We propose a model of common language acquisition, assuming an artificial community that consists of multiple agents ; each agent owns different grammar rules at the first stage, however they come to organize a common grammar in the community through a number of exchanges of sentences between them. We hypothesize that each agent has ability of abductive and inductive inference. In the early stage of the life-span of agents, they try to generate grammar rules abductively, to parse other's sentences, however in the later stage, they try to find rules inductively from a number of sentence examples they acquired so far. The communicative ability of agents is measured by energy. The energy score of each agent becomes high if he/she could recognize others' sentences, or his/her utterances could be recognized by others. According to this energy score, each agent changes his/her behavior ; when the score is high, he/she can increase the chances of utterance, anb can give more influence upon the grammar of the whole community. As each agent modifies his/her grammar by the inferences, the common grammar in the community keeps changing dynamically. In our computer simulation, we could show (1) that the adaptability and the robustness of the common grammar were realized if abductive/inductige inferences were adequately combined, (2) that the common grammar was developed when agents selected the proper inference autonomously, and (3) that the fusion and the bifurcation of grammar emerged through a larger-scale, longer-term experiment.