The emergent consensus on dimensional models of sentiment, appraisal, emotions, and values is on the semantics of the principal dimensions, typically interpreted as valence, arousal, and dominance. The notion of weak semantic maps was introduced recently as distribution of representations in abstract spaces that are not derived from human judgments, psychometrics, or any other a priori information about their semantics. Instead, they are defined entirely by binary semantic relations among representations, such as synonymy and antonymy. An interesting question concerns the ability of the antonymy-based semantic maps to capture all “universal” semantic dimensions. The present work shows that those narrow weak semantic maps are not complete in this sense and can be augmented with other semantic relations. Specifically, including hyponym-hypernym relations yields a new semantic dimension of the map labeled here “abstractness” (or ontological generality) that is not reducible to any dimensions represented by antonym pairs or to traditional affective space dimensions. It is expected that including other semantic relations (e.g., meronymy/holonymy) will also result in the addition of new semantic dimensions to the map. These findings have broad implications for automated quantitative evaluation of the meaning of text and may shed light on the nature of human subjective experience. 1. Introduction The idea of representing semantics geometrically is increasingly popular. Many mainstream approaches use vector space models, in which concepts, words, documents, and so forth are associated with vectors in an abstract multidimensional vector space. Other approaches use manifolds of more complex topology and geometry. In either case, the resultant space or manifold togetheD:\Finalization\VLSI\861691\861691r with its allocated representations is called a semantic space or a semantic (cognitive) map. Examples include spaces constructed with Latent Semantic Analysis (LSA)  and Latent Dirichlet Allocation (LDA) , as well as many related techniques, for example, ConceptNet [3, 4]. Other examples of techniques include Multi-Dimensional Scaling (MDS) , including Isomap , and related manifold-learning techniques , Gardenfors' conceptual spaces , very popular in the past models of self-organizing feature maps, and more. The majority of these approaches are based on the idea of a dissimilarity metrics, which is to capture semantic dissimilarity between representations (words, documents, concepts, etc.) with a geometrical distance between associated space
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