Communication: Words and Conceptual Systems
This work addresses foundational issues in knowledge representation and communication, potentially impacting fields like linguistics and AI, but it appears incremental as it builds on existing set theory concepts.
The paper tackles the problem of representing categories for knowledge representation and understanding by proposing a new category representation as a generalization of classic sets, with the economy principle to reduce complexity, and applies it to mathematically define and analyze conceptual systems, word relations, and communication.
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.