Results 1  10
of
494
Constraint Networks
, 1992
"... Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expression ..."
Abstract

Cited by 1149 (43 self)
 Add to MetaCart
Constraintbased reasoning is a paradigm for formulating knowledge as a set of constraints without specifying the method by which these constraints are to be satisfied. A variety of techniques have been developed for finding partial or complete solutions for different kinds of constraint expressions. These have been successfully applied to diverse tasks such as design, diagnosis, truth maintenance, scheduling, spatiotemporal reasoning, logic programming and user interface. Constraint networks are graphical representations used to guide strategies for solving constraint satisfaction problems (CSPs).
On the Hardness of Approximate Reasoning
, 1996
"... Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider va ..."
Abstract

Cited by 289 (13 self)
 Add to MetaCart
Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to modelcounting problems over a propositional domain. We prove that counting satisfying assignments of propositional languages is intractable even for Horn and monotone formulae, and even when the size of clauses and number of occurrences of the variables are extremely limited. This should be contrasted with the case of deductive reasoning, where Horn theories and theories with binary clauses are distinguished by the e...
The logic of constraint satisfaction
, 1992
"... The constraint satisfaction problem (CSP) formalization has been a productive tool within Artificial Intelligence and related areas. The finite CSP (FCSP) framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems. FCSP is formulated i ..."
Abstract

Cited by 269 (5 self)
 Add to MetaCart
The constraint satisfaction problem (CSP) formalization has been a productive tool within Artificial Intelligence and related areas. The finite CSP (FCSP) framework is presented here as a restricted logical calculus within a space of logical representation and reasoning systems. FCSP is formulated in a variety of logical settings: theorem proving in first order predicate calculus, propositional theorem proving (and hence SAT), the Prolog and Datalog approaches, constraint network algorithms, a logical interpreter for networks of constraints, the constraint logic programming (CLP) paradigm and propositional model finding (and hence SAT, again). Several standard, and some notsostandard, logical methods can therefore be used to solve these problems. By doing this we obtain a specification of the semantics of the common approaches. This synthetic treatment also allows algorithms and results from these disparate areas to be imported, and specialized, to FCSP; the special properties of FCSP are exploited to achieve, for example, completeness and to improve efficiency. It also allows export to the related areas. By casting CSP both as a generalization of FCSP and as a specialization of CLP it is observed that some, but not all, FCSP techniques lift to CSP and thereby to CLP. Various new connections are uncovered, in
Consistency techniques for numeric csps
, 1993
"... Many problems can be expressed in terms of a numeric constraint satisfaction problem over finite or continuous domains (numeric CSP). The purpose of this paper is to show that the consistency techniques that have been developed for CSPs can be adapted to numeric CSPs. Since the numeric domains are o ..."
Abstract

Cited by 241 (9 self)
 Add to MetaCart
Many problems can be expressed in terms of a numeric constraint satisfaction problem over finite or continuous domains (numeric CSP). The purpose of this paper is to show that the consistency techniques that have been developed for CSPs can be adapted to numeric CSPs. Since the numeric domains are ordered the underlying idea is to handle domains only by their bounds. The semantics that have been elaborated, plus the complexity analysis and good experimental results, confirm that these techniques can be used in real applications. 1
A Generic ArcConsistency Algorithm and its Specializations
 Artificial Intelligence
, 1992
"... Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arcconsistency algorithms have been proposed, originating from Waltz's filtering algorithm [26] and culminating in the optimal algorithm AC4 of ..."
Abstract

Cited by 213 (8 self)
 Add to MetaCart
(Show Context)
Consistency techniques have been studied extensively in the past as a way of tackling constraint satisfaction problems (CSP). In particular, various arcconsistency algorithms have been proposed, originating from Waltz's filtering algorithm [26] and culminating in the optimal algorithm AC4 of Mohr and Henderson [15]. AC4 runs in O(ed 2 ) in the worst case, where e is the number of arcs (or constraints) and d is the size of the largest domain. Being applicable to the whole class of (binary) CSP, these algorithms do not take into account the semantics of constraints. In this paper, we present a new generic arcconsistency algorithm AC5. This algorithm is parametrized on two specified procedures and can be instantiated to reduce to AC3 and AC4. More important, AC5 can be instantiated to produce an O(ed) algorithm for a number of important classes of constraints: functional, antifunctional, monotonic and their generalization to (functional, antifunctional, and monotonic) piecewise constraints. We also show that AC5 has an important application in constraint logic programming over finite domains [23]. The kernel of the constraint solver for such a programming language is an arcconsistency algorithm for a set of basic constraints. We prove that AC5, in conjunction with node consistency, provides a decision procedure for these constraints running in time O(ed).
SemiringBased Constraint Satisfaction and Optimization
 JOURNAL OF THE ACM
, 1997
"... We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be asso ..."
Abstract

