Superiority Based Revision of Defeasible Theories

Abstract

We propose a systematic investigation on how to modify a preference relation in a defeasible logic theory to change the conclusions of the theory itself. We argue that the approach we adopt is applicable to legal reasoning, where users, in general, cannot change facts and rules, but can propose their preferences about the relative strength of the rules. We provide a comprehensive study of the possible combinatorial cases and we identify and analyse the cases where the revision process is successful. IntroductionTypically skeptical non-monotonic formalisms are equipped with techniques to address conflicts, where a conflict is a combination of reasoning chains leading to a contradiction. The most common device to handle conflicts is a preference or superiority relation over the elements used by the formalism to reason. These elements can be formulae, axioms, rules or arguments, and the preference relation states that one of such elements is to be preferred to another one when both can be used.In this research we concentrate on a specific rule-based non-monotonic formalism, Defeasible Logic, but the motivation behind the particular technical development applies in general to other rule-based formalisms. In a rule based formalism, typically knowledge is described in facts (describing immutable propositions/statements about a case), rules (describing relationships between a set of premises and a conclusion), and preference relation or superiority relation (describing the relative strength of rules). A revision operation transforms a theory by changing some of its elements, that is: facts, rules and superiority relation. Revision based on change of facts corresponds to an update operation [1], revision based on modification of rules has been investigated in [2], to the best of our knowledge, revision of non-monotonic theories based on modifications of the underlying superiority relation has been neglected so far. In this paper we concentrate on this issue, and we argue that, while little attention has been dedicated to this topic, it has natural correspondences to reasoning patterns in legal reasoning.The paper is organised as follows: In Section 2 we motivate that reasoning over preferences on rules and on how to modify the preferences is a natural reasoning pattern in legal reasoning. Then in Section 3 we introduce Defeasible Logic, the formalism chosen for our investigation; in particular we introduce new auxiliary proof tags to describe derivations in Defeasible logic. The new proof tags do not modify the expressive power of the logic, but they identify patterns where instances of the superiority relation contribute to the derivation of a conclusion. Armed with this technical machinery,

Resource-Driven Substructural Defeasible Logic

“…As a consequence of the aforementioned notions we shall prove one property that regards acyclic RSDL. The Atom Dependency Graph 5 of a defeasible theory has been defined in many different contexts, specifically in the analysis of preferences, as in [6]. Acyclic RSDLs are theories in which no cycle appears in the Atom Dependency Graph.…”

A dynamic default revision mechanism for speculative computation

“…The proposal is based on the idea that fixed priorities between arguments in a real world problem are impractical. Similarly, in [6] the revision of rule priorities is considered in the legal domain. But, in it, defaults are revised to accommodate the preferred answers of participants.…”

A history of AI and Law in 50 papers: 25 years of the international conference on AI and Law

“…The novelty of the paper is that preference handling is dynamic, and we can reason about the preference rules. With a few exceptions, e.g., [210] and [13], the idea has been neglected until recently, when some impulse in this direction has arisen from work on extended abstract argumentation [183] and work on revision of preferences [108].…”