Inconsistent-tolerant base revision through Argument Theory Change

Reasoning and change over inconsistent knowledge bases (KBs) is of utmost relevance in areas like medicine and law. Argumentation may bring the possibility to cope with both problems. Firstly, by constructing an argumentation framework (AF) from the inconsistent KB, we can decide whether to accept or reject a certain claim through the interplay among arguments and counterarguments. Secondly, by handling dynamics of arguments of the AF, we might deal with the dynamics of knowledge of the underlying inconsistent KB. Dynamics of arguments has recently attracted attention and although some approaches have been proposed, a full axiomatization within the theory of belief revision was still missing. A revision arises when we want the argumentation semantics to accept an argument. Argument Theory Change (ATC) encloses the revision operators that modify the AF by analyzing dialectical trees-arguments as nodes and attacks as edges-as the adopted argumentation semantics. In this article, we present a simple approach to ATC based on propositional KBs. This allows to manage change of inconsistent KBs by relying upon classical belief revision, although contrary to it, consistency restoration of the KB is avoided. Subsequently, a set of rationality postulates adapted to argumentation is given, and finally, the proposed model of change is related to the postulates through the corresponding representation theorem. Though we focus on propositional logic, the results can be easily extended to more expressive formalisms such as first-order logic and description logics, to handle evolution of ontologies.

Base Revision for Ontology Debugging

Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite.

Pseudo-contractions in belief revision

Belief Revision addresses the problem of how to change epistemic states, usually represented in the literature by sets of logical sentences. Solid theoretical results were consolidated with the AGM paradigm, which deals with theories (logically closed sets of sentences). After that, the theory was extended to belief bases, that is, arbitrary sets of sentences. Besides all this theoretical framework, AI researchers face serious difficulties when trying to implement belief revision systems. One of the major complications is the closure required by AGM theory, which cannot be easily computed. Even belief bases, which do not require closure, seem to be improper for practical purposes, since their changes are usually very rigid (syntax dependent). Some operations, known as pseudo-contractions, are in the middle ground between belief set change and belief base change. In the present work we have proposed a new pseudo-contraction operation, studied its properties and characterized it. We have also found connections between this operator and some other pseudo-contractions.

Reason Maintenance Systems: Tools for Foundations-based Belief Revision

Dynamic and distributed environments are hard to model since they suffer from unexpected changes, incomplete knowledge, and conflicting perspectives and, thus, call for appropriate knowledge representation and reasoning (KRR) systems. Such KRR systems must handle sets of dynamic beliefs, be sensitive to communicated and perceived changes in the environment and, consequently, may have to drop current beliefs in face of new findings or disregard any new data that conflicts with stronger convictions held by the system. Not only do they need to represent and reason with beliefs, but also they must perform belief revision to maintain the overall consistency of the knowledge base. One way of developing such systems is to use reason maintenance systems (RMS). In this paper we provide an overview of the most representative types of RMS, which are also known as truth maintenance systems (TMS), which are computational instances of the foundations-based theory of belief revision. An RMS module works together with a problem solver. The latter feeds the RMS with assumptions (core beliefs) and conclusions (derived beliefs), which are accompanied by their respective foundations. The role of the RMS module is to store the beliefs, associate with each belief (core or derived belief) the corresponding set of supporting foundations and maintain the consistency of the overall reasoning by keeping, for each represented belief, the current supporting justifications. Two major approaches are used to reason maintenance: single-and multiple-context reasoning systems. Although in the single-context systems, each belief is associated to the beliefs that directly generated it—the justification-based TMS (JTMS) or the logic-based TMS (LTMS), in the multiple context counterparts, each belief is associated with the minimal set of assumptions from which it can be inferred—the assumption-based TMS (ATMS) or the multiple belief reasoner (MBR).

Argumentation as Distributed Belief Revision: Conflict Resolution in Decentralised Multi-agent Systems

Decentralised co-operative multi-agent systems are computational systems where conflicts are frequent due to the nature of the represented knowledge. Negotiation methodologies, in this case argumentation based negotiation methodologies, were developed and applied to solve unforeseeable and, therefore, unavoidable conflicts. The supporting computational model is a distributed belief revision system where argumentation plays the decisive role of revision. The distributed belief revision system detects, isolates and solves, whenever possible, the identified conflicts. The detection and isolation of the conflicts is automatically performed by the distributed consistency mechanism and the resolution of the conflict, or belief revision, is achieved via argumentation. We propose and describe two argumentation protocols intended to solve different types of identified information conflicts: context dependent and context independent conflicts. While the protocol for context dependent conflicts generates new consensual alternatives, the latter chooses to adopt the soundest, strongest argument presented. The paper shows the suitability of using argumentation as a distributed decentralised belief revision protocol to solve unavoidable conflicts.

Solving Conflicting Beliefs with a Distributed Belief Revision Approach

The ability to solve conflicting beliefs is crucial for multi- agent systems where the information is dynamic, incomplete and dis- tributed over a group of autonomous agents. The proposed distributed belief revision approach consists of a distributed truth maintenance sy- stem and a set of autonomous belief revision methodologies. The agents have partial views and, frequently, hold disparate beliefs which are au- tomatically detected by system’s reason maintenance mechanism. The nature of these conflicts is dynamic and requires adequate methodolo- gies for conflict resolution. The two types of conflicting beliefs addressed in this paper are Context Dependent and Context Independent Conflicts which result, in the first case, from the assignment, by different agents, of opposite belief statuses to the same belief, and, in the latter case, from holding contradictory distinct beliefs. The belief revision methodology for solving Context Independent Con- flicts is, basically, a selection process based on the assessment of the cre- dibility of the opposing belief statuses. The belief revision methodology for solving Context Dependent Conflicts is, essentially, a search process for a consensual alternative based on a “next best” relaxation strategy.

