AGM-like paraconsistent belief change

Abstract

Two systems of belief change based on paraconsistent logics are introduced in this paper by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic that extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGM•, is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator which allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations.

On Paraconsistent Belief Revision in LP

“…Note that none of these works provide a representation theorem, and none of them safely extend the classical AGM/KM framework. The only two works that we are aware of where the authors provide representation theorems are (Testa, Coniglio, and Ribeiro 2017) and (Testa et al 2018). But in both cases they use a logic with an explicit consistency connector, and the theorems are set for the basic postulates only, not for the full set of AGM postulates.…”

Belief Revision and Computational Argumentation: A Critical Comparison

“…When considering settings where autonomous agents are involved, Belief Revision describes how an agent is supposed to change its beliefs when new information arrives, restoring its belief state's consistency. 2 In three and a half decades of intense and fructiferous research, some extensions were introduced that propose the use of belief bases, a construct which distinguishes between fundamental and derived beliefs (Hansson 1998), and paraconsistent belief revision models that distinguish between incoherence and inconsistency (see for instance Rott 2001, Chapter 3 andCasini et al 2018;Testa et al 2017). Argumentation is concerned with establishing the agent's current beliefs from a potentially incomplete and inconsistent knowledge base, ensuring that these beliefs satisfy some desirable properties (for an overview see Baroni et al 2011.…”

“…Several different ways for inconsistency-tolerant belief revision can be found in the literature; among them is possible to mention the use of paraconsistent logic instead of classical logic (Priest 2001;Testa et al 2017Testa et al , 2018, the use of context sensitivity(Chopra and Parikh 1999;Hansson and Wassermann 2002), and the adoption of belief states(Fermé and Wassermann 2018).…”