Possession as Linear Knowledge

Epistemic logic analyzes reasoning governing localized knowledge, and is thus fundamental to multiagent systems. Linear logic treats hypotheses as consumable resources, allowing us to model evolution of state. Combining principles from these two separate traditions into a single coherent logic allows us to represent localized consumable resources and their flow in a distributed system. The slogan “possession is linear knowledge” summarizes the underlying idea. We walk through the design of a linear epistemic logic and discuss its basic metatheoretic properties such as cut elimination. We illustrate its expressive power with several examples drawn from an ongoing effort to design and implement a linear epistemic logic programming language for multi-agent distributed systems; see [GBB+06, DP09] for preliminary logic design and examples.