Optimizing the mutual intelligibility of linguistic agents in a shared world

We consider the problem of linguistic agents that communicate with each other about a shared world. We develop a formal notion of a language as a set of probabilistic associations between form (lexical or syntactic) and meaning (semantic) that has general applicability. Using this notion, we define a natural measure of the mutual intelligibility, F(L,Lʹ), between two agents, one using the language L and the other using Lʹ. We then proceed to investigate three important questions within this framework: (1) Given a language L, what language Lʹ maximizes mutual intelligibility with Lʹ We find surprisingly that Lʹ need not be the same as L and we present algorithms for approximating Lʹ arbitrarily well. (2) How can one learn to optimally communicate with a user of language L when L is unknown at the outset and the learner is allowed a finite number of linguistic interactions with the user of Lʹ We describe possible algorithms and calculate explicit bounds on the number of interactions needed. (3) Consider a population of linguistic agents that learn from each other and evolve over time. Will the community converge to a shared language and what is the nature of such a language? We characterize the evolutionarily stable states of a population of linguistic agents in a game-theoretic setting. Our analysis has significance for a number of areas in natural and artificial communication where one studies the design, learning, and evolution of linguistic communication systems.