Issues of representation arise in natural language processing, user interface design, art, and indeed, communication with any medium. This paper addresses such issues using algebraic semiotics, which draws on algebraic speci cation to give (among other things) an algebraic theory of representation, and a generalization of blending in the sense of cognitive linguistics.

Abstract: This paper proposes a new approach to style, arising from our work on computational media using structural blending, which enriches the conceptual blending of cognitive linguistics with structure building operations in order to encompass syntax and narrative as well as metaphor. We have implemented both conceptual and structural blending, and conducted initial experiments with poetry, including interactive multimedia poetry, although the approach generalizes to other media. The central idea is to analyze style in terms of blending principles, based on our finding that different principles from those of common sense blending are often needed for some contemporary poetic metaphors. 1

Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music as an example, this paper explores the structure of qualitative experience, demonstrating that it is multi-layer emergent, non-compositional, enacted, and situation dependent, among other non-Cartesian properties.

This note explores ways that style manifests in computer mediated texts, in a broad sense including cinema, video games, and even living. Much of our analysis relies on blending, enriched from cognitive linguistics with structure building operations to get structural blending, which we show encompasses metaphor, syntax, and narrative. Initial results concern poetry, but the approach generalizes to other media. One result is that optimality principles very dierent from those of common sense blending are needed for creative poetic blends.

Abstract. This paper explores reasoning about space and time, e.g., in metaphors of time as space; an important method is to find minimal assumptions needed to reach the same conclusions that humans reach. Some mathematical language, including the notion of triad, is introduced for this purpose, formalizing and generalizing the cognitive semantics approaches to conceptual spaces (in the senses of both Fauconnier & Turner and of Gärdenfors), blending, and metaphor; in particular, continuous mathematics is used to model space and time. A new explanation of emergent structure in blend spaces is also discussed, and proposed as a source of creativity. Four main examples illustrate the approach, and an appendix encapsulates the most difficult mathematics. 1