Belief merging within fragments of propositional logic

TL;DR

This paper introduces a general method for belief merging within fragments of propositional logic, ensuring the merged beliefs stay within the fragment, applicable beyond Horn to any fragment with certain closure properties.

Contribution

It proposes a novel approach to derive belief merging operators that preserve the logical fragment, extending previous work limited to Horn fragment.

Findings

Operators satisfy key merging postulates

Applicable to Horn and Krom fragments

Distance-based merging operators analyzed

Abstract

Recently, belief change within the framework of fragments of propositional logic has gained increasing attention. Previous works focused on belief contraction and belief revision on the Horn fragment. However, the problem of belief merging within fragments of propositional logic has been neglected so far. This paper presents a general approach to define new merging operators derived from existing ones such that the result of merging remains in the fragment under consideration. Our approach is not limited to the case of Horn fragment but applicable to any fragment of propositional logic characterized by a closure property on the sets of models of its formulae. We study the logical properties of the proposed operators in terms of satisfaction of merging postulates, considering in particular distance-based merging operators for Horn and Krom fragments.