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In an earlier paper, Banihashemi et al. proposed a general framework for agent abstraction based on the situation calculus. They used basic action theories (BATs) to represent agents’ behavior, and mappings to specify how high-level BATs relate to low-level ones. They then defined the concepts of sound/complete abstractions of BATs based on the notion of bisimulation between high-level and low-level models. However, they didn’t address the issue of the construction of an abstraction from a low-level action theory when given a mapping. It turns out that their concept of abstraction is closely related to the well-explored notion of forgetting. In this paper, we explore agent abstraction via forgetting. Firstly, we show that a correct (i.e., sound and complete) abstraction can be obtained via forgetting low-level symbols from the low-level action theory together with axioms for bisimulation. Secondly, we show how to compute via forgetting a correct abstraction in the form of a generalized BAT (i.e., where the initial database, action preconditions and successor state descriptions can be second-order formulas) under a suitable Markovian restriction. Finally, we show that in the propositional case, under the suitable Markovian restriction, correct abstractions are always computable.
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