On the Progression of Knowledge and Belief for Nondeterministic Actions in the Situation Calculus / 2955
Liangda Fang, Yongmei Liu, Ximing Wen
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In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Recently, Fang and Liu extended the situation calculus to account for multi-agent knowledge and belief change. In this paper, based on their framework, we investigate progression of both belief and knowledge in the single-agent propositional case. We first present a model-theoretic definition of progression of knowledge and belief. We show that for propositional actions, i.e., actions whose precondition axioms and successor state axioms are propositional formulas, progression of knowledge and belief reduces to forgetting in the logic of knowledge and belief, which we show is closed under forgetting. Consequently, we are able to show that for propositional actions, progression of knowledge and belief is always definable in the logic of knowledge and belief.