A beginner's guide to belief revision and truth maintenance systems

This brief note is intended to familiarize the non-TMS audience with some of the basic ideas surrounding classic TMS's (truth maintenance systems), namely the justification-based TMS and the assumption-based TMS. Topics of further interest include the relation between non-monotonic logics and TMS's, efficiency and search issues, complexity concerns, as well as the variety of TMS systems that have surfaced in the past decade or so. These include probabilistic-based TMS systems, fuzzy TMS systems, tri-valued belief systems, and so on

Truth maintenance in knowledge-based systems

Truth Maintenance Systems (TMS) have been applied in a wide range of domains, from diagnosing electric circuits to belief revision in agent systems. There also has been work on using the TMS in modern Knowledge-Based Systems such as intelligent agents and ontologies. This thesis investigates the applications of TMSs in such systems. For intelligent agents, we use a “light-weight” TMS to support query caching in agent programs. The TMS keeps track of the dependencies between a query and the facts used to derive it so that when the agent updates its database, only affected queries are invalidated and removed from the cache. The TMS employed here is “light-weight” as it does not maintain all intermediate reasoning results. Therefore, it is able to reduce memory consumption and to improve performance in a dynamic setting such as in multi-agent systems. For ontologies, this work extends the Assumption-based Truth Maintenance System (ATMS) to tackle the problem of axiom pinpointing and debugging in ontology-based systems with different levels of expressivity. Starting with finding all errors in auto-generated ontology mappings using a “classic” ATMS [23], we extend the ATMS to solve the axiom pinpointing problem in Description Logics-based Ontologies. We also attempt this approach to solve the axiom pinpointing problem in a more expressive upper ontology, SUMO, whose underlying logic is undecidable

On resolving conflicts between arguments

Argument systems are based on the idea that one can construct arguments for propositions; i.e., structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of \emph{which (sub-)arguments can be subject to defeat}? In legal argumentation, meta-rules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, \emph{can a conflict be resolved by considering only the last defeasible rules of the arguments involved}? We propose a new argument system where, instead of deriving a defeat relation between arguments, \emph{undercutting-arguments} for the defeat of defeasible rules are constructed. This system allows us, (\textit{i}) to resolve conflicts (a generalization of rebutting arguments) using only the last rules of the arguments for inconsistencies, (\textit{ii}) to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, (\textit{iii}) to establish a relation with Default Logic, and (\textit{iv}) to prove closure properties such as \emph{cumulativity}. We also propose an extension of the argument system that enables \emph{reasoning by cases}

The development of an expert system shell with a mixed knowledge representation, explicit control of reasoning and a truth maintenance system

Bibliography: pages 227-236.This thesis concentrates on several important issues in expert system research, namely - representation of knowledge - control of reasoning - implementation of non-monotonic logics via truth maintenance systems. There are three parts to this thesis. PART1 covers the background research in the above mentioned topics. PART2 discusses the WISE system and the way in which research from PART1 was applied to the development of the WISE shell. PART3 considers the features of other expert system shells

Truth maintenance in knowledge-based systems

Truth Maintenance Systems (TMS) have been applied in a wide range of domains, from diagnosing electric circuits to belief revision in agent systems. There also has been work on using the TMS in modern Knowledge-Based Systems such as intelligent agents and ontologies. This thesis investigates the applications of TMSs in such systems. For intelligent agents, we use a “light-weight” TMS to support query caching in agent programs. The TMS keeps track of the dependencies between a query and the facts used to derive it so that when the agent updates its database, only affected queries are invalidated and removed from the cache. The TMS employed here is “light-weight” as it does not maintain all intermediate reasoning results. Therefore, it is able to reduce memory consumption and to improve performance in a dynamic setting such as in multi-agent systems. For ontologies, this work extends the Assumption-based Truth Maintenance System (ATMS) to tackle the problem of axiom pinpointing and debugging in ontology-based systems with different levels of expressivity. Starting with finding all errors in auto-generated ontology mappings using a “classic” ATMS [23], we extend the ATMS to solve the axiom pinpointing problem in Description Logics-based Ontologies. We also attempt this approach to solve the axiom pinpointing problem in a more expressive upper ontology, SUMO, whose underlying logic is undecidable

Constructive Reasoning for Semantic Wikis

One of the main design goals of social software, such as wikis, is to support and facilitate interaction and collaboration. This dissertation explores challenges that arise from extending social software with advanced facilities such as reasoning and semantic annotations and presents tools in form of a conceptual model, structured tags, a rule language, and a set of novel forward chaining and reason maintenance methods for processing such rules that help to overcome the challenges. Wikis and semantic wikis were usually developed in an ad-hoc manner, without much thought about the underlying concepts. A conceptual model suitable for a semantic wiki that takes advanced features such as annotations and reasoning into account is proposed. Moreover, so called structured tags are proposed as a semi-formal knowledge representation step between informal and formal annotations. The focus of rule languages for the Semantic Web has been predominantly on expert users and on the interplay of rule languages and ontologies. KWRL, the KiWi Rule Language, is proposed as a rule language for a semantic wiki that is easily understandable for users as it is aware of the conceptual model of a wiki and as it is inconsistency-tolerant, and that can be efficiently evaluated as it builds upon Datalog concepts. The requirement for fast response times of interactive software translates in our work to bottom-up evaluation (materialization) of rules (views) ahead of time – that is when rules or data change, not when they are queried. Materialized views have to be updated when data or rules change. While incremental view maintenance was intensively studied in the past and literature on the subject is abundant, the existing methods have surprisingly many disadvantages – they do not provide all information desirable for explanation of derived information, they require evaluation of possibly substantially larger Datalog programs with negation, they recompute the whole extension of a predicate even if only a small part of it is affected by a change, they require adaptation for handling general rule changes. A particular contribution of this dissertation consists in a set of forward chaining and reason maintenance methods with a simple declarative description that are efficient and derive and maintain information necessary for reason maintenance and explanation. The reasoning methods and most of the reason maintenance methods are described in terms of a set of extended immediate consequence operators the properties of which are proven in the classical logical programming framework. In contrast to existing methods, the reason maintenance methods in this dissertation work by evaluating the original Datalog program – they do not introduce negation if it is not present in the input program – and only the affected part of a predicate’s extension is recomputed. Moreover, our methods directly handle changes in both data and rules; a rule change does not need to be handled as a special case. A framework of support graphs, a data structure inspired by justification graphs of classical reason maintenance, is proposed. Support graphs enable a unified description and a formal comparison of the various reasoning and reason maintenance methods and define a notion of a derivation such that the number of derivations of an atom is always finite even in the recursive Datalog case. A practical approach to implementing reasoning, reason maintenance, and explanation in the KiWi semantic platform is also investigated. It is shown how an implementation may benefit from using a graph database instead of or along with a relational database

Deploying expert systems in Ada

As the Department of Defense Ada mandate begins to be enforced actively, interest in deploying expert systems in Ada has increased. A prototype Ada based expert system tool is introduced called ART/Ada. This prototype was built to support research into the language and operational issues of expert systems in Ada. ART/Ada allows applications of a conventional expert system tool called ART-IM (Automated Reasoning Tool for Information Management) to be deployed in various Ada environments with efficient use of time and space. ART-IM, a C-based expert system tool, is used to generate Ada source code which is compiled and linked with an Ada base inference engine to produce an Ada executable image. ART/Ada will be used to implement several prototype expert systems for the Space Station Freedom Program testbeds