A probabilistic approach to modelling uncertain logical arguments

Abstract

Argumentation can be modelled at an abstract level using a directed graph where each node denotes an argument and each arc denotes an attack by one argument on another. Since arguments are often uncertain, it can be useful to quantify the uncertainty associated with each argument. Recently, there have been proposals to extend abstract argumentation to take this uncertainty into account. This assigns a probability value for each argument that represents the degree to which the argument is believed to hold, and this is then used to generate a probability distribution over the full subgraphs of the argument graph, which in turn can be used to determine the probability that a set of arguments is admissible or an extension. In order to more fully understand uncertainty in argumentation, in this paper, we extend this idea by considering logic-based argumentation with uncertain arguments. This is based on a probability distribution over models of the language, which can then be used to give a probability distribution over arguments that are constructed using classical logic. We show how this formalization of uncertainty of logical arguments relates to uncertainty of abstract arguments, and we consider a number of interesting classes of probability assignments.

Generalizations of Dung Frameworks and Their Role in Formal Argumentation

“…Concerning preferences, such further works include audience specific argumentation frameworks in which arguments can promote multiple values [46], uniform argumentation frameworks [7], and multi-contextual preference based argumentation frameworks [18]. Other generalizations incorporate probabilities [44,63] and certain forms of weights [32,35,47]. Concerning the frameworks focusing on generalizing the relations between arguments, we mention here three further representatives.…”

Constructing argument graphs with deductive arguments: a tutorial

“…With this definition more practical argument graphs can be constructed than with the definition for classical exhaustive graphs. Furthermore, using an appropriate definition for the preference relation, the definition for preference exhaustive graphs is structurally complete for graphs, and for some choices of preference relation and dialectical semantics, the consistent extension property holds (see, for example, the use of probability theory for obtaining preferences over arguments by Hunter 2013).…”

“…There have been a number of proposals for deductive arguments using classical propositional logic (Amgoud & Cayrol 2002, Besnard & Hunter 2001, Cayrol 1995, Gorogiannis & Hunter 2011, classical predicate logic (Besnard & Hunter 2005), description logic (Black, Hunter, & Pan 2009;Moguillansky, Wassermann, & Falappa 2010;Zhang & Lin 2013;Zhang, Zhang, Xu, & Lin 2010), temporal logic (Mann & Hunter 2008), simple (defeasible) logic (Governatori, Maher, Antoniou, & Billington 2004;Hunter 2010), conditional logic (Besnard, Gregoire, & Raddaoui 2013), and probabilistic logic (Haenni 1998, Haenni 2001, Hunter 2013). …”

Knowledge Science, Engineering and Management

“…Probabilistic approaches for modeling uncertainty in argumentation include the constellations approach and the epistemic approach [4]. The first is based on a probability distribution over the subgraphs of the argument graph ( [3] which extends [1] and [7]), and this can be used to represent the uncertainty over the structure of the graph (i.e.…”

“…whether a particular argument or attack appears in the argument graph under consideration). The second approach is the epistemic approach which involves a probability distribution over the subsets of the arguments [4,6,10]. This can be used to represent the uncertainty over which arguments are believed.…”