reference Grammar (Van Volin~ 1993) would be a potentially useful area to investigate. null</Paragraph>
  </Section>
  <Section position="6" start_page="0" end_page="0" type="metho">
    <SectionTitle>
4 A first sketch of the model
</SectionTitle>
    <Paragraph position="0"> The distinctions made above have been incorporated into the NLCA-model on the basis of the abstraction of FCA: the context. In the dyadic model of FCA, a context allows only two kinds of entities: object and attribute. Therefore, each lexical item has:to be classifted as one these, based on its lexical type. Typical objects are nouns; typical attributes are verbs (major predicates), and adjectives and adverbs (minor predicates). We refer to these attributes uniformly as major attributes (involving predication). Qualifiers are classified as attributes, as well. We call them minor attributes (involving qualification).</Paragraph>
    <Paragraph position="1"> A comment with respect to the classification of lexical items and its relation to Peirce's universal categories is in place. We mentioned that objects and attributes formalise the categories firstness and secondiaess. Each item of these classes may evoke a different relation (called interpretant) depending on the item's syntactic and semantic properties, and in general, the properties of the item as a sign (Liszka, 1996)..In NLCA these interpretants are instantiations of the linguistic relations formalising the category of thirdness. For example, the interpretant</Paragraph>
    <Paragraph position="3"> created by a verb, an instance of a major predication, may 'explain' how that verb binds its arguments together '~in a bundle of interlocking relationships&amp;quot; (Sowa, 1996).</Paragraph>
    <Paragraph position="4"> The surjective mapping from lexical types to the sets of the dyadic model can be defined without causing confusion. The set of lexical types defines a partition of L, the set of lexical items and semantic roles involved in the analysis, which is further partitioned according to the dyadic model, yielding the sets G and M. From G C_ L and M C L follows that there is an embedding of the relation R C G x M in L x L.</Paragraph>
    <Paragraph position="5"> This means that any pair (g, m) E R can be defined as the unique yield of 11 and l~ (ll, 12 E L) by the assignments ll ~ g and 12 ~-r m, where ~ respects the mapping of lexical types.</Paragraph>
    <Paragraph position="6"> As said above, each lexical item is classified according to its type. Furthermore, with each lexical item is associated a number of positions for internal and external arguments, denoted as suffixes, int and _ext, respectively, z Internal arguments contain information regarding the item itself. External arguments relate to combinatorial demands to make a complex linguistic unit, according to the linguistic relations described above. We say the input is well-formed if the combinatorial demands of each lexical item are satisfied.</Paragraph>
    <Paragraph position="7"> The internal argument positions are filled (i.e. assigned) by modifiers and qualifiers, which refer to distinct domains of analysis. For each domain holds that when an argument position is filled by more than a single element, these different elements have to be compatible (possibly depending on the context). For example, with multiple modifiers, e.g. two or more adjectives modifying a noun, the modifiers have to be semantically compatible in order to make a sensible construct: cf. the tall happy girl vs. ?the tall short girl.</Paragraph>
    <Paragraph position="8"> The external arguments of a verb (major predicate) are determined by the verb's valency: the sub-ject is also an external argument. These external arguments are involved in a symmetrical relation: an object fills the external argument position of an attribute, and vice versa, the attribute fills the external argument position of that object.</Paragraph>
    <Paragraph position="9"> The external argument of a modifier (minor predicate) is involved in an asymmetrical relation: an object fills the external argument position of an attribute, and the attribute fills the (modifier) internal argument position of that object.</Paragraph>
    <Paragraph position="10"> The qualifier-domain of the internal argument Sin procedural terms, argument position and argument correspond to formal and actual parameter, respectively.</Paragraph>
    <Paragraph position="11"> contains specific information that relates to the type of lexical item. For nouns, it is information regarding reference: specific/generic/unique reference; number. For verbs, it is information regarding finiteness/tense/aspect, etc. Thus, when the qualifier-domain of the internal argument of both the object and the major attribute is filled, there is explicit reference with respect to the action and the participants involved. Since qualifiers contain a specific type of information, they can be regarded as a syntactic pointer to the qualified element itself: if this domain of the internal argument is filled, there must also be an object/attribute of the type that the internal argument belongs to. In case the qualifier precedes its argument, this feature is reflected in the computational model by introducing placeholders, called Proto-items (cf. Sect. 6). Proto-items can only be introduced by qualifiers. When the argument of the qualifier is found, it replaces the Proto-item and fills the external argument position of that qualifier. The relations that the Proto-item is involved in are inherited by that argument.</Paragraph>
    <Paragraph position="12"> Besides these relations, NLCA applies a set of general principles, like word order (e.g. SVO), inheritance of relation and 'greedy' binding of lexical items. By the latter principle, the input string, forming the context of each lexical item, is evaluated from the perspective of that item and its needs: functors take the textually nearest arguments available, and vice versa. In NLCA input is analysed from left to right.</Paragraph>
    <Paragraph position="13"> Summarising thus far, we have incorporated the following aspects in our model:</Paragraph>
    <Paragraph position="15"> qualifiers and modifiers the external argument positions are filled by elements that are involved in the predication relation. null</Paragraph>
  </Section>
  <Section position="7" start_page="0" end_page="0" type="metho">
    <SectionTitle>
5 Relation Matrix
</SectionTitle>
    <Paragraph position="0"> The analysis of examples in NLCA is represented in terms of a so-called Relation Matrix (RM). A Relation Matrix shows the relation between objects (represented in rows) and attributes (columns).</Paragraph>
    <Paragraph position="1"> Conform to our definition in Sect. 4, we say a Relation Matrix is well-formed if each external argument position of each attribute is filled (meaning that the Kamphuis and Sarbo 209 Natural Language Concept Analysis semantic roles of major predicates are realized and that all other combinatorial demands of attributes have been fulfilled) and each object is the external argument of some attribute. This implies that the input corresponding to a well-formed RM must consist of one or more clauses. In this paper we focus on the case that there is only a single clause* We represent a symmetrical relation by a pair of asymmetrical relations, and an asymmetrical relation by a directed relation, called a pointer (PTR).</Paragraph>
    <Paragraph position="2"> Technically, the value of a matrix element, RM\[i,j\], is a tuple encoding a Boolean variable and a set of PTRs.</Paragraph>
    <Paragraph position="3"> In the graphical representation the value of a Boolean variable is represented by a '+' (true) or the empty string (false). We may also use the notation '+i' referring to the ith true-value assignment. A PTR is depicted as a directed edge* Internal argument positions of objects and attributes are displayed to their left-hand side (there is one argument position for the qualifiers, and one for the modifiers); external argument positions to their right. Empty argument positions are omitted.</Paragraph>
    <Paragraph position="4"> If the external argument position of an object (attribute) is filled by an attribute (object), we assign true to the Boolean variable of the corresponding cell in the RM. These variables will be used for the representation of linguistic structure. The assignments can take place after the analysis is completed, or, in most cases, during the analysis.</Paragraph>
    <Paragraph position="5"> Attributes may have more than one external argument position, and each of these may be involved in a different relation. Therefore, we use the convention that external argument positions of verbs are displayed in separate columns. The relation of attributes and their external argument positions can be traced back in the Relation Matrix, however, in the examples, we do not graphically represent it.</Paragraph>
  </Section>
class="xml-element"></Paper>