The origins of Zipf's meaning-frequency law
This provides a theoretical foundation for a linguistic law, potentially benefiting researchers in linguistics and cognitive science, though it appears incremental as it builds on Zipf's original observations.
The paper tackles the problem of explaining Zipf's meaning-frequency law, which states that more frequent words have more meanings, by showing that a single assumption on the joint probability of words and meanings suffices to derive this law, with the assumption justified as the outcome of a biased random walk in mental exploration.
In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two assumptions: that words follow Zipf's law for word frequencies (a power law dependency between frequency and rank) and Zipf's law of meaning distribution (a power law dependency between number of meanings and rank). Here we show that a single assumption on the joint probability of a word and a meaning suffices to infer Zipf's meaning-frequency law or relaxed versions. Interestingly, this assumption can be justified as the outcome of a biased random walk in the process of mental exploration.