Wiebke Petersen

A Set-Theoretical Approach for the Induction of Inheritance Hierarchies

An approach for the automatic construction of inheritance hierarchies is presented. It is based on the strict set-theoretical point of view in the mathematical theory of Formal Concept Analysis. The resulting hierarchies are concept lattices. An extension of the approach to the induction of nonmonotonic inheritance networks is also discussed. It turns out that the main ideas of Formal Concept Analysis, i. e. the formal context, the concept lattice and the set of implications, provide three dierent ways of looking at the data to be represented, each of which provides a dierent way to solve problems of knowledge representation.

Concept Composition in Frames: Focusing on Genitive Constructions

In this paper, we show how frames can be employed in the analysis of genitive constructions. We model the main approaches in the discussion about genitive constructions, i.e. the argument-only approach, the modifier-only approach and the split approach. Of these three, the split approach is modeled most naturally in frames. Thus, if frames are considered a cognitively adequate representation of concepts, our analysis supports the split approach to the interpretation of genitive constructions.

Conceptual Fingerprints: Lexical Decomposition by Means of Frames --- a Neuro-cognitive Model

Frames, i.e., recursive attribute-value structures, are a general format for the decomposition of lexical concepts. Attributes assign unique values to objects and thus describe functional relations. Concepts can be classified into four groups: sortal, individual, relational and functional concepts. The classification is reflected by different grammatical roles of the corresponding nouns. The paper aims at a cognitively adequate decomposition, particularly, of sortal concepts by means of frames. Using typed feature structures, an explicit formalism for the characterization of cognitive frames is developed. The frame model can be extended to account for typicality effects. Applying the paradigm of object-related neural synchronization, furthermore, a biologically motivated model for the cortical implementation of frames is developed. Cortically distributed synchronization patterns may be regarded as the fingerprints of concepts.

A Logical Approach to Data-Driven Classification

We present a flexible approach for extracting hierarchical classifications from data, which employs the logic of affirmative assertions. The basic observation is that each set of rules induced by the data canonically determines a classificational hierarchy. We give a characterization of how the chosen rule type affects the structure of the induced hierarchy. Moreover, we show how our approach is related to Formal Concept Analysis. The framework is then applied to the induction of hierarchical classifications from an amino acid database. Based on this example, the pros and cons of several types of hierarchies are discussed with respect to criteria such as compactness of representation, suitability for inference tasks, and intelligibility for the human user.

A Mathematical Analysis of Pāṇini&#8217s Śivasūtras

In Pānini’s grammar of Sanskrit one finds the Śivasūtras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pānini’s way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, which are, however, implicitly given in the way a language clusters its phonological inventory. The key idea is to link the graph of the Hasse-diagram of the set of natural classes closed under intersection to Śivasūtra-style representations of the classes. Moreover, the argument is so general that it allows one to decide for each set of sets whether it can be represented with Pānini’s method. Actually, Pānini had to modify the set of natural classes to define it by the Śivasūtras (the segment h plays a special role). We show that this modification was necessary and, in fact, the best possible modification. We discuss how every set of classes can be modified in such a way that it can be defined in a Śivasūtra-style representation.1

Inheritance-based models of the lexicon

A rapid and remarkable development took place within computational linguistics in the years immediately following the introduction of unification-based models of language, in particular Lexical Functional Grammar (LFG) and Generalized Phrase Structure Grammar (GPSG), which employ feature structures to represent linguistic information. By the end of the 1980s a consensus had emerged, according to which the lexicon, which pairs word forms with feature structures, constitutes the main repository of information in a language. Furthermore, hierarchical structuring had come to be viewed as an essential aspect or perhaps even the most salient characteristic of the lexicon (cf. Briscoe et al. 1993). GPSG, as conceived in Gazdar & Pullum (1982) and even in Gazdar et al. (1985), still largely represents the older, dichotomous view of the lexicon. Here major aspects of linguistic structure were encoded in syntactic rules, many of which later came to be regarded as stating the possible complement structures of verbs, i.e. lexical information. Later developments in the treatment of subcategorization are only alluded to in a footnote (cf. Gazdar et al. 1985: 107). While the question “How is a classification imposed on the content of the lexicon by the system of features” is raised (p. 13), the answer of GPSG does not explicitly model the hierarchical inheritance relations inherent in lexical classifications. Rather, these relations are captured in logical feature co-occurrence restrictions (FCRs) and feature specification defaults (FSDs), the latter of which, prophetically, are nonmonotonic. From the start the lexicalist orientation was prominent in LFG (cf. Bresnan 1982, therein Kaplan & Bresnan 1982) and reached a peak in the radical lexicalism of Karttunen (1986), which uses the framework of categorial grammar to shift the entirety of linguistic description to the lexicon. The move toward the lexicalist view was independent of hierarchical modelling, which emerged in other work. In particular, Flickinger (1987) pioneered the explicit description of relations between English verb classes in terms of inheritance hierarchies. On a separate front,

Why Chocolate Eggs Can Taste Old but Not Oval: A Frame-Theoretic Analysis of Inferential Evidentials

So-called phenomenon-based perception verbs such as ‘sound, taste (of)’, and ‘look (like)’ allow for a use in inferential evidential constructions of the type ‘The chocolate egg tastes old’. In this paper, we propose a frame-theoretic analysis of this use in which we pursue the question how well-formed inferential uses can be discriminated from awkward uses such as #‘The chocolate egg tastes oval’. We argue that object knowledge plays a central role in this respect and that this knowledge is ideally captured in frame representations in which object properties are easily translated into attributes such as TASTE, smell, age, and form. We represent the more general knowledge of the range and domain of the attributes in a type signature. In principle, an inference is recognized as admissible if the values of one attribute can be inferred from the values of another attribute. In the analysis, this kind of inferability is modeled as an inference structure defined on the type signature. The definitions of type signatures and inference structures enable us to establish two constraints which are sufficient to discriminate the admissible and inadmissible uses of phenomenon-based perception verbs in simple subject-verb-adjective constructions.

Linear Coding of Non-linear Hierarchies: Revitalization of an Ancient Classification Method

The article treats the problem of forcing entities into a linear order which could be more naturally organized in a non-linear hierarchy (e.g., books in a library, products in a warehouse or store, …). The key idea is to apply a technique for the linear coding of non-linear hierarchies which has been developed by the ancient grammarian Pāṇini for the concise representation of sound classes. The article introduces briefly Pāṇini’s technique and discusses a general theorem stating under which condition his technique can be applied.

On the Construction of Śivasūtras-Alphabets

In the present paper, a formalization of the technique used byPānini in his Śivasūtras for the denotation of soundclasses is given. Furthermore, a general notion ofŚivasūtras-alphabets and ofŚivasūtras-sortability is developed. The presented maintheorem poses three sufficient conditions for theŚivasūtras-sortability of sets of classes. Finally, theproblem of ordering sets of classes which are notŚivasūtras-sortable is tackled and an outlook on modernproblems which could be approached by Pānini technique isgiven.

How formal concept lattices solve a problem of ancient linguistics

In his grammar of ancient Sanskrit, Pāṅini represents the phonological classes as intervals of a list. This representation method and especially the actual list constructed by Pāṅini, which is called the Śivasūtras, earns universal admiration. The legend says that god Śiva revealed the Śivasūtras to Pāṅini in order to let him start developing his grammar of Sanskrit. A question still discussed is whether it is possible to shorten the Śivasūtras. In the course of this paper, I am going to prove that this question can be reduced to a question about the graph-theoretical form of a particular formal concept lattice. Furthermore, I show how the Śivasūtras can be reconstructed from Pāṅinis grammar.