Belief Revision in Multi-Agent Systems

The ability to respond sensibly to changing and conflicting beliefs is an integral part of intelligent agency. To this end, we outline the design and implementation of a Distributed Assumption-based Truth Maintenance System (DATMS) appropriate for controlling cooperative problem solving in a dynamic real world multi-agent community. Our DATMS works on the principle of local coherence which means that different agents can have different perspectives on the same fact provided that these stances are appropriately justified. The belief revision algorithm is presented, the meta-level code needed to ensure that all system-wide queries can be uniquely answered is described, and the DATMS’ implementation in a general purpose multi-agent shell is discussed.

Improving Assumption based Distributed Belief Revision

Belief revision is a critical issue in real world DAI applications. A Multi-Agent System not only has to cope with the intrinsic incompleteness and the constant change of the available knowledge (as in the case of its stand alone counterparts), but also has to deal with possible conflicts between the agents’ perspectives. Each semi-autonomous agent, designed as a combination of a problem solver – assumption based truth maintenance system (ATMS), was enriched with improved capabilities: a distributed context management facility allowing the user to dynamically focus on the more pertinent contexts, and a distributed belief revision algorithm with two levels of consistency. This work contributions include: (i) a concise representation of the shared external facts; (ii) a simple and innovative methodology to achieve distributed context management; and (iii) a reduced inter-agent data exchange format. The different levels of consistency adopted were based on the relevance of the data under consideration: higher relevance data (detected inconsistencies) was granted global consistency while less relevant data (system facts) was assigned local consistency. These abilities are fully supported by the ATMS standard functionalities.

Distributed Belief Revision and Environmental Decision Support

This article discusses the development of an Intelligent Distributed Environmental Decision Support System, built upon the association of a Multi-agent Belief Revision System with a Geographical Information System (GIS). The inherent multidisciplinary features of the involved expertises in the field of environmental management, the need to define clear policies that allow the synthesis of divergent perspectives, its systematic application, and the reduction of the costs and time that result from this integration, are the main reasons that motivate the proposal of this project. This paper is organised in two parts: in the first part we present and discuss the developed - Distributed Belief Revision Test-bed - DiBeRT; in the second part we analyse its application to the environmental decision support domain, with special emphasis on the interface with a GIS.

Distributed Belief Revision and Environmental Decision Support

This article discusses the development of an Intelligent Distributed Environmental Decision Support System, built upon the association of a Multi-agent Belief Revision System with a Geographical Information System (GIS). The inherent multidisciplinary features of the involved expertises in the field of environmental management, the need to define clear policies that allow the synthesis of divergent perspectives, its systematic application, and the reduction of the costs and time that result from this integration, are the main reasons that motivate the proposal of this project. This paper is organised in two parts: in the first part we present and discuss the developed ; in the second part we analyse its application to the environmental decision support domain, with special emphasis on the interface with a GIS.

Consistency and Context Management in a Multi Agent Belief Revision Testbed

Multi-agent architectures are well suited for complex inherently distributed problem solving domains. From the many challenging aspects that arise within this framework, a crucial one emerges: how to incorporate dynamic and conflicting agent beliefs? While the belief revision activity in a single agent scenario is concentrated on incorporating new information while preserving consistency, in a multi-agent system it also has to deal with possible conflicts between the agents perspectives. To provide an adequate framework, each agent, built as a combination of an assumption based belief revision system and a cooperation layer, was enriched with additional features: a distributed search control mechanism allowing dynamic context management, and a set of different distributed consistency methodologies. As a result, a Distributed Belief Revision Testbed (DiBeRT) was developed. This paper is a preliminary report presenting some of DiBeRT contributions: a concise representation of external beliefs; a simple and innovative methodology to achieve distributed context management; and a reduced inter-agent data exchange format.

Belief Propagation and Revision in Networks with Loops

Local belief propagation rules of the sort proposed by Pearl(1988) are guaranteed to converge to the optimal beliefs for singly connected networks. Recently, a number of researchers have empirically demonstrated good performance of these same algorithms on networks with loops, but a theoretical understanding of this performance has yet to be achieved. Here we lay the foundation for an understanding of belief propagation in networks with loops. For networks with a single loop, we derive ananalytical relationship between the steady state beliefs in the loopy network and the true posterior probability. Using this relationship we show a category of networks for which the MAP estimate obtained by belief update and by belief revision can be proven to be optimal (although the beliefs will be incorrect). We show how nodes can use local information in the messages they receive in order to correct the steady state beliefs. Furthermore we prove that for all networks with a single loop, the MAP estimate obtained by belief revisionat convergence is guaranteed to give the globally optimal sequence of states. The result is independent of the length of the cycle and the size of the statespace. For networks with multiple loops, we introduce the concept of a "balanced network" and show simulati.

Reasoning about Requirements Evolution Using Clustered Belief Revision

During the development of system requirements, software system specifications are often inconsistent. Inconsistencies may arise for different reasons, for example, when multiple conflicting viewpoints are embodied in the specification, or when the specification itself is at a transient stage of evolution. These inconsistencies cannot always be resolved immediately. As a result, we argue that a formal framework for the analysis of evolving specifications should be able to tolerate inconsistency by allowing reasoning in the presence of inconsistency without trivialisation, and circumvent inconsistency by enabling impact analyses of potential changes to be carried out. This paper shows how clustered belief revision can help in this process. Clustered belief revision allows for the grouping of requirements with similar functionality into clusters and the assignment of priorities between them. By analysing the result of a cluster, an engineer can either choose to rectify problems in the specification or to postpone the changes until more information becomes available.