Observations and the probabilistic situation calculus
Paulo Mateus, António Pacheco, Javier A. Pinto · 2002
In this article we propose a Probabilistic Situation Calculus logical language to represent and reason with knowledge about dynamical worlds in which actions have uncertain effects. Two essential tasks are addressed when reasoning about change in worlds: Probabilistic Temporal Projection and Probabilistic Belief Update. Uncertain effects are modeled by dividing an action into two subparts: a deterministic input (agent produced) and a probabilistic reaction (nature produced). The probability distributions of the reactions are assumed to be known. Our logical language is an extension to Situation Calculae in the style proposed by Raymond Reiter. There are three aspects to this work. First, we extend the language to accommodate terms dealing with belief and probability. Second, we provide a operational semantics based on Randomly Timed Automata. Finally, we develop Monte-Carlo algorithms to efficiently interpret the probability and belief terms. With the framework proposed we discuss how to develop a reasoning system in Mathematica capable of performing temporal projection and belief update in the Probabilistic Situation Calculus. Finally, we present a sound basis to set rewards and observation planning. (1) Center for Logic and Computation, Departamento de Matematica, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. email: [email protected]. Supported by FCT SFRH/BPD/5625/2001 and the FibLog initiative. (2) Applied Mathematics Center, Departamento de Matematica, IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. email: [email protected] (3) Unfortunately J. Pinto passed away in an accident while this paper was being prepared. Formerly, he was at Bell Labs, Database Systems Research Dept., 600 Mountain Ave., New Jersey 07974, U.S.A. OBSERVATIONS AND THE P...