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In order to introduce vagueness as a proper object of formal-mathematical modeling, Max Black [5] developed the notion of Other than classical logics constrained by the , consistency profiles allow mapping the transition from negative to positive predication to any degree. This enabled Black to provide a framework for the classification of predicates according to their vagueness and ambiguity. In other words: .

This article is a sequel to an article titled “A New Direction in AI – Toward a Computational Theory of Perceptions”, which appeared in the Spring 2001 issue of (volume 22, No. 1, 73–84). The concept of precisiated natural language (PNL) was briefly introduced in that article, and PNL was employed as a basis for computation with perceptions. In what follows, the conceptual structure of PNL is described in greater detail, and PNL’s role in knowledge representation, deduction, and concept definition is outlined and illustrated by examples. What should be understood is that PNL is in its initial stages of development and that the exposition that follows is an outline of the basic ideas that underlie PNL rather than a definitive theory.

The purpose of this paper is twofold. First, we discuss the various issues of linguistic approximation in the context of intelligent systems. Second, we address one of the approximation issues in particular, which seems to be somewhat neglected in the literature.

A key topic in the work of Burghard Rieger is the notion of meaning. To explore this notion, he and his collaborators developed a most sophisticated approach combining theoretical ideas and concepts of semiotics with empirical and numerical tools of computational linguistics (see [29] for a most recent comprehensive account). In the present contribution, relations of Rieger’s achievements to some issues of interest in the physics and philosophy of complex systems will be addressed.

We study a generalization of the models of semantic spaces introduced by Rieger. The focus will be on the following aspects. We show to what extent different choices of conceptual freedom leads to dramatically different behaviour. For instance, the linguistic differentiation process introduced by Rieger is highly dependent on the underlying metric space. Also, we introduce certain invariants that may be seen as leading to new approaches for identifying meaning and relevance. In particular, we study a normalized limiting process in Rieger’s original model that may help to identify certain key elements of corpora. Also, we show how sensitivities in defining associated measurements like dependency trees might be used to identify linguistic relevance.

This contribution gives an overview about different approaches to semantic spaces. It is not a exhaustive survey, but rather a personal view on different approaches which use metric spaces for the representation of meanings of linguistic units. The aim is to demonstrate the similarities of apparently different approaches and to inspire the generalisation of semantic spaces tailored to the representation of texts to arbitrary semiotic artefacts.

This chapter introduces a variant of the principle of compositionality in quantitative text semantics as an alternative to the bag-of-features approach. The variant includes effects of context-sensitive interpretation as well as processes of meaning constitution and change in the sense of usage-based semantics. Its starting point is a combination of semantic space modeling and text structure analysis. The principle is implemented by means of a hierarchical constraint satisfaction process which utilizes the notion of hierarchical text structure superimposed by graph-inducing coherence relations. The major contribution of the chapter is a conceptualization and formalization of the principle of compositionality in terms of semantic spaces which tackles some well known deficits of existing approaches. In particular this relates to the missing linguistic interpretability of statistical meaning representations.

Recent advances in the quantitative analysis of natural language call for a theoretical framework that explains, how these advances are possible. This helps to unify different approaches and algorithms in quantitative linguistics. We consider the linguistic tradition of structuralism as a basis for such a framework. In what follows, we focus on syntagmatic and paradigmatic relations and attempt to describe them in a coherent way. We present an abstract version of a (neo-)structuralist language model and show how already known algorithms fit into it. We also show how new algorithms can be derived from it. As has already been predicted by linguists like Firth and Harris, it is possible to construct a computational model of language based on linguistic structuralism and statistical mathematics. The model we propose specifically helps to explain fully unsupervised algorithms for natural language processing which are based on well known methods like co-occurrence measures and clustering.

This paper describes a first attempt to set up and test a basic synergeticlinguistic model of a syntactic subsystem in analogy to the existing models of lexical and morphological subsystems, which have been tested successfully. The modelling is based on selected syntactic units, properties, and interrelations, which are integrated into a common model structure. The empirical testing is performed on data from the “SUSANNE” corpus [15].

A special kind of analysis of the denotative structure of a text can be performed by partitioning the text in denotative units called [18]. The hreb, which was called so in honor of its discoverer, L. Hřebíček, is the set of all entities of a text referring to the same object in reality or the same object in the text. Up to now, the has been defined [10, 11, 12, 13, 14] as the set of sentences with common reference, allowing the sentence to belong to different hrebs. The coherence of the text can be measured using the affiliation of sentences to hrebs.