Complexity classifications for nonmonotonic reasoning and enumeration

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Artificial intelligence and its application in architectural design

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Complexity classifications for Propositional Abduction in Post's framework

International audienceIn this article, we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behaviour, it aims at finding an explanation for some observed manifestation. In this article, we consider propositional abduction, where the knowledge base and the manifestation are represented by propositional formulae. The problem of deciding whether there exists an explanation has been shown to be Sigma(p)(2)-complete in general. We focus on formulae in which the allowed connectives are taken from certain sets of Boolean functions. We consider different variants of the abduction problem in restricting both the manifestations and the hypotheses. For all these variants, we obtain a complexity classification for all possible sets of Boolean functions. In this way, we identify easier cases, namely NP-complete, coNP-complete and polynomial cases. Thus, we get a detailed picture of the complexity of the propositional abduction problem, hence highlighting the sources of intractability. Further, we address the problem of counting the full explanations and prove a trichotomous classification theorem

Sticks and Stones May Break My Bones but Words Will Never Hurt Me...Until I See Them: A Qualitative Content Analysis of Trolls in Relation to the Gricean Maxims and (IM)Polite Virtual Speech Acts

The troll is one of the most obtrusive and disruptive bad actors on the internet. Unlike other bad actors, the troll interacts on a more personal and intimate level with other internet users. Social media platforms, online communities, comment boards, and chatroom forums provide them with this opportunity. What distinguishes these social provocateurs from other bad actors are their virtual speech acts and online behaviors. These acts aim to incite anger, shame, or frustration in others through the weaponization of words, phrases, and other rhetoric. Online trolls come in all forms and use various speech tactics to insult and demean their target audiences. The goal of this research is to investigate trolls\u27 virtual speech acts and the impact of troll-like behaviors on online communities. Using Gricean maxims and politeness theory, this study seeks to identify common vernacular, word usage, and other language behaviors that trolls use to divert the conversation, insult others, and possibly affect fellow internet users’ mental health and well-being

Complexy classifications for nonmonotonic reasoning and enumeration

Nous considérons dans cette thèse la complexité algorithmique de problèmes émanant de deux formalismes de raisonnement non-monotone: l'abduction et l'argumentation. Le premier est destiné à formaliser le processus de trouver des explications pour une manifestation observée, le second (et plus récent) offre un cadre théorique pour formaliser le processus de l'argumentation. Nous nous concentrons sur le problème d'existence d'une explication pour l'abduction et sur le problème d'existence d'un argument pour l'argumentation. Dans le cadre de la logique propositionnelle dans son ensemble ces problèmes sont considérés comme étant des tâches algorithmiques difficiles (ils sont souvent situés au deuxième niveau de l'hiérarchie polynomial). Notre but est d'une part de comprendre les sources de difficulté, et d'autre part d'identifier des fragments de la logique propositionnelle dans lequels ces problèmes sont résolubles efficacement. Pour cela nous considérons ces problèmes d'abduction et d'argumentation dans deux cadres bien-établis qui permettent des classifications de complexité : Le cadre de Post et celui de Schaefer. Dans le cadre de Post, des restrictions sont faites sur les connecteurs autorisés dans les formules utilisées. Dans le cadre de Schaefer, on considère les formules en forme normale conjonctive généralisée, les "clauses" sont alors des applications de relations booléennes à des variables et on restreint le type des relations autorisées.In this thesis we consider the computational complexity of problems from two central formalisms of nonmonotonic reasoning: abduction and argumentation. The first one is designed to formalize the process of finding explanations for some observed manifestation, the second (and more recent) one gives a theoretical framework to formalize the process of argumentation. We focus on the explanation-existence problem for abduction and on the argument-existence problem for argumentation. Considered in full propositional logic these problems are believed to be computationally costly tasks (they are often situated at the second level of the polynomial hierarchy). With the purpose of understanding sources of hardness and of identifying tractable fragments of propositional logic we consider several abduction and argumentation problems in two well-established settings allowing for complexity classifications. In the first one, Post's Framework, restrictions are made on the allowed connectives in the used formulae, whereas in the second one, Schaefer's Framework, one considers formulae in conjunctive normal form, where the clauses are generalized to applications of arbitrary Boolean relations to variables and one restricts the allowed type of relations. We discuss differences and common features between the explanation-existence and the argument-existence problem in function of the two chosen frameworks. Finally, we consider enumeration. In particular we consider the problem of enumerating all solutions (models) of a propositional formula by non-decreasing weight in Schaefer's framework (the weight of a model being the number of variables assigned to true)