We present a family of sound and complete logics for reasoning about deliberation strategies for SimpleAPL programs. SimpleAPL is a fragment of the agent programming language 3APL designed for the implementation of cognitive agents with beliefs, goals and plans. The logics are variants of PDL, and allow us to prove safety and liveness properties of SimpleAPL agent programs under different deliberation strategies. We show how to axiomatize different deliberation strategies for SimpleAPL programs, and, for each strategy we consider, prove a correspondence between the operational semantics of SimpleAPL and the models of the corresponding logic. We illustrate the utility of our approach with an example in which we show how to verify correctness properties for a simple agent program under different deliberation strategies.
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