Probabilistic Argumentation. An Equational Approach

There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: a. the nature of the arguments involved; b. the membership relation in the set S of arguments; c. the attack relation; and d. the choice of extensions. Generically to add a new aspect (probabilistic, or fuzzy, or temporal, etc) to an argumentation network can be done by adding this feature to each component a-d. This is a brute-force method and may yield a non-intuitive or meaningful result. A better way is to meaningfully translate the object system into another target system which does have the aspect required and then let the target system endow the aspect on the initial system. In our case we translate argumentation into classical propositional logic and get probabilistic argumentation from the translation. Of course what we get depends on how we translate. In fact, in this paper we introduce probabilistic semantics to abstract argumentation theory based on the equational approach to argumentation networks. We then compare our semantics with existing proposals in the literature including the approaches by M. Thimm and by A. Hunter. Our methodology in general is discussed in the conclusion

A Labelling Framework for Probabilistic Argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature

Argumentation and Logic Programming for Explainable and Ethical AI

In this paper we sketch a vision of explainability of intelligent systems as a logic approach suitable to be injected into and exploited by the system actors once integrated with sub-symbolic techniques. In particular, we show how argumentation could be combined with different extensions of logic programming – namely, abduction, inductive logic programming, and probabilistic logic programming – to address the issues of explainable AI as well as to address some ethical concerns about AI

Explainable and Ethical AI: A Perspective on Argumentation and Logic Programming

In this paper we sketch a vision of explainability of intelligent systems as a logic approach suitable to be injected into and exploited by the system actors once integrated with sub-symbolic techniques. In particular, we show how argumentation could be combined with different extensions of logic programming – namely, abduction, inductive logic programming, and probabilistic logic programming – to address the issues of explainable AI as well as some ethical concerns about AI