Strong Equivalence for LPMLN Programs

TL;DR

This paper investigates strong equivalence in LPMLN, a probabilistic logic programming framework, providing methods to verify equivalence using classical logic and answer set solvers, and proposing reformulations of LPMLN semantics.

Contribution

It introduces a reduction of strong equivalence verification in LPMLN to classical logic and here-and-there logic, enabling practical checking with existing solvers and offering new semantic reformulations.

Findings

Verification reduces to classical logic equivalence checking.

Answer set solvers can be used for strong equivalence verification.

Proposes reformulations of LPMLN semantics using choice rules and here-and-there logic.

Abstract

LPMLN is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. We study the concept of strong equivalence in LPMLN, which is a useful mathematical tool for simplifying a part of an LPMLN program without looking at the rest of it. We show that the verification of strong equivalence in LPMLN can be reduced to equivalence checking in classical logic via a reduct and choice rules as well as to equivalence checking under the "soft" logic of here-and-there. The result allows us to leverage an answer set solver for LPMLN strong equivalence checking. The study also suggests us a few reformulations of the LPMLN semantics using choice rules, the logic of here-and-there, and classical logic.