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Title

Probabilistic Situation Calculus
Authors

Paulo Mateus
Organization: CMA, Departamento de Matemática, Lisbon, Portugal
António Pacheco
Organization: CMA, Departamento de Matemática, Lisbon, Portugal
Javier Pinto
Organization: Bell Labs; P. Universidad Católica de Chile, Santiago, Chile
Amílcar Sernadas
Organization: CMA, Departamento de Matemática, Lisbon, Portugal
Cristina Sernadas
Organization: CMA, Departamento de Matemática, Lisbon, Portugal
Journal / Anthology

Annals of Mathematics and Artificial Intelligence
Year: 2001
Volume: 32
Page range: 393-431
Description

In this article we propose a probabilistic Sitaution Calculus logical language to represent and reason with knowledge about dynamic worlds in which actions have uncertain effects. Uncertain effects are modeled by dividing an action into two subparts: a deterministic (agent-produced) input and a probabilistic reaction (produced by nature). We assume that the probabilities of the reactions have known distributions. 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 in order to accomodate the necessary distinctions (e.g., the separation of actions into inputs and reactions). Second, we develop the notion of randomly reactive automata in order to specify the sematics of our Probabilistic Situation Calculus. Finally, we develop a reasoning system in Mathematica capable of performing temporal projection in the Probabilistic Situation Calculus.
Subject

*Mathematics > Foundations of Mathematics > Logic
Keywords

probability logic, probabilistic automata, Situation Calculus, theory of action, Mathematica