Communication: Words and Conceptual Systems

TL;DR

This paper introduces a new, generalized way to represent categories through words and symbols, aiming to improve understanding and communication by analyzing conceptual systems and their relations mathematically.

Contribution

It proposes a novel category representation method based on an economy principle, extending classic set theory, and provides a mathematical framework for analyzing conceptual systems and communication.

Findings

A new category representation generalizing classic sets.

Mathematical definitions of conceptual systems and word relations.

Insights into the dependence of conceptual systems on situations.

Abstract

Words (phrases or symbols) play a key role in human life. Word (phrase or symbol) representation is the fundamental problem for knowledge representation and understanding. A word (phrase or symbol) usually represents a name of a category. However, it is always a challenge that how to represent a category can make it easily understood. In this paper, a new representation for a category is discussed, which can be considered a generalization of classic set. In order to reduce representation complexity, the economy principle of category representation is proposed. The proposed category representation provides a powerful tool for analyzing conceptual systems, relations between words, communication, knowledge, situations. More specifically, the conceptual system, word relations and communication are mathematically defined and classified such as ideal conceptual system, perfect communication and so on; relation between words and sentences is also studied, which shows that knowledge are words. Furthermore, how conceptual systems and words depend on situations is presented, and how truth is defined is also discussed.