Cited by 207 (26 self)
 Add to MetaCart
(Show Context)
We introduce a general framework for constraint satisfaction and optimization where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. The framework is based on a semiring structure, where the set of the semiring specifies the values to be associated with each tuple of values of the variable domain, and the two semiring operations (1 and 3) model constraint projection and combination respectively. Local consistency algorithms, as usually used for classical CSPs, can be exploited in this general framework as well, provided that certain conditions on the semiring operations are satisfied. We then show how this framework can be used to model both old and new constraint solving and optimization schemes, thus allowing one to both formally justify many informally taken choices in existing schemes, and to prove that local consistency techniques can be used also in newly defined schemes.
Structural descriptions and inexact matching
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 1981
"... AbstractIn this paper we formally define the structural description of an object and the concepts of exact and inexact matching of two structural descriptions. We discuss the problems associated with a bruteforce backtracking tree search for inexact matching and develop several different algorithm ..."
Abstract

Cited by 200 (5 self)
 Add to MetaCart
AbstractIn this paper we formally define the structural description of an object and the concepts of exact and inexact matching of two structural descriptions. We discuss the problems associated with a bruteforce backtracking tree search for inexact matching and develop several different algorithms to make the tree search more efficient. We develop the formula for the expected number of nodes in the tree for backtracking alone and with a forward checking algorithm. Finally, we present experimental results showing that forward checking is the most efficient of the algorithms tested. Index TermsBacktracking, forward checking, inexact matching, lookahead matching, relational homomorphism, relaxation, structural description, tree search. I.
Reasoning about Temporal Relations: A Maximal Tractable Subclass of Allen's Interval Algebra
 Journal of the ACM
, 1995
"... We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient ..."
Abstract

Cited by 195 (8 self)
 Add to MetaCart
(Show Context)
We introduce a new subclass of Allen's interval algebra we call "ORDHorn subclass," which is a strict superset of the "pointisable subclass." We prove that reasoning in the ORDHorn subclass is a polynomialtime problem and show that the pathconsistency method is sufficient for deciding satisfiability. Further, using an extensive machinegenerated case analysis, we show that the ORDHorn subclass is a maximal tractable subclass of the full algebra (assuming<F NaN> P6=NP). In fact, it is the unique greatest tractable subclass amongst the subclasses that contain all basic relations. This work has been supported by the German Ministry for Research and Technology (BMFT) under grant ITW 8901 8 as part of the WIP project and under grant ITW 9201 as part of the TACOS project. 1 1 Introduction Temporal information is often conveyed qualitatively by specifying the relative positions of time intervals such as ". . . point to the figure while explaining the performance of the system . . . "...
Applying interval arithmetic to real, integer and Boolean constraints
 JOURNAL OF LOGIC PROGRAMMING
, 1997
"... We present in this paper a general narrowing algorithm, based on relational interval arithmetic, which applies to any nary relation on!. The main idea is to define, for every such relation ae, a narrowing function \Gamma! ae based on the approximation of ae by a block which is the cartesian product ..."
Abstract

Cited by 186 (20 self)
 Add to MetaCart
We present in this paper a general narrowing algorithm, based on relational interval arithmetic, which applies to any nary relation on!. The main idea is to define, for every such relation ae, a narrowing function \Gamma! ae based on the approximation of ae by a block which is the cartesian product of intervals. We then show how, under certain conditions, one can compute the narrowing function of relations defined in terms of unions and intersections of simpler relations. We apply the use of the narrowing algorithm, which is the core of the CLP language BNRProlog, to integer and disequality constraints, to boolean constraints and to relations mixing numerical and boolean values. The result is a language, called CLP(BNR), where constraints are expressed in a unique structure, allowing the mixing of real numbers, integers and booleans. We end by the presentation of several examples showing the advantages of such approach from the point of view of the expressiveness, and give some computational results from a first prototype