A logic of intention and action for regular BDI agents based on bisimulation of agent programs

We address the problem of providing a computationally grounded semantics for belief, desire, intention (BDI) agents that explicitly relates intention to action, using as a basis for this connection a notion of bisimulation for agent programs. We first define regular BDI agents, a class of BDI agents inspired by the procedural reasoning system architecture, under the restriction that agent programs are representable as regular expressions. The operational semantics of regular agent programs is formalized using agent program execution graphs, an extension of the process graphs used to formalize regular processes. An agent's executed program represents an attempt to perform an intended plan and can include branches for both successful execution and the failure of action attempts; intended execution paths are defined in terms of successful executions, and intentions in terms of future successfully executed agent programs. We present Agent Dynamic Logic ($$\mathsf {ADL}$$ADL), a logic of intention and action that faithfully represents the operational semantics of regular BDI agents. $$\mathsf {ADL}$$ADL is a logic in the spirit of BDI logic but also includes the dynamic logic of actions and a reduction of the logic of intention to the logics of action and time. A main contribution of the paper is a completeness result for a subclass of finite $$\mathsf {ADL}$$ADL theories with explicit representations of agent plans.