Belief Contraction in Non-classical logics as Hyperintensional Belief Change

Abstract

AGM's belief revision is one of the main paradigms in the study of belief change operations. Despite its popularity and importance to the area, it is well recognised that AGM's work relies on a strong idealisation of the agent's capabilities and the nature of beliefs themselves. Particularly, it is recognised in the literature that Belief and Knowledge are hyperintensional attitudes, i.e. they can differentiate between contents that are necessarily equivalent, but to our knowledge, only a few works have explicitly considered how hyperintensionality affects belief change. This work investigates abstract operations of hyperintensional belief change and their connection to belief change in non-classical logics, such as belief contraction operations for Horn Logics and Description Logics. Our work points to hyperintensional belief change as a general framework to unify results in belief change for non-classical logics.

Hyperintensional Partial Meet Contractions

“…Our work follows directly the line delineated in (Souza 2020) and (Souza and Wassermann 2021), expanding their framework and establishing connections with belief change in non-classical logics and between different notions of hyperintensional belief change investigated in these previous works.…”

“…substituting B L ϕ for B L C ϕ or B L C ϕ, substituting CnpBq for CpBq, etc. These variations give rise to different operations previously investigated in the literature by Santos et al (2018), Souza (2020) and Souza and Wassermann (2021), as well as some interesting new ones. In this work, we will focus on only two of them.…”

“…Work on belief change for non-classical logics, such as that of Girard and Tanaka (2016), have investigated dynamic belief change operators, which in principle could be used to model some hyperintensional notions, as classical consequences need not be valid in such logics. Similarly, Santos et al (2018) investigate pseudo-contractions, which can be used to study a particular kind of hyperintensional belief change, called by Souza and Wassermann (2021) Cdependent contractions. These strategies, however, deal with hyperintensionality in an implicit way, not providing theoretical and philosophical connections that allow us to understand their underlying commitments.…”

“…Other work soon followed, such as Özgün and Berto (2020) who dynamify Berto's conditional logic, proposing a dynamic logic of hyperintensional belief revision. On the other hand, Souza (2020) and Souza and Wassermann (2021) investigate hyperintensional belief change operations using tools similar to that of the AGM framework, based on abstract logics. These authors propose connections between hyperintensional belief change and belief change in nonclassical logics, showing that for several logics of interest to AI, we can obtain partial meet-like operations based on a classical logic.…”

“…In this work, we explore further the notion of hyperintensional belief change, as studied by Souza (2020) and Souza and Wassermann (2021), aiming to overcome their deficiencies. Further, by differentiating between the notions of hyperintensional belief base change and hyperintensional belief set change, we can study the connections between AGM contractions and partial meet contractions in a more general setting, establishing relations to earlier work on the definability of AGM contractions for non-classical logics, such as that of Flouris (2006) on AGM-compatibility and that of Ribeiro (2013) on partial meet contractions for non-classical logics.…”