Probabilistic Argumentation: An Equational Approach

Abstract

Abstract. 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 S, R 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.

The attack as strong negation, part I

“…There are many papers on probabilistic argumentation. Our paper [18] offers a comprehensive approach based on probability models of classical logic. We shall therefore compare the probabilistic use of CN with the approach in [18].…”

“…The main difference is that we are giving probabilities to 2-valued models in [18] and using CN we are using 3-valued models.…”

A labelling framework for probabilistic argumentation

“…Besides the constellations approach, other works interpret probabilities associated with abstract arguments according to the epistemic approach which is originally introduced in [59] and further developed in [29,30]. An equational approach to probabilistic abstract argumentation which bears some similarity with the epistemic approach of [59] is studied in [20], where a syntactical and a semantical method to the definition of the probabilities of arguments are proposed. [4] explored an alternative setting for epistemic probabilities in abstract argumentation by using De Finetti's theory of subjective probabilities [10] rather than Kolmogorov's axiomatization.…”

Probabilistic Reasoning with Abstract Argumentation Frameworks

“…• In the epistemic approach, the topology of the argument graph is fixed, but there is uncertainty about whether an argument is believed (Thimm, 2012;Hunter, 2013;Baroni, Giacomin, & Vicig, 2014;Hunter, 2014bHunter, , 2014aHunter & Thimm, 2014d, 2014bHunter, 2015;Gabbay & Rodrigues, 2015;Hunter, 2016aHunter, , 2016b. A core idea of the epistemic approach is that the more likely an agent is to believe in an argument, the less likely it is to believe in an argument attacking it.…”

“…Dung and Thang (2010) provided the first proposal to extend abstract argumentation with a probability distribution over sets of arguments which they use with a version of assumption-based argumentation in which a subset of the rules are probabilistic rules. Another approach to augmenting abstract argumentation with probabilities has used equations based on the structure of the graph to constrain the probability assignments, and these can be solved to calculate probabilities (Gabbay & Rodrigues, 2015). In another rule-based system for argumentation, the belief in the premises of an argument is used to calculate the belief in the argument (Riveret, Rotolo, Sartor, Prakken, & Roth, 2007).…”