  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.
