Finding Common Ground for Incoherent Horn Expressions

TL;DR

The paper addresses how autonomous systems can find shared understanding among incoherent sets of rules using formal methods, conditions for guaranteed common ground, and an efficient algorithm for computation.

Contribution

It introduces a formal notion of common ground for Horn expressions, identifies conditions ensuring its existence, and provides a polynomial-time algorithm for computing it.

Findings

Common ground exists under specific conditions for Horn expressions.

A polynomial-time algorithm computes common ground when conditions are met.

Removing any condition may lead to non-existence of common ground.

Abstract

Autonomous systems that operate in a shared environment with people need to be able to follow the rules of the society they occupy. While laws are unique for one society, different people and institutions may use different rules to guide their conduct. We study the problem of reaching a common ground among possibly incoherent rules of conduct. We formally define a notion of common ground and discuss the main properties of this notion. Then, we identify three sufficient conditions on the class of Horn expressions for which common grounds are guaranteed to exist. We provide a polynomial time algorithm that computes common grounds, under these conditions. We also show that if any of the three conditions is removed then common grounds for the resulting (larger) class may not exist.