Merging operators on stratified belief bases equipped with argumentative inference

Abstract

This work considers the formalisation of the merging process of stratified belief bases, where beliefs are stored in different layers or strata. Their strata are ranked, following a total order, employing the value the agent using the belief base assigns to these beliefs. The agent uses an argumentation mechanism to reason from the belief base and obtain the final inferences. We present two ways of merging stratified belief bases: the first is defined by merging two strata without belief preservation, and the second by merging two strata with belief preservation. For these operators, as layers merge, it is possible that some information has to be deleted from the stratum to maintain consistency. The latter merge operator will be defined as performing their actions so that information removed from the stratum is preserved after the merging by moving it to a stratum containing information perceived as having a lower value and where those beliefs may trigger a new revision, possibly starting a cascading effect.

KEYWORDS:

• Argumentation
• belief revision
• stratified belief bases

Acknowledgments

We would like to thank to the anonymous referees for very valuable comments on earlier versions of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Given a set of sentences S, a minimal inconsistent subset of S is a set $S^{\prime }$ such that $S^{\prime }\subseteq S$, $S^{\prime }⊢\mathrm{\perp }$, and if $S^{″}\subset S^{\prime }$ then $S^{″}⊬\mathrm{\perp }$. Making use of the notation introduced in Definition 4.1 this postulate can be formulated in the following alternative way: If $(K\cup A){}^{\perp \perp }\mathrm{\perp }=(H\cup B){}^{\perp \perp }\mathrm{\perp }$ then $(K\cup A)\setminus \left(K\circ A\right)=(H\cup B)\setminus \left(H\circ B\right)$.

Additional information

Funding

This work is partially supported by Universidad Nacional del Sur (UNS) [grant numbers PGI 24/N055 and PGI 24/ZN37] and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) from Argentina.