In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argument-based frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper presents Possibilistic Logic Programming (P-DeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on Gödel fuzzy logic. One of the applications of P-DeLP is providing an intelligent agent with non-monotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two non-monotonic operators which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studied.Key words: Possibilistic logic, vague knowledge, defeasible argumentation, intelligent systems 1 This paper revises and extends two previous authors' papers [20] and [22].

Twitter has become a widely used social network to discuss ideas about many domains. This leads to a growing interest in understanding what are the major accepted or rejected opinions in different domains by social network users. At the same time, checking what are the topics that produce the most controversial discussions among users can be a good tool to discover topics that can be divisive, what can be useful, e.g., for policy makers. With the aim to automatically discover such information from Twitter discussions, we present an analysis system based on Valued Abstract Argumentation to model and reason about the accepted and rejected opinions. We consider different schemes to weight the opinions of Twitter users, such that we can tune the relevance of opinions considering different information sources from the social network. Towards having a fully automatic system, we also design a relation labeling system for discovering the relation between opinions. Regarding the underlying acceptability semantics, we use ideal semantics to compute accepted/rejected opinions. We define two measures over sets of accepted and rejected opinions to quantify the most controversial discussions. In order to validate our system, we analyze different real Twitter discussions from the political domain. The results show that different weighting schemes produce different sets of socially accepted opinions and that the controversy measures can reveal significant differences between discussions.

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Abstract. We present a new branch and bound algorithm for Max-SAT which incorporates original lazy data structures, a new variable selection heuristics and a lower bound of better quality. We provide experimental evidence that our solver outperforms some of the best performing Max-SAT solvers on a wide range of instances.