In online debates, as in offline ones, individual utterances or arguments support or attack each other, leading to some subset of arguments winning (potentially from different sides of the debate). However, online conversations are much larger in scale than offline ones, with often hundreds of thousands of users weighing in, and so, readers are often forced to sample a subset of the arguments or arguments being put forth. Since such sampling is rarely done in a principled manner, users may not get all the relevant "winning" arguments to get a full picture of the debate from a sample. This paper is interested in answering the question of how users should sample online conversations to selectively favour winning arguments. We apply techniques from argumentation theory and complex networks to build a model that predicts the probabilities of the normatively winning arguments given their location in idealised online discussions. Online discussions are modeled as reply networks where nodes represent the comments exchanged and directed edges represent replies that can either be supporting or attacking. Our model shows that the proportion of replies that are supporting in the network, the network's in-degree distribution and the locations of unrebutted arguments ("the last words") all determine the behaviour of the probability that a comment is a winning argument given its location. This is also verified with data scraped from the online debating platform Kialo. In predicting the locations of the winning arguments in reply networks, we can therefore suggest which arguments a reader should sample and read if he or she would like to grasp the winning opinions in such discussions. Our models have important implications for the design of future online discussion platforms.
Given our arguments @math and their disagreements @math , how can a subset of arguments be seen as winning''? The two basic requirements is that no pair of arguments in such a set are attacking (a consistency requirement), and that this set of arguments can defend itself from outside attacks @cite_29 . More precisely, given an argumentation framework @math , let @math and @math . We say @math is iff no two arguments in @math attack each other. Graph-theoretically, conflict-free sets are independent sets. We say @math or an argument @math iff every attacker of @math is in turn attacked by some argument in @math . We say @math is iff for all @math , @math is defended by @math . We say @math is iff @math is conflict-free and self-defending.
@cite_29
1825730661 2949121808 2078438690 2072643736
Abstract We explore a framework for argumentation (based on classical logic) in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item (which is a formula). We provide some basic definitions for arguments, and various kinds of counter-arguments (defeaters). This leads us to the definition of canonical undercuts which we argue are the only defeaters that we need to take into account. We then motivate and formalise the notion of argument trees and argument structures which provide a way of exhaustively collating arguments and counter-arguments. We use argument structures as the basis of our general proposal for argument aggregation. There are a number of frameworks for modelling argumentation in logic. They incorporate formal representation of individual arguments and techniques for comparing conflicting arguments. In these frameworks, if there are a number of arguments for and against a particular conclusion, an aggregation function determines whether the conclusion is taken to hold. We propose a generalisation of these frameworks. In particular, our new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against. We compare our framework with a number of other types of argument systems, and finally discuss an application in reasoning with structured news reports. Let @math be a @math -ary predicate over a finite alphabet. Consider a random CSP @math instance @math over @math variables with @math constraints. When @math the instance @math will be unsatisfiable with high probability, and we want to find a refutation - i.e., a certificate of unsatisfiability. When @math is the @math -ary OR predicate, this is the well studied problem of refuting random @math -SAT formulas, and an efficient algorithm is known only when @math . Understanding the density required for refutation of other predicates is important in cryptography, proof complexity, and learning theory. Previously, it was known that for a @math -ary predicate, having @math constraints suffices for refutation. We give a criterion for predicates that often yields efficient refutation algorithms at much lower densities. Specifically, if @math fails to support a @math -wise uniform distribution, then there is an efficient algorithm that refutes random CSP @math instances @math whp when @math . Indeed, our algorithm will "somewhat strongly" refute @math , certifying @math , if @math then we get the strongest possible refutation, certifying @math . This last result is new even in the context of random @math -SAT. Regarding the optimality of our @math requirement, prior work on SDP hierarchies has given some evidence that efficient refutation of random CSP @math may be impossible when @math . Thus there is an indication our algorithm's dependence on @math is optimal for every @math , at least in the context of SDP hierarchies. Along these lines, we show that our refutation algorithm can be carried out by the @math -round SOS SDP hierarchy. Finally, as an application of our result, we falsify assumptions used to show hardness-of-learning results in recent work of Daniely, Linial, and Shalev-Shwartz. 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. Given a semantics @s, two argumentation frameworks (AFs) F and G are said to be standard equivalent if they possess the same extensions and strongly equivalent if, for any AF H, F conjoined with H and G conjoined with H are standard equivalent. Argumentation is a dynamic process and, in general, new arguments occur in response to a former argument or, more precisely, attack a former argument. For this reason, rather than considering arbitrary expansions we focus here on expansions where new arguments and attacks may be added but the attacks among the old arguments remain unchanged. We define and characterize two new notions of equivalence between AFs (which lie in-between standard and strong equivalence), namely normal and strong expansion equivalence. Furthermore, using the characterization theorems proved in this paper, we draw the connections between all mentioned notions of equivalence including further equivalence relations, so-called weak and local expansion equivalence.