scholarly journals A Hierarchy of Tractable Subsets for Computing Stable Models

1996 ◽  
Vol 5 ◽  
pp. 27-52 ◽  
Author(s):  
R. Ben-Eliyahu
Keyword(s):  
Artificial Intelligence ◽  
Knowledge Base ◽  
Knowledge Bases ◽  
Default Logic ◽  
Autoepistemic Logic ◽  
Computational Problem ◽  
Maintenance Systems ◽  
Truth Maintenance ◽  
Truth Maintenance Systems ◽  
Stable Models

Finding the stable models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of truth maintenance systems, autoepistemic logic, and default logic. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases, Omega_1,Omega_2,..., with the following properties: first, Omega_1 is the class of all stratified knowledge bases; second, if a knowledge base Pi is in Omega_k, then Pi has at most k stable models, and all of them may be found in time O(lnk), where l is the length of the knowledge base and n the number of atoms in Pi; third, for an arbitrary knowledge base Pi, we can find the minimum k such that Pi belongs to Omega_k in time polynomial in the size of Pi; and, last, where K is the class of all knowledge bases, it is the case that union{i=1 to infty} Omega_i = K, that is, every knowledge base belongs to some class in the hierarchy.

scholarly journals Explanation in Constraint Satisfaction: A Survey

2021 ◽  
Author(s):  
Sharmi Dev Gupta ◽  
Begum Genc ◽  
Barry O'Sullivan
Keyword(s):  
Artificial Intelligence ◽  
Constraint Satisfaction ◽  
Boolean Satisfiability ◽  
Machine Learning Methods ◽  
General Field ◽  
History Of ◽  
Maintenance Systems ◽  
Truth Maintenance ◽  
Truth Maintenance Systems ◽  
Explanation Generation

Much of the focus on explanation in the field of artificial intelligence has focused on machine learning methods and, in particular, concepts produced by advanced methods such as neural networks and deep learning. However, there has been a long history of explanation generation in the general field of constraint satisfaction, one of the AI's most ubiquitous subfields. In this paper we survey the major seminal papers on the explanation and constraints, as well as some more recent works. The survey sets out to unify many disparate lines of work in areas such as model-based diagnosis, constraint programming, Boolean satisfiability, truth maintenance systems, quantified logics, and related areas.

USING ATMS TO EFFICIENTLY VERIFY THE TERMINATION OF REWRITE RULE PROGRAMS

1992 ◽  
Vol 02 (04) ◽  
pp. 547-565 ◽  
Author(s):  
MASAHITO KURIHARA ◽  
HISASHI KONDO ◽  
AZUMA OHUCHI
Keyword(s):  
Artificial Intelligence ◽  
Software Engineering ◽  
Communication Protocol ◽  
Engineering Problem ◽  
Maintenance Systems ◽  
Rewrite Rules ◽  
Truth Maintenance ◽  
Truth Maintenance Systems ◽  
Overall Efficiency ◽  
Problem Solvers

Assumption-based truth maintenance systems (ATMS) have become powerful and widely used tools in artificial intelligence problem solvers. In this paper, we apply ATMS to verification of termination of computer programs written as a set of rewrite rules. Compared with the traditional methods based on the ordinary backtracking, our method can greatly improve the overall efficiency by virtue of the ATMS's ability to avoid futile backtracking, rediscovering inferences, and rediscovering contradictions. The originality of our work lies in the practical use of the ATMS in a software engineering problem and in the communication protocol between the termination verifier and the ATMS.

MODIFIED BACKJUMPING ALGORITHMS FOR SOLVING CONSTRAINT SATISFACTION PROBLEMS

1999 ◽  
Vol 13 (01) ◽  
pp. 133-147
Author(s):  
U. CHOWDHURY ◽  
D. K. GUPTA
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Search Technique ◽  
Dead End ◽  
Consistent Manner ◽  
Maintenance Systems ◽  
Truth Maintenance ◽  
Truth Maintenance Systems ◽  
Is Failure ◽  
Selection Of

The backtracking algorithm is a prominent search technique in AI, particularly due to its use in Constraint Satisfaction Problems (CSPs), Truth Maintenance Systems (TMS), and PROLOG. In the context of CSPs, Dechter5 and Gashnig10 proposed two variants of the backtracking algorithm known as backjumping algorithms. One is graph-based and the other is failure-based backjumping algorithm. These algorithms attempt to backjump to the source of failure in case of a dead-end situation. This improves the backtracking performance. However, these algorithms are not consistent in the selection of the variable to backjump. In this paper, the modifications of both types of backjumping algorithms are proposed. These algorithms adopt a technique to select the variable to backjump in a consistent manner. This further increases the search efficiency in them. The merits of these modified algorithms are investigated theoretically. Experimental results on the zebra problem and random problems show that the modified algorithms give better results on most occasions.

COMBINING DEFAULT LOGIC DATABASES

1994 ◽  
Vol 03 (03) ◽  
pp. 319-348 ◽  
Author(s):  
CHITTA BARAL ◽  
SARIT KRAUS ◽  
JACK MINKER ◽  
V. S. SUBRAHMANIAN
Keyword(s):  
Knowledge Representation ◽  
Knowledge Base ◽  
Large Scale ◽  
Future Generation ◽  
Knowledge Bases ◽  
Default Logic ◽  
Integrity Constraints ◽  
Specialized Knowledge ◽  
The Past ◽  
The Future

During the past decade, it has become increasingly clear that the future generation of large-scale knowledge bases will consist, not of one single isolated knowledge base, but a multiplicity of specialized knowledge bases that contain knowledge about different domains of expertise. These knowledge bases will work cooperatively, pooling together their varied bodies of knowledge, so as to be able to solve complex problems that no single knowledge base, by itself, would have been able to address successfully. In any such situation, inconsistencies are bound to arise. In this paper, we address the question: "Suppose we have a set of knowledge bases, KB1, …, KBn, each of which uses default logic as the formalism for knowledge representation, and a set of integrity constraints IC. What knowledge base constitutes an acceptable combination of KB1, …, KBn?"

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