A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
The Concept of Weak Substitution in Theorem-Proving
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Subsumption and Connectionsgraphs
GWAI '81 Proceedings of the German Workshop on Artificial Intelligence
Efficient Database Access from Prolog
IEEE Transactions on Software Engineering
Termination of programs in constraint query languages
SAC '94 Proceedings of the 1994 ACM symposium on Applied computing
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
Structuring Resolution Proofs by Introducing New Lemmata
Journal of Automated Reasoning
A New Technique for Verifying and Correcting Logic Programs
Journal of Automated Reasoning
An Algorithm for Dual Transformation in First-Order Logic
Journal of Automated Reasoning
Implicational Completeness of Signed Resolution
Selected Papers from Automated Deduction in Classical and Non-Classical Logics
Theta-Subsumption in a Constraint Satisfaction Perspective
ILP '01 Proceedings of the 11th International Conference on Inductive Logic Programming
Algorithms, Datastructures, and other Issues in Efficient Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
DS '01 Proceedings of the 4th International Conference on Discovery Science
Handbook of automated reasoning
Combining superposition, sorts and splitting
Handbook of automated reasoning
Fast Theta-Subsumption with Constraint Satisfaction Algorithms
Machine Learning
Computing cores for data exchange: new algorithms and practical solutions
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Efficient core computation in data exchange
Journal of the ACM (JACM)
Deciding expressive description logics in the framework of resolution
Information and Computation
WSMO-MX: A hybrid Semantic Web service matchmaker
Web Intelligence and Agent Systems
Tree Automata and Automated Model Building
Fundamenta Informaticae
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The costs of subsumption algorithms are analyzed by an estimation of the maximal number of unification attempts (worst-case unification complexity) made for deciding whether a clause C subsumes a clause D. For this purpose the clauses C and D are characterized by the following parameters: number of variables in C, number of literals in C, number of literals in D, and maximal length of the literals. The worst-case unification complexity immediately yields a lower bound for the worst-case time complexity.First, two well-known algorithms (Chang-Lee, Stillman) are investigated. Both algorithms are shown to have a very high worst-case time complexity. Then, a new subsumption algorithm is defined, which is based on an analysis of the connection between variables and predicates in C. An upper bound for the worst-case unification complexity of this algorithm, which is much lower than the lower bounds for the two other algorithms, is derived. Examples in which exponential costs are reduced to polynomial costs are discussed. Finally, the asymptotic growth of the worst-case complexity for all discussed algorithms is shown in a table (for several combinations of the parameters).