Abundantia Verborum

5. Workshops and cognitive linguistics

5.2 Workshops

5.2.2 The label mechanism as a formal approach

In the current section, which reopens the topic of section 5.1.2 Formal approaches and cognitive linguistics, we will claim that the label mechanism in Abundantia Verborum is an appropriate formalism for representing concepts at the intensional level in a non-classical framework.

fuzzy sets of label sets

Table 1 below roughly is a copy of table 1 in 5.1.2 Formal approaches and cognitive linguistics. The most important difference is that the intensional non-classical field contains "fuzzy sets of label sets".

In the closing lines of 5.1.2 Formal approaches and cognitive linguistics, we argued that in Abundantia Verborum, a tool for analysis rather than for modeling, and moreover a tool that does not want to impose the use of theory dependent machinery, descriptive adequacy is more important than explanatory adequacy (if the reader permits us to use these not quite theory neutral terms). Put simply, let the program describe and the researcher explain, and let the theory-neutral description be detailed enough so that explanation within the framework in which the linguist works is possible. Moreover, to make the description as clear and straightforward as possible, minimal sufficient expressive power is desired, by which we mean that superfluous machinery should be excluded. We now argue that all that needs to be added to the classical intensional representation for achieving descriptive adequacy is the notion "fuzzy".

If in table 1 the intensional non-classical field is filled in on the basis of analogy with the shift at the extensional level, a completely analogous shift renders "fuzzy feature sets". The situation in Abundantia Verborum differs from that 'simplest solution' in three points:

• The more neutral term label replaces the term feature. The former is preferable because the term "feature" sometimes is taken to refer exclusively to 'innate primitive information units that are part of the language module', and we want the broader sense of 'atomic pieces of information, representing either linguistic or other knowledge'
• Rather than fuzzy sets of labels, fuzzy sets of sets of labels are used. The use of fuzzy sets of labels would mean that each label is assigned a weight, a real number value between zero and one, that represents its importance for the concept to be applicable. But this would not allow for labels to influence each other's importance. And Cohen and Murphy 1984 illustrate the possibility of such correlations, be it in a psychological rather than in a linguistics context. Translated to our terminology their example would be that for the concept MAN, in the sense of male specimen of the human kind, the weight of the label "bald" would depend on whether the label "old" is also present or the label "young". Such correlations can simply not be described with fuzzy label sets. The problem is overcome if weights are not assigned to isolated labels but to labels sets, so that {bald, old} and {bald, young} can be assigned different weights. This is not a modification, but rather a proper extension of using sets of fuzzy labels, because the case of independent labels is still expressible, and identifiable through statistical calculation.
• The third point in a sense is a disambiguation rather that a modification: weights receive a frequency interpretation. Given the affinity of Abundantia Verborum with corpus-based empirical research, it is straightforward, from the perspective of the program, that the weight of a label set X, subset of the set Y of all labels of some type (say, all semantic labels), is identified with the (relative) number of observations that are assigned all labels of X and are assigned no other labels of Y. But if we want to make the link with cognitive linguistics, the weight of our formalism would have to correspond to the notion of "centrality" as explained in 5.1.3 Representational formats in cognitive linguistics, and as we saw there frequency is only one, not even the most common, instantiation of "centrality". Other instantiations are degree of prominence in the mental representation of a concept, and degree of logical centrality in the semasiological profile. We will come back to the consequences of this difference below, and once more in section 5.2.3 Graphs as representational formats.

prototypicality effects

Can this formalism represent prototypicality effects? Since we are working on the intensional level, let us recall what we, on the basis of Geeraerts 1989a, mentioned as intensional prototypicality effects in 5.1.1 The broader field. We mentioned two phenomena:

• intensional non-rigidity: no conjunction of atomic criteria can adequately function as condition for applicability of the concept
• intensional non-equality: rather than meeting a common condition the referents to which the concept is applicable partially resemble each other, forming chains of family resemblance; some of these referents have more of the features that take part in the family resemblance than others.

