Background and techniques for formalizing deductive argumentation in a logic-based framework for artificial intelligence. Logic-based formalizations of argumentation, which assume a set of formulae and then lay out arguments and counterarguments that can be obtained from these formulae, have been refined in recent years in an attempt to capture more closely real-world practical argumentation. In Elements of Argumentation, Philippe Besnard and Anthony Hunter introduce techniques for formalizing deductive argumentation in artificial intelligence, emphasizing emerging formalizations for practical argumentation. Besnard and Hunter discuss how arguments can be constructed, how key intrinsic and extrinsic factors can be identified, and how these analyses can be harnessed for formalizing argumentation for use in real-world problem analysis and decision making. The book focuses on a monological approach to argumentation, in which there is a set of possibly conflicting pieces of information (each represented by a formula) that has been collated by an agent or a pool of agents. The role of argumentation is to construct a collection of arguments and counterarguments pertaining to some particular claim of interest to be used for analysis or presentation. Elements of Argumentation is the first book to elucidate and formalize key elements of deductive argumentation. It will be a valuable reference for researchers in computer science and artificial intelligence and of interest to scholars in such fields as logic, philosophy, linguistics, and cognitive science.

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.

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