Algorithms for Constructing Minimal Deduction Graphs

Authors:
Chao-Chih Yang;Jennifer Janu-Yin Chen;H. Lewis Chau
Affiliations:
Univ. of North Texas, Denton;CompData Corp., King of Prussia, PA;Univ. of California, Los Angeles
Venue:
IEEE Transactions on Software Engineering
Year:
1989

Citing 12
Cited 0

Foundations of logic programming

Foundations of logic programming
Programming in Prolog (2nd ed.)

Programming in Prolog (2nd ed.)
Programming expert systems in OPS5: an introduction to rule-based programming

Programming expert systems in OPS5: an introduction to rule-based programming
Implementation of logical query languages for databases

ACM Transactions on Database Systems (TODS)
Rule-based systems

Communications of the ACM
Relational databases

Relational databases
An algorithm for logically deducing Horn clauses and processing logic queries

International Journal of Pattern Recognition and Artificial Intelligence
Deduction Graphs: An Algorithm and Applications

IEEE Transactions on Software Engineering
Horn clauses and database dependencies

Journal of the ACM (JACM)
Graph Algorithms for Functional Dependency Manipulation

Journal of the ACM (JACM)
Logic for Problem Solving

Logic for Problem Solving
Rule Based Expert Systems: The Mycin Experiments of the Stanford Heuristic Programming Project (The Addison-Wesley series in artificial intelligence)

Rule Based Expert Systems: The Mycin Experiments of the Stanford Heuristic Programming Project (The Addison-Wesley series in artificial intelligence)

Quantified Score

Hi-index	0.01

Visualization

Abstract

Two algorithms for constructing minimal deduction graphs (MDG) for inferring rules and facts in an extended version of the Horn clause logic are described. A deduction graph (DG) is minimal if the number of arcs in the graph is minimized. Horn clauses (HC) are extended to Horn formulas (HF), such that the head or the body of an HF can be a conjunction of positive literals or a disjunction of the bodies of some rule instances, respectively. Each algorithm constructs an MDG from its source to its sink, whose arcs infer the HF 'if source then sink'. The construction of an MDG is based on a sound and complete set of inference rules of reflexivity, transitivity, and conjunction for HFs which proceeds by expanding a tree rooted at its sink until its source has a successful backtracking to the root. Then the MDG is extracted from the tree. The nodes being expanded in such a tree are classified into seven types, which are assigned by different priorities for their growing into subtrees or for their pruning to reduce the tree space.