For two reasons this perspective to non-classical phenomena cannot be applied directly to our case study:

• A first reason is that the above description refers to the semantics of concepts, whereas in the case study the semantics of lexical items is described. So we'll have to speak of lexical items instead of concepts.
• A second reason is that, as explained in 5.1.4 The case study "vers", the description in our case study adopts a slightly different perspective on "meaning" than the one underlying the above formulations. Rather than describing semantics in terms of "conditions for applicability of a lexical item" (which we feel to be a relict of the classical ambition to apply a mathematical definitions style of description to natural language), we describe the semantic specification of a lexical item in terms of "the information contributed to the overall message by the lexical item" (which we feel to be a less artificial form of description).

There is an important pitfall lurking if we would simply reformulate the description of prototypicality effects on the basis of these modifications. More in particular, the first of the two modifications is far from trivial. As was already touched upon in 5.1.3 Representational format in cognitive linguistics, there doesn't have to be an isomorphic relation between concepts and lexical items. At the semasiological level such isomorphism is violated whenever a lexical item may refer to what we intuitively feel to be different concepts. We'll come back to this complication in 5.2.3 Graphs as representational formats. For now, let us simplify matters and only look at lexical items the semasiological profile of which does corresponds to one concept (i.e. that is monosemous). For these cases we can now describe prototypicality effects as follows:

• intensional non-rigidity: no conjunction of atomic units of information can adequately function as semantic specification of a lexical item, i.e. as specification of the information contributed by the lexical item to the general message of the utterance in which it appears
• intensional non-equality: rather than being identical in each observation, the most adequate semantic specifications of a lexical item in different observations just resemble each other, forming chains of family resemblance; some of these specifications contain more atomic units of information that take part in the family resemblance than others.

If we now identify atomic units of information with labels and further identify the weight of a label set with the relative frequency of the cases where the semantic specification of the lexical item is exactly this label set, we have a straightforward way to represent both classical structures and prototypicality effects with the formalism of "fuzzy sets of label sets". A monosemous lexical item has a rigid semasiological profile if, considering the set of semantic labels, one label set has weight one and all others have weight zero. In all other cases the profile is non-rigid. A monosemous lexical item is has an equal semasiological profile if, considering the set of semantic labels, all label set with a weight higher than zero have an identical weight. In all other cases the profile is non-equal. We postpone the discussion of the general case, including polysemous lexical items, until section 5.2.3 Graphs as representational formats. The reason for this is that, in the general case, we will describe how to use graphical techniques to detect non-classical phenomena, translating prototypicality effects to features of Abundantia Verborum graphs.

the nature of the representations

Now that we have laid the basis for a representation of semasiological profiles in Abundantia Verborum, we would like to make a few remarks about the nature of the representation, before we move to the illustration of how to work with it in 5.2.3 Graphs as representational formats. The formalism is a tool for representing enriched language data in such a way that it is easy for the user of the program to detect system and irregularity in the global picture that emerges from the pool of data. To take the example of the "vers" case study, what the program can show after all individual observations have been assigned semantics labels, is how a multitude of local interpretations by a subject add up to a global picture that can then serve as the basis for the linguist to try and construct a theory-dependent model of the semasiological profile. The question whether the resulting model will be psychologically or linguistically plausible or adequate will depend on the decisions by the linguist, not on calculations the program. All the program does is give fast access to descriptive quantitative data so that the linguist can take this information into account. Answers to questions such as whether the resulting model will be psychologically and linguistically plausible can, by lack of theory-dependent primitives in the formalism, not even be expressed directly in the formalism, let alone that one could expect the program to automatically derive these answers from the data. In summary, by the nature of the formalism its representations are not adequate within any cognitive linguistic or psychological framework, because they are outside of these frameworks and still demand for an extra translation step to such a framework. This is the linguist's responsibility.

This does not mean that theory-dependent models cannot be expressed in Abundantia Verborum. For instance, although we use a description of schemata in the schema group that does not directly rely upon any particular theory, nothing would prevent us from using any theory-dependent representational format that can be expressed with the symbols that are on a keyboard. But these, from the perspective of the program, are not part of its formal representations, because their internal structure is completely isolated from the building blocks of the "fuzzy sets of label sets" formalism.