Algebraic Semiotics.


Quoting the introduction to this UCSD paper online.

Short Overview
Algebraic semiotics is a new approach to meaning and representation, and in particular to user interface design, that builds on five important insights from the last hundred years:

* Semiotics: Signs are not isolated items; they come in systems, and the structure of a sign is to a great extent inherited from the system to which it belongs. Signs do not have pre-given “Platonic” meanings, but rather their meaning is relational, because signs are always interpreted in particular contexts. (The first sentence reflects the influence of Saussure, the second that of Pierce.)
* Social Context: Signs are used by people as part of their participation in social groups; meaning is primarily a social phenomenon; its purpose is communication. (This reflects some concerns of post-structuralism.)
* Morphisms: If some class of objects is interesting, then structure preserving maps or morphisms of those objects are also interesting – perhaps even more so. For semiotics, these morphisms are representations. Objects and morphisms together form structures known as categories.
* Blending and Colimits: If some class of objects is interesting, then putting those objects together in various ways is probably also interesting. Morphisms can be used to indicate that certain subojects are to be shared in such constructions, and colimits of various kinds are a category theoretic formalization of ways to put objects together. In cognitive linguistics, blending has been identified as an important way to combine conceptual systems.
* Algebraic Specification: Sign systems and their morphisms can be described and studied in a precise way using semantic methods based on equational logic that were developed for the theory of abstract data types.



Computational semiotics is an interdisciplinary field that applies, conducts, and draws on research in logic, mathematics, the theory and practice of computation, formal and natural language studies, the cognitive sciences generally, and semiotics proper. A common theme of this work is the adoption of a sign-theoretic perspective on issues of artificial intelligence and knowledge representation. Many of its applications lie in the field of computer-human interaction (CHI).   (from Wikipedia) Read more >>


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