The paper proposes a condition for preserving the KD45 property of a Kripke model when a sequence of update models is applied to it. The paper defines the notions of a primitive update model and a semi-reflexive KD45 (or sr-KD45) Kripke model. It proves that updating a sr-KD45 Kripke model using a primitive update model results in a sr-KD45 Kripke model, i.e., a primitive update model preserves the properties of a sr-KD45 Kripke model. It shows that several update models for modeling well-known actions found in the literature are primitive. This result provides guarantees that can be useful in presence of multiple applications of actions in multi-agent system (e.g., multi-agent planning).

Abstract The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful transformations in logics of knowledge (e.g., to support multi-agent planning with knowledge actions and degrees of visibility) have been proposed. This paper explores the use of logic programming (LP) to encode interesting forms of logics of knowledge and compute Kripke models. The LP modeling is expanded with useful operators on Kripke structures, to support multi-agent planning in the presence of both world-altering and knowledge actions. This results in the first ever implementation of a planner for this type of complex multi-agent domains.