Abstract
Alternating Time Temporal Logic (ATL) is widely used for the verification of multi-agent systems. We consider Resource Agent Logic (RAL), which extends ATL to allow the verification of properties of systems where agents act under resource constraints. The model checking problem for RAL with unbounded production and consumption of resources is known to be undecidable. We review existing (un)decidability results for fragments of RAL, tighten some existing undecidability results, and identify several aspects which affect decidability of model checking. One of these aspects is the availability of a ‘do nothing’, or idle action, which does not produce or consume resources. Analysis of undecidability results allows us to identify a significant new fragment of RAL for which model checking is decidable.
Highlights
Many problems in AI and multi-agent systems research are most naturally formulated in terms of the abilities of a group or coalition of agents
First we show that both the resource-flat and the proponentrestricted fragments of resource agent logic remain undecidable in the presence of idle actions
We show that the model checking problem for Resource Agent Logic (RAL), i.e., the logic without any additional restrictions, remains undecidable over iRBMs
Summary
Many problems in AI and multi-agent systems research are most naturally formulated in terms of the abilities of a group or coalition of agents. The decidability result in [6] was proven in the presence of two major restrictions, called, in the terminology of [2], resource flat and proponent restricted The former assumes that agents are always re-equipped with fresh resources when they reconsider their strategies; the latter assumes that only the proponents act under resource bounds (i.e., agents outside the coalition are not resource bounded). We investigate the effects of various semantic choices, such as the availability of an idle action, on the decidability of the model checking problem for resource logics. We identify and motivate a significant, non-resource-flat fragment that has a decidable model checking property in the presence of idle actions, and is not decidable otherwise. With whatever resources are left, the agents need a strategy to perform the rescue In this example, the model checking problem essentially corresponds to finding two nested conditional resource-constrained plans, see e.g., [10].
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