Communicating with sentences: A multi-word naming game model

Naming game simulates the process of naming a single object by a single word, in which a population of communicating agents can reach global consensus asymptotically through iteratively pair-wise conversations. In this paper, we propose an extension of the single-word naming game, to a multi-word naming game (MWNG), which simulates the naming game process when agents name an object by a sentence (i.e., a series of multiple words) for describing a complex object such as an opinion or an event. We first define several categories of words, and then organize sentences by combining words from different word categories. We refer to a formatted combination of several words as a pattern. In such an MWNG, through a pair-wise conversation, it requires the hearer to achieve consensus with the speaker with respect to both every single word in the sentence as well as the sentence pattern, so as to guarantee the correct meaning of the saying; otherwise, they fail reaching consensus in the interaction. We employ three typical topologies used for the underlying communication network, namely random-graph, small-world and scale-free networks. We validate the model by using both conventional English language patterns and man-made test sentence patterns in performing the MWNG. Our simulation results show that: 1) the new sentence sharing model is an extension of the classical lexicon sharing model; 2) the propagating, learning and converging processes are more complicated than that in the conventional naming game; 3) the convergence time is non-decreasing as the network becomes better connected; 4) the agents are prone to accept short sentence patterns. These new findings may help deepen our understanding of the human language development from a network science perspective.