# Strong equivalence for $\rm LP^{MLN}$ programs

## TL;DR

This paper extends the concept of strong equivalence to $
m LP^{MLN}$, a probabilistic logic programming framework, by reducing the problem to classical logic equivalence checking, enabling more effective program analysis.

## Contribution

It introduces a method to verify strong equivalence in $
m LP^{MLN}$ using classical logic tools and proposes reformulations of its semantics for better understanding.

## Key findings

- Verification of strong equivalence reduces to classical logic equivalence checking.
- Leverages answer set solvers for strong equivalence verification in $
m LP^{MLN}$.
- Proposes reformulations of $
m LP^{MLN}$ semantics using various logical frameworks.

## Abstract

Strong equivalence is a well-studied and important concept in answer set programming (ASP). $\rm LP^{MLN}$ is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. Because of the semantic differences, strong equivalence for ASP does not simply carry over to $\rm LP^{MLN}$. I study the concept of strong equivalence in $\rm LP^{MLN}$ with the goal of extending strong equivalence to $\rm LP^{MLN}$ programs. My study shows that the verification of strong equivalence in $\rm LP^{MLN}$ can be reduced to equivalence checking in classical logic plus weight consideration.The result allows us to leverage an answer set solver for checking strong equivalence in $\rm LP^{MLN}$. Furthermore, this study also suggests us a few reformulations of the $\rm LP^{MLN}$ semantics using choice rules, logic of here and there, and the second-order logic. I will present my work result of strong equivalence for $\rm LP^{MLN}$ and talk about my next steps for research: one is approximately strong equivalence, and another is the integration of fuzzy logic with neural network.