Inconsistency Management from the Standpoint of Possibilistic Logic

International audienceUncertainty and inconsistency pervade human knowledge. Possibilistic logic, where propositional logic formulas are associated with lower bounds of a necessity measure, handles uncertainty in the setting of possibility theory. Moreover, central in standard possibilistic logic is the notion of inconsistency level of a possibilistic logic base, closely related to the notion of consistency degree of two fuzzy sets introduced by L. A. Zadeh. Formulas whose weight is strictly above this inconsistency level constitute a sub-base free of any inconsistency. However, several extensions, allowing for a paraconsistent form of reasoning, or associating possibilistic logic formulas with information sources or subsets of agents, or extensions involving other possibility theory measures, provide other forms of inconsistency, while enlarging the representation capabilities of possibilistic logic. The paper offers a structured overview of the various forms of inconsistency that can be accommodated in possibilistic logic. This overview echoes the rich representation power of the possibility theory framework

Epistemic extensions of answer set programming

but due to the non-monotonic nature of ASP; the weight can reflect the certainty that the rule itself is correct. ASP programs with incorrect rules may have erroneous conclusions; omitting a correct rule may also lead to errors. To derive the most certain conclusions from an uncertain ASP program; the weight can reflect the certainty with which we can conclude the head of a rule when its body is satisfied. This corresponds with how the weight is understood when defining semantics for PASP in terms of constraints on possibility distributions. On the other hand; we highlight how the weight attached to a rule in PASP can be interpreted in different ways. On the one hand; some decision problems are easier. Thirdly; while the complexity of most reasoning tasks coincides with disjunction in ordinary ASP; called weak disjunction; that has not been previously considered in the ASP literature. When examining the complexity of weak disjunction we unearth that; we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction; since ASP is a special case of PASP in which all the rules are entirely certain; we show how semantics for PASP can be defined in terms of constraints on possibility distributions. These new semantics adhere to a different intuition for negation-as-failure than current work on PASP to avoid unintuitive conclusions in specific settings. In addition; where the first leader has the first say and may remove models that he or she finds unsatisfactory. Using this particular communication mechanism allows us to capture the entire polynomial hierarchy. Secondly; where each program in the sequence may successively remove some of the remaining models. This mimics a sequence of leaders; we modify the communication mechanism to also allow us to focus on a sequence of communicating programs; it is shown that the addition of this easy form of communication allows us to move one step up in the polynomial hierarchy. Furthermore; i.e. they can communicate. For the least complex variant of ASP; simple programs; one ASP program can conceptually query another program as to whether it believes some literal to be true or not; which is a framework that allows us to study the formal properties of communication and the complexity of the resulting system in ASP. It is based on an extension of ASP in which we consider a network of ordinary ASP programs. These communicating programs are extended with a new kind of literal based on the notion of asking questions. As such; we introduce Communicating Answer Set Programming (CASP); namely Possibilistic Answer Set Programming (PASP); there are contexts in which the current semantics for PASP lead to unintuitive results. In this thesis we address these issues in the followings ways. Firstly; ASP lacks the means to easily model and reason about uncertain information. While extensions of ASP have been proposed to deal with uncertainty; where each context encodes a different aspect of the real world. Extensions of ASP have been proposed to model such multi-context systems; but the exact effect of communication on the overall expressiveness remains unclear. In addition; it is not an ideal framework to model common-sense reasoning. For example; in ASP we cannot model multi-context systems; while ASP similarly allows us to revise knowledge; we conclude that the bird can fly. When new knowledge becomes available (e.g. the bird is a penguin) we may need to retract conclusions. However; in common-sense reasoning; Answer Set Programming (ASP) is a declarative programming language based on the stable model semantics and geared towards solving complex combinatorial problems. The strength of ASP stems from the use of a non-monotonic operator. This operator allows us to retract previously made conclusions as new information becomes available. Similarly; we may arrive at conclusions based on the absence of information. When an animal is for example a bird; and we do not know that this bird is a penguin; we thus need to consider all situations in which some; none; or all of the least certain rules are omitted. This corresponds to treating some rules as optional and reasoning about which conclusions remain valid regardless of the inclusion of these optional rules. Semantics for PASP are introduced based on this idea and it is shown that some interesting problems in Artificial Intelligence can be expressed in terms of optional rules. For both CASP and the new semantics for PASP we show that most of the concepts that we introduced can be simulated using classical ASP. This provides us with implementations of these concepts and furthermore allows us to benefit from the performance of state-of-the-art ASP solvers

