This paper is concerned with a multi-agent system which performs speculative computation under incomplete communication environments. In a master–slave style multi-agent system with speculative computation, a master agent asks queries to slave agents in problem solving, and proceeds computation with default answers when answers from slave agents are delayed. In this paper, we first provide a semantics for speculative computation using default logic. Speculative computation is considered in which reply messages from slave agents to a master are tentative and may change from time to time. In this system, default values used in speculative computation are only partially determined in advance. Next, we propose a procedure to compute speculative computation using a first-order consequence-finding procedure SOL with the answer literal method. The use of a consequence-finding procedure is convenient for updating agents' beliefs according to situation changes in the world. Then, we further refine the SOL calculus using conditional answer computation and skip-preference in SOL. The conditional answer format has a great advantage of explicitly representing how a conclusion depends on tentative replies and defaults. This dependency representation is important to avoid unnecessary recomputation of tentative conclusions. On the other hand, the skip-preference method has the great ability of preventing irrational/redundant derivations. Finally, we implemented a mechanism of process maintenance to avoid duplicate computation when slave agents change their answers. As long as new answers from slave agents do not conflict with any previously encountered situation, the obtained conclusions are never recomputed. We applied the proposed system to the meeting-room reservation problem to see the usefulness of the framework.