This paper studies the design of a software system that uses natural language to interact with human experts and large-scale language models (LLMs) for data analysis tasks. For complex problems, the LLMs can leverage human expertise and creativity to find previously unattainable solutions. While this interaction typically involves multiple human prompts and LLM responses, this paper investigates a more structured approach based on an abstract protocol for agent-to-agent interaction (see [3]). This protocol is modeled as two communicating finite-state machines, based on the concept of "two-way intelligibility." We implement this protocol and present empirical evidence demonstrating its use in mediating interactions between LLMs and human agents in two scientific fields: radiology and drug design. Through controlled experiments using human surrogates (databases) and uncontrolled experiments using human subjects, we demonstrate the protocol's ability to capture one-way and two-way intelligibility in human-LLM interactions, supporting the utility of two-way intelligibility in the design of human-machine systems.
