Experimental Analysis of Numeric and Symbolic Constraint Satisfaction Techniques for Temporal Reasoning

Many temporal applications like planning and scheduling can be viewed as special cases of the numeric and symbolic temporal constraint satisfaction problem. Thus we have developed a temporal model, TemPro, based on the interval Algebra, to express such applications in term of qualitative and quantitative temporal constraints. TemPro extends the interval algebra relations of Allen to handle numeric information. To solve a constraint satisfaction problem, different approaches have been developed. These approaches generally use constraint propagation to simplify the original problem and backtracking to directly search for possible solutions. The constraint propagation can also be used during the backtracking to improve the performance of the search. The objective of this paper is to assess different policies for finding if a TemPro network is consistent. The main question we want to answer here is how much constraint propagation is useful for finding a single solution for a TemPro constraint graph. For this purpose, we have experimented by randomly generating large consistent networks for which either arc and/or path consistency algorithms (AC-3, AC-7 and PC-2) were applied. The main result of this study is an optimal policy combining these algorithms either at the symbolic (Allen relation propagation) or at the numerical level.     

Constraint Reasoning about Repeating Events: Satisfaction and Optimization

Effective manipulation of temporal information about periodic events is required for solving complex problems such as long‐range scheduling or querying temporal information. Furthermore, many problems involving repeating events involve the optimization of temporal aspects of these events (e.g., minimizing make‐span in job‐shop scheduling). In this paper, a constraint‐based formulation of reasoning problems with repeating events is presented, and its complexity is analyzed for a range of problems. Optimization constraints are interpreted formally using the Semiring CSPs (SCSP) representation of optimization in constraint reasoning. This allows for familiar algorithms such as branch‐and‐bound to be applied to solving them.     

Solution Techniques for Constraint Satisfaction Problems: Foundations

The Constraint Satisfaction Problem (CSP) is ubiquitous in artificialintelligence. It has a wide applicability, ranging from machine visionand temporal reasoning to planning and logic programming. This paperattempts a systematic and coherent review of the foundations ofthe techniques for constraint satisfaction. It discusses in detail thefundamental principles and approaches. This includes an initialdefinition of the constraint satisfaction problem, a graphical meansof problem representation, conventional tree search solutiontechniques, and pre-processing algorithms which are designed to makesubsequent tree search significantly easier.     

Solution Techniques for Constraint Satisfaction Problems: Advanced Approaches

Conventional techniques for the constraint satisfaction problem (CSP)have had considerable success in their applications. However,there are many areas in which the performance of the basic approachesmay be improved. These include heuristic ordering of certain tasksperformed by the CSP solver, hybrids which combine compatible solutiontechniques and graph based methods which exploit the structure of theconstraint graph representation of a CSP. Also, conventionalconstraint satisfaction techniques only address problems with hardconstraints (i.e. each of which are completely satisfied or completelyviolated, and all of which must be satisfied by a validsolution). Many real applications require a more flexible approachwhich relaxes somewhat these rigid requirements. To address theseissues various approaches have been developed. This paper attempts asystematic review of them.     

Temporal Constraint Satisfaction Techniques in Job Shop Scheduling Problem Solving

We describe a restriction of Dechter, Meiri and Pearl's TCSPs (Temporal Constraint Satisfaction Problems) sufficiently expressive to represent any job shop scheduling problem. A solver based on the restriction is then described, which is similar to Ladkin and Reinefeld's qualitative interval network solver; except, however, that the filtering method used during the search is not path consistency but either ULT (Upper-Lower Tightening) or LPC (Loose Path- Consistency), which are both less effective but have the advantage of getting rid of the so-called fragmentation problem.     

