Focusing ATMS Problem-Solving: A Formal Approach

The Assumption-based Truth Maintenance System (ATMS) is a general and powerful problem-solving tool in AI. Unfortunately, its generality usually entails a high computational cost. In this paper, we study how a general notion of cost function can be incorporated into the design of an algorithm for focusing the ATMS, called BF-ATMS. The BF-ATMS algorithm explores a search space of size polynomial in the number of assumptions, even for problems which are proven to have exponential size labels. Experimental results indicate significant speedups over the standard ATMS for such problems. In addition to its improved efficiency, the BF-ATMS algorithm retains the multiple-context capability of an ATMS, and the important properties of consistency, minimality, soundness, as well as the property of bounded completeness. The usefulness of the new algorithm is demonstrated by its application to the task of consistency-based diagnosis, where dramatic efficiency improvements, with respect to the standard solution technique, are obtained

The Common Order-Theoretic Structure of Version Spaces and ATMS\u27s

This paper exposes the common order-theoretic properties of the structures manipulated by the version space algorithm [Mit78]and the assumption-based truth maintenance systems (ATMS) [dk86a,dk86b] by recasting them in the framework of convex spaces. Our analysis of version spaces in this framework reveals necessary and sufficient conditions for ensuring the preservation of an essential finite representability property in version space merging. This analysis is used to formulate several sufficient conditions for when a language will allow version spaces to be represented by finite sets of concepts (even when the universe of concepts may be infinite). We provide a new convex space based formulation of computation performs by an ATMS which extends the expressiveness of disjunctions in the systems. This approach obviates the need for hyper-resolution in dealing with disjunction and results in simpler label-update algorithms

DISCRETE CONCEPT FORMATION

Master'sMASTER OF SCIENC

Convex spaces as an order-theoretic basis for problem-solving

The ability to represent and use a body of knowledge or information is fundamental to all problem solvers. It is well recognized that different problems require different representations so that the corresponding algorithms can be implemented efficiently. This thesis advocates that ordered structures play an important role in many problem domains. In particular, we focus on the study of an ordered structure called a convex space. We demonstrate that this particular ordered structure helps answer some of the important questions concerning problem solving tasks in the fields of Artificial Intelligence and Database Systems that are of major interest from both theoretical and practical points of view. Specifically, we study how convex spaces can be used to formulate the algorithms related to version spaces, querying independent databases, Assumption-based Truth Maintenance Systems (ATMS), and the generation of prime implicates. This results in a unifying framework for studying and understanding the representation used in these seemingly unrelated areas. Consequently, we derive general admissibility criteria for version space learning, a semantics for describing a useful database merging procedure in addition to some standard relational database operations, and a consistent semantics for the basic and extended ATMS\u27s. Moreover, the order-theoretic study leads to tile derivation and implementation of better algorithms to replace some of the existing algorithms. Most noteworthy are a more general prime implicate generation algorithm that can also function as very efficient abductive reasoner and theorem prover, an ordered-theoretic based extended ATMS algorithm which eliminates the necessity of inefficient resolution procedures, and a focused ATMS algorithm that supports an efficient diagnostic system. The complexity issues of various algorithms are discussed and some empirical results are presented

The Common Order-Theoretic Structure of Version Spaces and ATMS's

We demonstrate how order-theoretic abstractions can be useful in identifying, formalizing, and exploiting relationships between seemingly dissimilar AI algorithms that perform computations on partially-ordered sets. In particular, we show how the order-theoretic concept of an anti-chain can be used to provide an efficient representation for such sets when they satisfy certain special properties. We use anti-chains to identify and analyze the basic operations and representation optimizations in the version space learning algorithm [10] and the assumption-based truth maintenance system (ATMS) [2, 3]. Our analysis allows us to (1) extend the known theory [7, 10, 8] of admissibility of concept spaces for incremental version space merging, and (2) develop new, simpler label-update algorithms for ATMS's with DNF assumption formulas. Contents 1 Introduction 2 2 Representing Sets as Anti-Chains 4 3 Version Spaces 17 4 Assumption-Based Truth Maintenance Systems 32 5 Extended ATMS's 46 6 Ackno..

New on-line cash check scheme

Proceedings of the ACM Conference on Computer and Communications Security111-11621