Other uncertainty theories based on capacities

International audienceThe two main uncertainty representations in the literature that tolerate imprecision are possibility distributions and random disjunctive sets. This chapter devotes special attention to the theories that have emerged from them. The first part of the chapter discusses epistemic logic and derives the need for capturing imprecision in information representations. It bridges the gap between uncertainty theories and epistemic logic showing that imprecise probabilities subsume modalities of possibility and necessity as much as probability. The second part presents possibility and evidence theories, their origins, assumptions and semantics, discusses the connections between them and the general framework of imprecise probability. Finally, chapter points out the remaining discrepancies between the different theories regarding various basic notions, such as conditioning, independence or information fusion and the existing bridges between them

Computational Complexity of Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments arecalled semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. Recently, the notion of strong admissibility has been introduced for ADFs. In the current work we study the computational complexityof the following reasoning tasks under strong admissibility semantics. We address 1. the credulous/skeptical decision problem; 2. the verification problem; 3. the strong justification problem; and 4. the problem of finding a smallest witness of strong justification of a queried argument

Possibilistic decision theory: from theoretical foundations to influence diagrams methodology

Le domaine de prise de décision est un domaine multidisciplinaire en relation avec plusieurs disciplines telles que l'économie, la recherche opérationnelle, etc. La théorie de l'utilité espérée a été proposée pour modéliser et résoudre les problèmes de décision. Ces théories ont été mises en cause par plusieurs paradoxes (Allais, Ellsberg) qui ont montré les limites de son applicabilité. Par ailleurs, le cadre probabiliste utilisé dans ces théories s'avère non approprié dans certaines situations particulières (ignorance totale, incertitude qualitative). Pour pallier ces limites, plusieurs travaux ont été élaborés concernant l'utilisation des intégrales de Choquet et de Sugeno comme critères de décision d'une part et l'utilisation d'une théorie d'incertitude autre que la théorie des probabilités pour la modélisation de l'incertitude d'une autre part. Notre idée principale est de profiter de ces deux directions de recherche afin de développer, dans le cadre de la décision séquentielle, des modèles de décision qui se basent sur les intégrales de Choquet comme critères de décision et sur la théorie des possibilités pour la représentation de l'incertitude. Notre objectif est de développer des modèles graphiques décisionnels, qui représentent des modèles compacts et simples pour la prise de décision dans un contexte possibiliste. Nous nous intéressons en particulier aux arbres de décision et aux diagrammes d'influence possibilistes et à leurs algorithmes d'évaluation.The field of decision making is a multidisciplinary field in relation with several disciplines such as economics, operations research, etc. Theory of expected utility has been proposed to model and solve decision problems. These theories have been questioned by several paradoxes (Allais, Ellsberg) who have shown the limits of its applicability. Moreover, the probabilistic framework used in these theories is not appropriate in particular situations (total ignorance, qualitative uncertainty). To overcome these limitations, several studies have been developed basing on the use of Choquet and Sugeno integrals as decision criteria and a non classical theory to model uncertainty. Our main idea is to use these two lines of research to develop, within the framework of sequential decision making, decision models based on Choquet integrals as decision criteria and possibility theory to represent uncertainty. Our goal is to develop graphical decision models that represent compact models for decision making when uncertainty is represented using possibility theory. We are particularly interested by possibilistic decision trees and influence diagrams and their evaluation algorithms

Proceedings of the 11th Workshop on Nonmonotonic Reasoning

These are the proceedings of the 11th Nonmonotonic Reasoning Workshop. The aim of this series is to bring together active researchers in the broad area of nonmonotonic reasoning, including belief revision, reasoning about actions, planning, logic programming, argumentation, causality, probabilistic and possibilistic approaches to KR, and other related topics. As part of the program of the 11th workshop, we have assessed the status of the field and discussed issues such as: Significant recent achievements in the theory and automation of NMR; Critical short and long term goals for NMR; Emerging new research directions in NMR; Practical applications of NMR; Significance of NMR to knowledge representation and AI in general

Coordinated constraint relaxation using a distributed agent protocol

The interactions among agents in a multi-agent system for coordinating a distributed, problem solving task can be complex, as the distinct sub-problems of the individual agents are interdependent. A distributed protocol provides the necessary framework for specifying these interactions. In a model of interactions where the agents' social norms are expressed as the message passing behaviours associated with roles, the dependencies among agents can be specified as constraints. The constraints are associated with roles to be adopted by agents as dictated by the protocol. These constraints are commonly handled using a conventional constraint solving system that only allows two satisfactory states to be achieved - completely satisfied or failed. Agent interactions then become brittle as the occurrence of an over-constrained state can cause the interaction between agents to break prematurely, even though the interacting agents could, in principle, reach an agreement. Assuming that the agents are capable of relaxing their individual constraints to reach a common goal, the main issue addressed by this thesis is how the agents could communicate and coordinate the constraint relaxation process. The interaction mechanism for this is obtained by reinterpreting a technique borrowed from the constraint satisfaction field, deployed and computed at the protocol level.The foundations of this work are the Lightweight Coordination Calculus (LCC) and the distributed partial Constraint Satisfaction Problem (CSP). LCC is a distributed interaction protocol language, based on process calculus, for specifying and executing agents' social norms in a multi-agent system. Distributed partial CSP is an extension of partial CSP, a means for managing the relaxation of distributed, over-constrained, CSPs. The research presented in this thesis concerns how distributed partial CSP technique, used to address over-constrained problems in the constraint satisfaction field, could be adopted and integrated within the LCC to obtain a more flexible means for constraint handling during agent interactions. The approach is evaluated against a set of overconstrained Multi-agent Agreement Problems (MAPs) with different levels of hardness. Not only does this thesis explore a flexible and novel approach for handling constraints during the interactions of heterogeneous and autonomous agents participating in a problem solving task, but it is also grounded in a practical implementation

