Computing Probabilistic Assumption-Based Argumentation
We develop inference procedures for a recently proposed model of probabilistic argumentation called PABA, taking advantages of well-established dialectical proof procedures for Assumption-based Argumentation and Bayesian Network algorithms. We establish t
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Abstract. We develop inference procedures for a recently proposed model of probabilistic argumentation called PABA, taking advantages of well-established dialectical proof procedures for Assumption-based Argumentation and Bayesian Network algorithms. We establish the soundness and termination of our inference procedures for a general class of PABA frameworks. We also discuss how to translate other models of probabilistic argumentation into this class of PABA frameworks so that our inference procedures can be used for these models as well.
Keywords: Probabilistic argumentation Bayesian networks
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Inference procedures
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Introduction
Standard Abstract Argumentation (AA [3]) is inadequate in capturing argumentation processes involved probabilities such as the following. Example 1 (Borrowed from [5]). John sued Henry for the damage caused to him when he drove off the road to avoid hitting Henry’s cow. – John: Henry should pay damage because Henry is the owner of the cow and the cow caused the accident (J1 ). – Henry: John was negligent as evidences at the accident location show that John was driving fast. Hence the cow was not the cause of the accident (H1 ). Let’s try to construct an AA framework F = (AR, Att) to represent the judge’s beliefs. The judge may consider J1 as an argument proper, but not H1 because according to him, the evidences at the accident location gives only some probability (p0 ) that John was driving fast; and even if John was driving fast, the accident is caused by his fast-driving with some other probability p1 . Hence while the representation of J1 is quite simple: J1 ∈ AR, there is no perfect representation for H1 . H1 ∈ AR (resp. H1 ∈ AR) would mean that the judge would undoubtedly find for John (resp. Henry). However, in fact the chance that a party wins depends on the values that the judge assigns to p0 and p1 . c Springer International Publishing Switzerland 2016 R. Booth and M.-L. Zhang (Eds.): PRICAI 2016, LNAI 9810, pp. 152–166, 2016. DOI: 10.1007/978-3-319-42911-3 13
Computing Probabilistic Assumption-Based Argumentation
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To remedy the above situation, several authors extend AA with probability theory, resulting in different models of Probabilistic Argumentation. Of our interest is the Probabilistic Assumption-based Argumentation framework of [5] (P ABA) extending an instance of AA called Assumption-based Argumentation (ABA [2,4]). To anchor our contributions, let’s loosely recall some technicalities. An ABA framework comprises inference rules in the form c ← b1 , . . . bn , representing that proposition c holds whenever propositions b1 , . . . bn hold (bi can be an assumption but not c). An P ABA framework is a triple (Ap , Rp , F) where Ap is a set of (positive) probabilistic assumptions, Rp is a set of probabilistic rules and F is an ABA framework. A probabilistic rule in P ABA also has the same form as an inference rule, except that its head is a proposition of the form [α : x] representing that the probability of probabilistic assumption α is x. Example 2 (Cont. Exa
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