Epistemic JAADL: A Modal Logic for Joint Abilities with Imperfect Information

Abstract

Coordination and joint ability are important problems in representation and reasoning about multi-agent systems. Ghaderi et al. presented a formalization of joint ability of coalitions in the expressive first-order language of the situation calculus. Essentially, a coalition has joint ability to achieve a goal if after iterated elimination of dominated strategies, any remaining joint strategy achieves the goal. Based on their work, Liu et al. proposed JAADL, a modal logic for joint abilities under strategy commitments. In this paper, we propose EJAADL, an epistemic extension of JAADL, for imperfect information games where agents may have incomplete knowledge or even false beliefs about the world. Like Ghaderi et al.’s work, elimination of dominated strategies is now based on beliefs about the world, rather than facts about the world as in JAADL. Strategies are required to be uniform, i.e., they select the same action in all accessible histories. We illustrate EJAADL with examples, analyze its properties, and show that model checking memoryless EJAADL is in EXPTIME. Moreover, we consider the fragment of EJAADL without the iterated elimination operator, and show that model-checking the memoryless version of this fragment can be done in PSPACE.