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New capabilitiesin geometric processing of symbolic information in intellectual systems

Keywords:

A.A. Eidlin - Post-graduate Student, Department “Kibernetika”, National Research Nuclear University MEPhI (Moscow)
E-mail: a.aidlin@gmail.com
A.V. Samsonovich - Ph.D. (Eng.), Professor, Department “Kibernetika”, National Research Nuclear University MEPhI (Moscow)
E-mail: alexei.samsonovich@gmail.com


Modern development of computational methods of information processing leads to the emergence of new approaches that use the principles of geometry and topology applied to symbolic information. In recent years, new methods of text processing based on vector spaces became popular, among which are semantic maps. A semantic map is understood here as a mapping from a set of symbolic representations characterized by a certain meanings (they are called here “chunks”: e.g., words or word senses) to locations in an abstract metric space that captures certain semantic aspects of representations. Examples of semantic maps include the “strong” maps based on dissimilarity metrics, such as those resulting from the latent semantic analysis (LSA), Topics, latent Dirichlet allocation (LDA), hyperspace analogy of language (HAL), Eigenwords, and related techniques, as well as “weak” maps, such as feature spaces and affective spaces, including Circumplex, EPA and PAD models, and maps derived from lexical graphs, with coordinates representing definite semantic features or contrasts, e.g., Sentic map or Antomap. To build a meaningful multi-dimensional semantic map, one needs to take into account requirements imposed by the metric of dissimilarity, that limit possibilities of geometric representation of the relationships between chunks, and vice versa. Therefore, one needs to define a measure of semantic dissimilarity for any two chunks that can be interpreted as distance with a direction.The next question refers to the notion of semantic space that provides an infrastructure for the map. In cognitive psychology and linguistics, there were many limited attempts to make the idea of semantic space mathematically precise. The state of the art in linguistics related to the semantic space idea is represented by LSA and its variations. Here, in contrast, we assume that it is possible to map any given set of chunks to points in a universal semantic space endowed with a metric that captures semantic relations among chunks. These relationsmay include dissimilarity and antonymy. The conflict between the former and the latter notions can be resolved in favor of either a strong or a weak semantic map. In the latter case, a map may tend to pull all synonyms together and all antonyms apart. The question of their unification remains open. A proposal to build a universal semantic cognitive map capable of accommodating all possible human knowledge implies a huge program for many generations to come. This work makes a small step toward the goal, showing how geometric representations of antonymy and synonymy, holonymy and hypernymycan be used toderive practically useful inferences. The authors are grateful to Dr. Galina V. Rybina, a Professor atthe National Research Nuclear University “MEPhI”, Moscow, Russian Federation, for her stimulating support and discussions. ThisworkwassupportedbytheRSFGrant # 15-11-30014.

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