# Elaboration Tolerant Representation of Markov Decision Process via Decision-Theoretic Extension of Probabilistic Action Language pBC+

## TL;DR

This paper extends probabilistic action language pBC+ with utility concepts, enabling a decision-theoretic MDP representation that allows for more elaboration-tolerant modeling and efficient policy computation.

## Contribution

It introduces a decision-theoretic extension of pBC+ and a system that leverages MDP solvers for optimal policy computation from pBC+ descriptions.

## Key findings

- The extended pBC+ can be semantically interpreted as an MDP.
- The system pbcplus2mdp effectively computes optimal policies.
- The approach enhances the expressiveness and computational efficiency of probabilistic action languages.

## Abstract

We extend probabilistic action language pBC+ with the notion of utility as in decision theory. The semantics of the extended pBC+ can be defined as a shorthand notation for a decision-theoretic extension of the probabilistic answer set programming language LPMLN. Alternatively, the semantics of pBC+ can also be defined in terms of Markov Decision Process (MDP), which in turn allows for representing MDP in a succinct and elaboration tolerant way as well as to leverage an MDP solver to compute pBC+. The idea led to the design of the system pbcplus2mdp, which can find an optimal policy of a pBC+ action description using an MDP solver. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).