Epistemic graphs for representing and reasoning with positive and negative influences of arguments

Abstract

This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine-grained alternative to the standard Dung's approaches when it comes to determining the status of a given argument. Furthermore, the flexibility of the epistemic approach allows us to both model the rationale behind the existing semantics as well as completely deviate from them when required. Epistemic graphs can model both attack and support as well as relations that are neither support nor attack. The way other arguments influence a given argument is expressed by the epistemic constraints that can restrict the belief we have in an argument with a varying degree of specificity. The fact that we can specify the rules under which arguments should be evaluated and we can include constraints between unrelated arguments permits the framework to be more context-sensitive. It also allows for better modelling of imperfect agents, which can be important in multi-agent applications.Example 3 (Adapted from [23,24]). The work in [23] has investigated the problem of reinstatement in argumentation using an instantiated theory and preferences. We draw attention to two scenarios considered in the study, concerning weather forecast and car purchase, where each comes in the basic (without the last sentence) and extended (full text) version.The weather forecasting service of the broadcasting company AAA says that it will rain tomorrow. Meanwhile, the forecast service of the broadcasting company BBB says that it will be cloudy tomorrow but that it will not rain. It is also well known that the forecasting service of BBB is more accurate than the one of AAA. However, yesterday the trustworthy newspaper CCC published an article which said that BBB has cut the resources for its weather forecasting service in the past months, thus making it less reliable than in the past.You are planning to buy a second-hand car, and you go to a dealership with BBB, a mechanic whom has been recommended you by a friend. The salesperson AAA shows you a car and says that it needs very little work done to it. BBB says it will require quite a lot of work, because in the past he had to fix several issues in a car of the same model. While you are at the dealership, your friend calls you to tell you that he knows (beyond a shadow of a doubt) that BBB made unnecessary repairs to his car last month.The formal representation of the base (resp. extended) versions of these scenarios is equivalent (we refer to [23,24] for more details). However, the findings show that they are not judged in the same way and suggest that the domain dependent knowledge of the participants has affected their performance of the tasks. This shows the importance of modelling context-sensitivity and allowing an agent to evaluate structurally equivalent graphs differently.

A polynomial-time fragment of epistemic probabilistic argumentation

“…When we consider support edges, new constraints are necessary. In [29], a general constraint language has been introduced that allows expressing the previous constraints, but also more flexible constraints that can take account of support relations or of both support and attack relations simultaneously. In particular, constraints can contain complex formulas of arguments and constraints can be connected via logical connectives.…”

“…We explain the epistemic probabilistic argumentation approach from [26,31,56] in more detail in Section 2 and introduce a slight generalization of the computational problems considered in [31]. Even more general variants of these problems have been considered in [29], but these variants are too general to obtain polynomial runtime guarantees as we will explain in Section 6 and 7 . In Section 4, we show that reasoning with probability labellings is equivalent to reasoning with probability functions when only atomic probability statements are considered and use this observation to show that both the satisfiability and the entailment problem considered in [31] and their generalizations can be solved in polynomial time.…”

Polynomial-Time Updates of Epistemic States in a Fragment of Probabilistic Epistemic Argumentation

“…The epistemic probabilistic argumentation approach developed in [40,13,20,18] defines semantics of attack and support relations by means of constraints over probability functions. Some constraints can be automatically derived from the relations between arguments.…”

“…To allow this flexibility, a general constraint language has been introduced in [18,17]. We will focus on the fragment of linear atomic constraints here because it is sufficiently expressive for most of the constraints considered in [40,13,20] and sometimes allows polynomial-time computations [34].…”

“…Probabilistic epistemic argumentation [40,13,20,18] is an extension of Dung's classical argumentation framework [8]. While the original framework allows only for talking about attacks and accepting or rejecting arguments, probabilistic epistemic argumentation also allows more general relationships between arguments like support [5,30,6] and allows expressing more fine-grained beliefs by means of probabilities.…”