SAT for argumentation

Peer reviewe

Summary Report of The First International Competition on Computational Models of Argumentation

Computational models of argumentation are an active research discipline within Artificial Intelligence that has grown since the beginning of the 1990s (Dung 1995). While still a young field when compared to areas such as SAT solving and Logic Programming, the argumentation community is very active, with a conference series (COMMA, which began in 2006) and a variety of workshops and special issues of journals. Argumentation has also worked its way into a variety of applications. For example, Williams et al. (2015) described how argumentation techniques are used for recommending cancer treatments, while Toniolo et al. (2015) detail how argumentation-based techniques can support critical thinking and collaborative scientific inquiry or intelligence analysis. Many of the problems that argumentation deals with are computationally difficult, and applications utilising argumentation therefore require efficient solvers. To encourage this line of research, we organised the First International Competition on Computational Models of Argumentation (ICCMA), with the intention of assessing and promoting state of the art solvers for abstract argumentation problems, and to identify families of challenging benchmarks for such solvers. The objective of ICCMA’15 is to allow researchers to compare the performance of different solvers systematically on common benchmarks and rules. Moreover, as witnessed by competitions in other AI disciplines such as planning and SAT solving, we see ICCMA as a new pillar of the community which provides information and insights on the current state of the art, and highlights future challenges and developments. This article summarises the first ICCMA held in 2015 (ICCMA’15). In this competition, solvers were invited to address standard decision and enumeration problems of abstract argumentation frameworks (Dunne and Wooldridge 2009). Solvers’ performance is evaluated based on their time taken to provide a correct solution for a problem; incorrect results were discarded. More information about the competition, including complete results and benchmarks, can be found on the ICCMA website

A Preference-Based Approach to Backbone Computation with Application to Argumentation

The backbone of a constraint satisfaction problem consists of those variables that take the same value in all solutions. Algorithms for determining the backbone of propositional formulas, i.e., Boolean satisfiability (SAT) instances, find various real-world applications. From the knowledge representation and reasoning (KRR) perspective, one interesting connection is that of backbones and the so-called ideal semantics in abstract argumentation. In this paper, we propose a new backbone algorithm which makes use of a "SAT with preferences" solver, i.e., a SAT solver which is guaranteed to output a most preferred satisfying assignment w.r.t. a given preference over literals of the SAT instance at hand. We also show empirically that the proposed approach is specifically effective in computing the ideal semantics of argumentation frameworks, noticeably outperforming an other state-of-the-art backbone solver as well as the winning approach of the recent ICCMA 2017 argumentation solver competition in the ideal semantics track.Peer reviewe

Self-reported price of cigarettes, consumption and compensatory behaviours in a cohort of Mexican smokers before and after a cigarette tax increase

This paper presents a novel SAT-based approach for the computation of extensions in abstract argumentation, with focus on preferred semantics, and an empirical evaluation of its performances. The approach is based on the idea of reducing the problem of computing complete extensions to a SAT problem and then using a depth-first search method to derive preferred extensions. The proposed approach has been tested using two distinct SAT solvers and compared with three state-of-the-art systems for preferred extension computation. It turns out that the proposed approach delivers significantly better performances in the large majority of the considered cases

A principled approach to the implementation of argumentation models

Argumentation theory combines philosophical concepts and computational models to deliver a practical approach to reasoning that handles uncertain information and possibly conflicting viewpoints. This paper focuses on the structured approach to argumentation that incorporates domain specific knowledge and argumentation schemes. There is a lack of implementations and implementation methods for most structured models. This paper shows how taking a principled approach, using the programming language Haskell, helps addressing this problem. We construct a framework for developing structured argumentation models and translations between models (given intertranslatability of models). We furthermore provide a methodology to quickly test and formally prove desirable properties of such implementations using a theorem prover. We demonstrate our approach on the Carneades argumentation model and Dung's abstract argumentation frameworks, implementing both the models and a translation from Carneades into AFs. We then provide implementations of correspondence properties and an initial formalisation of Dung's AFs into a theorem prover. The final result is a verified pipeline from the structured model Carneades into existing efficient SAT-based implementations of Dung's AFs

Algorithms for Dynamic Argumentation Frameworks: An Incremental SAT-Based Approach

Peer reviewe

How we designed winning algorithms for abstract argumentation and which insight we attained

In this paper we illustrate the design choices that led to the development of ArgSemSAT, the winner of the preferred semantics track at the 2017 International Competition on Computational Models of Arguments (ICCMA 2017), a biennial contest on problems associated to the Dung’s model of abstract argumentation frameworks, widely recognised as a fundamental reference in computational argumentation. The algorithms of ArgSemSAT are based on multiple calls to a SAT solver to compute complete labellings, and on encoding constraints to drive the search towards the solution of decision and enumeration problems. In this paper we focus on preferred semantics (and incidentally stable as well), one of the most popular and complex semantics for identifying acceptable arguments. We discuss our design methodology that includes a systematic exploration and empirical evaluation of labelling encodings, algorithmic variations and SAT solver choices. In designing the successful ArgSemSAT, we discover that: (1) there is a labelling encoding that appears to be universally better than other, logically equivalent ones; (2) composition of different techniques such as AllSAT and enumerating stable extensions when searching for preferred semantics brings advantages; (3) injecting domain specific knowledge in the algorithm design can lead to significant improvements

Counting Complexity for Reasoning in Abstract Argumentation

In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1