Forgetting an Argument

in Proceedings of the AAAI Conference on Artificial Intelligence (2020)

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming ... [more ▼]

The notion of forgetting, as considered in the famous paper by Lin and Reiter in 1994 has been extensively studied in classical logic and more recently, in non-monotonic formalisms like logic programming. In this paper, we convey the idea of forgetting to another major AI formalism, namely Dung-style argumentation frameworks. Our approach is axiomatic-driven and not limited to any specific semantics: we propose semantical and syntactical desiderata encoding different criteria for what forgetting an argument might mean; analyze how these criteria relate to each other; and check whether the criteria can be satisfied in general. The analysis is done for a number of widely used argumentation semantics. Our investigation shows that almost all desiderata are individually satisfiable. However, combinations of semantical and/or syntactical conditions reveal a much more interesting landscape. For instance, we found that the ad hoc approach to forgetting an argument, i.e., by the syntactical removal of the argument and all of its associated attacks, is too restrictive and only compatible with the two weakest semantical desiderata. Amongst the several interesting combinations identified, we showed that one satisfies a notion of minimal change and presented an algorithm that given an AF F and argument x, constructs a suitable AF G satisfying the conditions in the combination. [less ▲]

Further Applications of the Gabbay-Rodrigues Iteration Schema in Argumentation and Revision Theories

in Computational Models of Rationality, Essays dedicated to Gabriele Kern-Isberner on the occasion of her 60th birthday (2016)

Probabilistic Argumentation. An Equational Approach

in Logica Universalis (2015), abs/1503.05501

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 ... [more ▼]

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 hS, R i 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. [less ▲]

An equational approach to the merging of argumentation networks

in Journal of Logic and Computation (2014), 24(6), 1253--1277

A Numerical Approach to the Merging of Argumentation Networks

in Fisher, Michael; Torre, Leon; Dastani, Mehdi (Eds.) et al Computational Logic in Multi-Agent Systems (2012)

In this paper, we propose a numerical approach to the problem of merging of argumentation networks. The idea is to consider an augmented network containing the arguments and attacks of all networks to be ... [more ▼]

In this paper, we propose a numerical approach to the problem of merging of argumentation networks. The idea is to consider an augmented network containing the arguments and attacks of all networks to be merged and then associate a weight to each of its components based on how they are perceived by the agents associated with the local networks. The combined weighted network is then used to define a system of equations from which the overall strength of the arguments is calculated. [less ▲]

Belief Revision

in Handbook of Philosophical Logic (2008)