Inconsistent-tolerant base revision through Argument Theory Change

Abstract

Reasoning and change over inconsistent knowledge bases (KBs) is of utmost relevance in areas like medicine and law. Argumentation may bring the possibility to cope with both problems. Firstly, by constructing an argumentation framework (AF) from the inconsistent KB, we can decide whether to accept or reject a certain claim through the interplay among arguments and counterarguments. Secondly, by handling dynamics of arguments of the AF, we might deal with the dynamics of knowledge of the underlying inconsistent KB.Dynamics of arguments has recently attracted attention and although some approaches have been proposed, a full axiomatization within the theory of belief revision was still missing. A revision arises when we want the argumentation semantics to accept an argument. Argument Theory Change (ATC) encloses the revision operators that modify the AF by analyzing dialectical trees -arguments as nodes and attacks as edges-as the adopted argumentation semantics.In this article, we present a simple approach to ATC based on propositional KBs. This allows to manage change of inconsistent KBs by relying upon classical belief revision, although contrary to it, consistency restoration of the KB is avoided. Subsequently, a set of rationality postulates adapted to argumentation is given, and finally, the proposed model of change is related to the postulates through the corresponding representation theorem. Though we focus on propositional logic, the results can be easily extended to more expressive formalisms such as first-order logic and description logics, to handle evolution of ontologies.

Argument Revision

“…Postulates for dynamics in structured argumentation are proposed in [36], which is based on Argument Theory Change (ATC) [35,39]. As we noted in Section 2, ATC defines a new model (based on Dung's abstract frameworks) that incorporates a model of dynamics; in the present work, we have applied a model of dynamics to an existing model of argumentation.…”

“…As we noted in Section 2, ATC defines a new model (based on Dung's abstract frameworks) that incorporates a model of dynamics; in the present work, we have applied a model of dynamics to an existing model of argumentation. The postulates defined in [36] adapt the argumentation postulates of success, consistency, inclusion, vacuicty, core-retainment and uniformity. These have certain similarities and differences to our proposed postulates for Argument Revision: success is analogous to (AT+2) (all input arguments are acceptable); consistency is analogous to (AT+5) (all revised theories are well-formed, which ensures consistency in extensions); vacuicty is analogous to (AT+3\4) (if the union of the extension with all sub-arguments of the input arguments is conflict-free, then simply add the input arguments).…”

A principle-based robustness analysis of admissibility-based argumentation semantics

“…For example, the question of whether and how an argumentation framework can be changed in order to enforce some result, such as the acceptance of a given set of arguments, is referred to as the enforcement problem [11,12,20,39,52,53,62]. Change in argumentation has furthermore been related to (or modelled using tools of) theories of belief change, often taking an AGM-inspired approach [13,14,25,34,[36][37][38]45,[48][49][50]57,59]. Computational issues in a dynamic setting have also been studied, such as efficiently (re)computing extensions after an argumentation framework changes [1,6,46].…”

Dynamics of knowledge in DeLP through Argument Theory Change

“…In the recently published article (Moguillansky et al 2011), ATC is applied to a propositional argumentation framework (AF) with the objective of dealing with the dynamics of knowledge of an underlying inconsistent propositional KB from where the AF is built. Thus, similarly to the proposal given in the present article, handling dynamics of arguments of the AF allows to deal with the dynamics of knowledge of the underlying inconsistent KB.…”