Exploring the rationality of some syntactic merging operators (extended version)

TL;DR

This paper introduces syntactical merging operators based on logic programming principles, analyzing their rationality properties and compliance with established postulates, aiming for computational efficiency in belief merging.

Contribution

It defines new syntactical merging operators constrained to logic-program-like belief bases and analyzes their rationality using adapted postulates, offering a computationally simpler alternative.

Findings

Operators satisfy some rationality postulates

Analysis shows trade-offs between different operator classes

Provides a framework for rational belief merging with lower complexity

Abstract

Most merging operators are defined by semantics methods which have very high computational complexity. In order to have operators with a lower computational complexity, some merging operators defined in a syntactical way have be proposed. In this work we define some syntactical merging operators and exploring its rationality properties. To do that we constrain the belief bases to be sets of formulas very close to logic programs and the underlying logic is defined through forward chaining rule (Modus Ponens). We propose two types of operators: arbitration operators when the inputs are only two bases and fusion with integrity constraints operators. We introduce a set of postulates inspired of postulates LS, proposed by Liberatore and Shaerf and then we analyzed the first class of operators through these postulates. We also introduce a set of postulates inspired of postulates KP, proposed by Konieczny and Pino P\'erez and then we analyzed the second class of operators through these postulates.