概念知识表示和推理

Nilsson教授首先提出了代数格应用于概念知识表示的思想．其优点在于知识表示的代数特性和图示特性，在此基础上．表文把代数格与PROLOG相结合．定义了一种基于概念的逻辑编程语言．其语言具有比PROLOG更抽象、更方便的编程风格．此外．给出了该逻辑编程语言的匹配算法．     

Random Constraint Satisfaction: Flaws and Structure

A recent theoretical result by Achlioptas et al. shows that many models of random binary constraint satisfaction problems become trivially insoluble as problem size increases. This insolubility is partly due to the presence of flawed variables, variables whose values are all flawed (or unsupported). In this paper, we analyse how seriously existing work has been affected. We survey the literature to identify experimental studies that use models and parameters that may have been affected by flaws. We then estimate theoretically and measure experimentally the size at which flawed variables can be expected to occur. To eliminate flawed values and variables in the models currently used, we introduce a flawless generator which puts a limited amount of structure into the conflict matrix. We prove that such flawless problems are not trivially insoluble for constraint tightnesses up to 1/2. We also prove that the standard models B and C do not suffer from flaws when the constraint tightness is less than the reciprocal of domain size. We consider introducing types of structure into the constraint graph which are rare in random graphs and present experimental results with such structured graphs.     

Mendelian Error Detection in Complex Pedigrees Using Weighted Constraint Satisfaction Techniques

With the arrival of high throughput genotyping techniques, the detection of likely genotyping errors is becoming an increasingly important problem. In this paper we are interested in errors that violate Mendelian laws. The problem of deciding if a Mendelian error exists in a pedigree is NP-complete (Aceto et al., J Comp Sci Technol 19(1):42–59, 2004). Existing tools dedicated to this problem may offer different level of services: detect simple inconsistencies using local reasoning, prove inconsistency, detect the source of error, propose an optimal correction for the error. All assume that there is at most one error. In this paper we show that the problem of error detection, of determining the minimum number of errors needed to explain the data (with a possible error detection) and error correction can all be modeled using soft constraint networks. Therefore, these problems provide attractive benchmarks for weighted constraint network (WCN) solvers. Because of their sheer size, these problems drove us into the development of a new WCN solver toulbar2 which solves very large pedigree problems with thousands of animals, including many loops and several errors.     

Semantically-Guided Goal-Sensitive Reasoning: Model Representation

SGGS (Semantically-Guided Goal-Sensitive reasoning) is a clausal theorem-proving method, which generalizes to first-order logic the Davis-Putnam-Loveland-Logemann procedure with conflict-driven clause learning (DPLL-CDCL). SGGS starts from an initial interpretation, and works towards modifying it into a model of a given set of clauses, reporting unsatisfiability if there is no model. The state of the search for a model is described by a structure, called SGGS clause sequence. We present SGGS clause sequences as a formalism to represent models; and we prove their properties related to the mechanisms of SGGS for clausal propagation, conflict solving, and conflict-driven model repair at the first-order level.     

Periodic Constraint Satisfaction Problems: Tractable Subclasses

We study a generalization of the constraint satisfaction problem (CSP), the periodic constraint satisfaction problem. An input instance of the periodic CSP is a finite set of generating constraints over a structured variable set that implicitly specifies a larger, possibly infinite set of constraints; the problem is to decide whether or not the larger set of constraints has a satisfying assignment. This model is natural for studying constraint networks consisting of constraints obeying a high degree of regularity or symmetry. Our main contribution is the identification of two broad polynomial-time tractable subclasses of the periodic CSP.     

Representation and Reasoning with Multi-Point Events

Allen's Interval Algebra (IA) and Vilain & Kautz's Point Algebra (PA) consider an interval and a point as basic temporal entities (i.e., events) respectively. However, in many situations we need to deal with recurring events that include multiple points, multiple intervals or combinations of points and intervals. In this paper, we present a framework to model recurring events as multi-point events (MPEs) by extending point algebra. The reasoning tasks are formulated as binary constraint satisfaction problems. We propose a polynomial time algorithm (based on van Beek's algorithm) for finding all feasible relations. For the problem of finding a consistent scenario, we propose a backtracking method with a local search heuristic. We also describe an implementation and a detail empirical evaluation of the proposed algorithms. Our empirical results indicate that the MPE-based approach performs better than the existing approaches.     

