A Translation of Probabilistic Event Calculus into Markov Decision Processes

TL;DR

This paper presents a formal translation of Probabilistic Event Calculus into Markov Decision Processes, enhancing PEC's goal-directed reasoning by leveraging MDP algorithms while maintaining interpretability.

Contribution

It introduces a novel translation framework from PEC to MDPs, enabling goal-directed planning and reasoning in PEC's narrative domain.

Findings

Supports temporal reasoning and planning tasks

Allows mapping learned policies back to PEC representations

Extends PEC capabilities with MDP algorithms

Abstract

Probabilistic Event Calculus (PEC) is a logical framework for reasoning about actions and their effects in uncertain environments, which enables the representation of probabilistic narratives and computation of temporal projections. The PEC formalism offers significant advantages in interpretability and expressiveness for narrative reasoning. However, it lacks mechanisms for goal-directed reasoning. This paper bridges this gap by developing a formal translation of PEC domains into Markov Decision Processes (MDPs), introducing the concept of "action-taking situations" to preserve PEC's flexible action semantics. The resulting PEC-MDP formalism enables the extensive collection of algorithms and theoretical tools developed for MDPs to be applied to PEC's interpretable narrative domains. We demonstrate how the translation supports both temporal reasoning tasks and objective-driven planning, with methods for mapping learned policies back into human-readable PEC representations, maintaining interpretability while extending PEC's capabilities.