Argumentation Frameworks as Constraint Satisfaction Problems

This paper studies how to encode the problem of computing the extensions of an argumentation framework (under a given semantics) as a constraint satisfaction problem (CSP). Such encoding is of great importance since it makes it possible to use the very efficient solvers (developed by the CSP community) for computing the extensions. We focus on three families of frameworks: Dung’s abstract framework, its constrained version and preference-based argumentation frameworks

Arguing satisfaction of security requirements

This chapter presents a process for security requirements elicitation and analysis, based around the construction of a satisfaction argument for the security of a system. The process starts with the enumeration of security goals based on assets in the system, then uses these goals to derive security requirements in the form of constraints. Next, a satisfaction argument for the system is constructed, using a problem-centered representation, a formal proof to analyze properties that can be demonstrated, and structured informal argumentation of the assumptions exposed during construction of the argument. Constructing the satisfaction argument can expose missing and inconsistent assumptions about system context and behavior that effect security, and a completed argument provides assurances that a system can respect its security requirements

Explanation for case-based reasoning via abstract argumentation

Case-based reasoning (CBR) is extensively used in AI in support of several applications, to assess a new situation (or case) by recollecting past situations (or cases) and employing the ones most similar to the new situation to give the assessment. In this paper we study properties of a recently proposed method for CBR, based on instantiated Abstract Argumentation and referred to as AA-CBR, for problems where cases are represented by abstract factors and (positive or negative) outcomes, and an outcome for a new case, represented by abstract factors, needs to be established. In addition, we study properties of explanations in AA-CBR and define a new notion of lean explanations that utilize solely relevant cases. Both forms of explanations can be seen as dialogical processes between a proponent and an opponent, with the burden of proof falling on the proponent

Generalising tractable VCSPs defined by symmetric tournament pair multimorphisms

We study optimisation problems that can be formulated as valued constraint satisfaction problems (VCSP). A problem from VCSP is characterised by a \emph{constraint language}, a fixed set of cost functions taking finite and infinite costs over a finite domain. An instance of the problem is specified by a sum of cost functions from the language and the goal is to minimise the sum. We are interested in \emph{tractable} constraint languages; that is, languages that give rise to VCSP instances solvable in polynomial time. Cohen et al. (AIJ'06) have shown that constraint languages that admit the MJN multimorphism are tractable. Moreover, using a minimisation algorithm for submodular functions, Cohen et al. (TCS'08) have shown that constraint languages that admit an STP (symmetric tournament pair) multimorphism are tractable. We generalise these results by showing that languages admitting the MJN multimorphism on a subdomain and an STP multimorphisms on the complement of the subdomain are tractable. The algorithm is a reduction to the algorithm for languages admitting an STP multimorphism.Comment: 14 page

Belief Revision in Structured Probabilistic Argumentation

In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data with varying degrees of uncertainty attached. Likewise, an important aspect of the effort associated with maintaining knowledge bases is deciding what information is no longer useful; pieces of information (such as intelligence reports) may be outdated, may come from sources that have recently been discovered to be of low quality, or abundant evidence may be available that contradicts them. In this paper, we propose a probabilistic structured argumentation framework that arises from the extension of Presumptive Defeasible Logic Programming (PreDeLP) with probabilistic models, and argue that this formalism is capable of addressing the basic issues of handling contradictory and uncertain data. Then, to address the last issue, we focus on the study of non-prioritized belief revision operations over probabilistic PreDeLP programs. We propose a set of rationality postulates -- based on well-known ones developed for classical knowledge bases -- that characterize how such operations should behave, and study a class of operators along with theoretical relationships with the proposed postulates, including a representation theorem stating the equivalence between this class and the class of operators characterized by the postulates