约束编程与约束满足在产品装配中的应用

约束编程与约束满足问题是近三十年来在人工智能领域发展起来的一个研究方向。产品配置器近十几年来发展起来的一项技术。文中介绍约束编程及约束满足问题在按订单装配型产品配置器中的应用,并通过讨论说明了相对于传统配置方案求解过程,应用约束满足的优越性。     

Algorithms for Distributed Constraint Satisfaction: A Review

When multiple agents are in a shared environment, there usually exist constraints among the possible actions of these agents. A distributed constraint satisfaction problem (distributed CSP) is a problem to find a consistent combination of actions that satisfies these inter-agent constraints. Various application problems in multi-agent systems can be formalized as distributed CSPs. This paper gives an overview of the existing research on distributed CSPs. First, we briefly describe the problem formalization and algorithms of normal, centralized CSPs. Then, we show the problem formalization and several MAS application problems of distributed CSPs. Furthermore, we describe a series of algorithms for solving distributed CSPs, i.e., the asynchronous backtracking, the asynchronous weak-commitment search, the distributed breakout, and distributed consistency algorithms. Finally, we show two extensions of the basic problem formalization of distributed CSPs, i.e., handling multiple local variables, and dealing with over-constrained problems.     

Neural Networks and Structured Knowledge: Knowledge Representation and Reasoning

This collection of articles is the first of two parts of a special issue on Neural Networks and Structured Knowledge. The contributions to the first part shed some light on the issues of knowledge representation and reasoning with neural networks. Their scope ranges from formal models for mapping discrete structures like graphs or logical formulae onto different types of neural networks, to the construction of practical systems for various types of reasoning. In the second part to follow, the emphasis will be on the extraction of knowledge from neural networks, and on applications of neural networks and structured knowledge to practical tasks.     

Random Constraint Satisfaction: A More Accurate Picture

In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly, experimental results with various models for generating random CSP instances suggest that the probability of such problems having a solution exhibits a threshold–like behavior. In this spirit, some preliminary theoretical work has been done in analyzing these models asymptotically, i.e., as the number of variables grows. In this paper we prove that, contrary to beliefs based on experimental evidence, the models commonly used for generating random CSP instances do not have an asymptotic threshold. In particular, we prove that asymptotically almost all instances they generate are overconstrained, suffering from trivial, local inconsistencies. To complement this result we present an alternative, single–parameter model for generating random CSP instances and prove that, unlike current models, it exhibits non–trivial asymptotic behavior. Moreover, for this new model we derive explicit bounds for the narrow region within which the probability of having a solution changes dramatically.     

Solving Mixed and Conditional Constraint Satisfaction Problems

Constraints are a powerful general paradigm for representing knowledge in intelligent systems. The standard constraint satisfaction paradigm involves variables over a discrete value domain and constraints which restrict the solutions to allowed value combinations. This standard paradigm is inapplicable to problems which are either:(a) mixed, involving both numeric and discrete variables, or(b) conditional,¹ containing variables whose existence depends on the values chosen for other variables, or(c) both, conditional and mixed.We present a general formalism which handles both exceptions in an integral search framework. We solve conditional problems by analyzing dependencies between constraints that enable us to directly compute all possible configurations of the CSP rather than discovering them during search. For mixed problems, we present an enumeration scheme that integrates numeric variables with discrete ones in a single search process. Both techniques take advantage of enhanced propagation rule for numeric variables that results in tighter labelings than the algorithms commonly used. From real world examples in configuration and design, we identify several types of mixed constraints, i.e. constraints defined over numeric and discrete variables, and propose new propagation rules in order to take advantage of these constraints during problem solving.     

Topological Spatio–Temporal Reasoning and Representation

We present here a theory of motion from a topological point of view, in a symbolic perspective. Taking space–time histories of objects as primitive entities, we introduce temporal and topological relations on the thus defined space–time to characterize classes of spatial changes. The theory thus accounts for qualitative spatial information, dealing with underspecified, symbolic information when accurate data are not available or unnecessary. We show that these structures give a basis for commonsense spatio–temporal reasoning by presenting a number of significant deductions in the theory. This can serve as a formal basis for languages describing motion events in a qualitative way.