Belief Change in Reasoning Agents: Axiomatizations, Semantics and Computations

The capability of changing beliefs upon new information in a rational and efficient way is crucial for an intelligent agent. Belief change therefore is one of the central research fields in Artificial Intelligence (AI) for over two decades. In the AI literature, two different kinds of belief change operations have been intensively investigated: belief update, which deal with situations where the new information describes changes of the world; and belief revision, which assumes the world is static. As another important research area in AI, reasoning about actions mainly studies the problem of representing and reasoning about effects of actions. These two research fields are closely related and apply a common underlying principle, that is, an agent should change its beliefs (knowledge) as little as possible whenever an adjustment is necessary. This lays down the possibility of reusing the ideas and results of one field in the other, and vice verse. This thesis aims to develop a general framework and devise computational models that are applicable in reasoning about actions. Firstly, I shall propose a new framework for iterated belief revision by introducing a new postulate to the existing AGM/DP postulates, which provides general criteria for the design of iterated revision operators. Secondly, based on the new framework, a concrete iterated revision operator is devised. The semantic model of the operator gives nice intuitions and helps to show its satisfiability of desirable postulates. I also show that the computational model of the operator is almost optimal in time and space-complexity. In order to deal with the belief change problem in multi-agent systems, I introduce a concept of mutual belief revision which is concerned with information exchange among agents. A concrete mutual revision operator is devised by generalizing the iterated revision operator. Likewise, a semantic model is used to show the intuition and many nice properties of the mutual revision operator, and the complexity of its computational model is formally analyzed. Finally, I present a belief update operator, which takes into account two important problems of reasoning about action, i.e., disjunctive updates and domain constraints. Again, the updated operator is presented with both a semantic model and a computational model

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

Representing archaeological uncertainty in cultural informatics

This thesis sets out to explore, describe, quantify, and visualise uncertainty in a cultural informatics context, with a focus on archaeological reconstructions. For quite some time, archaeologists and heritage experts have been criticising the often toorealistic appearance of three-dimensional reconstructions. They have been highlighting one of the unique features of archaeology: the information we have on our heritage will always be incomplete. This incompleteness should be reflected in digitised reconstructions of the past. This criticism is the driving force behind this thesis. The research examines archaeological theory and inferential process and provides insight into computer visualisation. It describes how these two areas, of archaeology and computer graphics, have formed a useful, but often tumultuous, relationship through the years. By examining the uncertainty background of disciplines such as GIS, medicine, and law, the thesis postulates that archaeological visualisation, in order to mature, must move towards archaeological knowledge visualisation. Three sequential areas are proposed through this thesis for the initial exploration of archaeological uncertainty: identification, quantification and modelling. The main contributions of the thesis lie in those three areas. Firstly, through the innovative design, distribution, and analysis of a questionnaire, the thesis identifies the importance of uncertainty in archaeological interpretation and discovers potential preferences among different evidence types. Secondly, the thesis uniquely analyses and evaluates, in relation to archaeological uncertainty, three different belief quantification models. The varying ways that these mathematical models work, are also evaluated through simulated experiments. Comparison of results indicates significant convergence between the models. Thirdly, a novel approach to archaeological uncertainty and evidence conflict visualisation is presented, influenced by information visualisation schemes. Lastly, suggestions for future semantic extensions to this research are presented through the design and development of new plugins to a search engine

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework

A Probabilistic Modelling Approach for Rational Belief in Meta-Epistemic Contexts

This work is part of the larger project INTEGRITY. Integrity develops a conceptual frame integrating beliefs with individual (and consensual group) decision making and action based on belief awareness. Comments and criticisms are most welcome via email. The text introduces the conceptual (internalism, externalism), quantitative (probabilism) and logical perspectives (logics for reasoning about probabilities by Fagin, Halpern, Megiddo and MEL by Banerjee, Dubois) for the framework