Graphical preference representation under a possibilistic framework

La modélisation structurée de préférences, fondée sur les notions d'indépendance préférentielle, a un potentiel énorme pour fournir des approches efficaces pour la représentation et le raisonnement sur les préférences des décideurs dans les applications de la vie réelle. Cette thèse soulève la question de la représentation des préférences par une structure graphique. Nous proposons une nouvelle lecture de réseaux possibilistes, que nous appelons p-pref nets, où les degrés de possibilité représentent des degrés de satisfaction. L'approche utilise des poids de possibilité non instanciés (appelés poids symboliques), pour définir les tables de préférences conditionnelles. Ces tables donnent naissance à des vecteurs de poids symboliques qui codent les préférences qui sont satisfaites et celles qui sont violées dans un contexte donné. Nous nous concentrons ensuite sur les aspects théoriques de la manipulation de ces vecteurs. En effet, la comparaison de ces vecteurs peut s'appuyer sur différentes méthodes: celles induites par la règle de chaînage basée sur le produit ou celle basée sur le minimum que sous-tend le réseau possibiliste, les raffinements du minimum le discrimin, ou leximin, ainsi que l'ordre Pareto, et le Pareto symétrique qui le raffine. Nous prouvons que la comparaison par produit correspond exactement au celle du Pareto symétrique et nous nous concentrons sur les avantages de ce dernier par rapport aux autres méthodes. En outre, nous montrons que l'ordre du produit est consistant avec celui obtenu en comparant des ensembles de préférences satisfaites des tables. L'image est complétée par la proposition des algorithmes d'optimisation et de dominance pour les p-pref nets. Dans ce travail, nous discutons divers outils graphiques pour la représentation des préférences. Nous nous focalisons en particulier sur les CP-nets car ils partagent la même structure graphique que les p-pref nets et sont basés sur la même nature de préférences. Nous prouvons que les ordres induits par les CP-nets ne peuvent pas contredire ceux des p-pref nets et nous avons fixé les contraintes nécessaires pour raffiner les ordres des p-pref nets afin de capturer les contraintes Ceteris Paribus des CP-nets. Cela indique que les CP-nets représentent potentiellement une sous-classe des p-pref nets avec des contraintes. Ensuite, nous fournissons une comparaison approfondie entre les différents modèles graphiques qualitatifs et quantitatifs, et les p-pref nets. Nous en déduisons que ces derniers peuvent être placés à mi- chemin entre les modèles qualitatifs et les modèles quantitatifs puisqu'ils ne nécessitent pas une instanciation complète des poids symboliques alors que des informations supplémentaires sur l'importance des poids peuvent être prises en compte. La dernière partie de ce travail est consacrée à l'extension du modèle proposé pour représenter les préférences de plusieurs agents. Dans un premier temps, nous proposons l'utilisation de réseaux possibilistes où les préférences sont de type tout ou rien et nous définissons le conditionnement dans le cas de distributions booléennes. Nous montrons par ailleurs que ces réseaux multi-agents ont une contrepartie logique utile pour vérifier la cohérence des agents. Nous expliquons les étapes principales pour transformer ces réseaux en format logique. Enfin, nous décrivons une extension pour représenter des préférences nuancées et fournissons des algorithmes pour les requêtes d'optimisation et de dominance.Structured modeling of preference statements, grounded in the notions of preferential independence, has tremendous potential to provide efficient approaches for modeling and reasoning about decision maker preferences in real-life applications. This thesis raises the question of representing preferences through a graphical structure. We propose a new reading of possibilistic networks, that we call p-pref nets, where possibility weights represent satisfaction degrees. The approach uses non-instantiated possibility weights, which we call symbolic weights, to define conditional preference tables. These conditional preference tables give birth to vectors of symbolic weights that reflect the preferences that are satisfied and those that are violated in a considered situation. We then focus on the theoretical aspects of handling of these vectors. Indeed, the comparison of such vectors may rely on different orderings: the ones induced by the product-based, or the minimum based chain rule underlying the possibilistic network, the discrimin, or leximin refinements of the minimum- based ordering, as well as Pareto ordering, and the symmetric Pareto ordering that refines it. We prove that the product-based comparison corresponds exactly to symmetric Pareto and we focus on its assets compared to the other ordering methods. Besides, we show that productbased ordering is consistent with the ordering obtained by comparing sets of satisfied preference tables. The picture is then completed by the proposition of algorithms for handling optimization and dominance queries. In this work we discuss various graphical tools for preference representation. We shed light particularly on CP-nets since they share the same graphical structure as p-pref nets and are based on the same preference statements. We prove that the CP-net orderings cannot contradict those of the p-pref nets and we found suitable additional constraints to refine p-pref net orderings in order to capture Ceteris Paribus constraints of CP-nets. This indicates that CP-nets potentially represent a subclass of p-pref nets with constraints. Finally, we provide an thorough comparison between the different qualitative and quantitative graphical models and p-pref nets. We deduce that the latter can be positioned halfway between qualitative and quantitative models since they do not need a full instantiation of the symbolic weights while additional information about the relative strengths of these weights can be taken into account. The last part of this work is dedicated to extent the proposed model to represent multiple agents preferences. As a first step, we propose the use of possibilistic networks for representing all or nothing multiple agents preferences and define conditioning in the case of Boolean possibilities. These multiple agents networks have a logical counterpart helpful for checking agents consistency. We explain the main steps for transforming multiple agents networks into logical format. Finally, we outline an extension with priority levels of these networks and provide algorithms for handling optimization and dominance queries