Logic for computer science: foundations of automatic theorem proving
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Information Processing Letters
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Implication of clauses is undecidable
Theoretical Computer Science
New Generation Computing - Selected papers from the international workshop on algorithmic learning theory,1990
Sub-unification: a tool for efficient induction of recursive programs
ML92 Proceedings of the ninth international workshop on Machine learning
Inverting implication with small training sets
ECML-94 Proceedings of the European conference on machine learning on Machine Learning
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Inductive Logic Programming: Techniques and Applications
Inductive Logic Programming: Techniques and Applications
Machine Learning
Inductive Logic Programming: Derivations, Successes and Shortcomings
ECML '93 Proceedings of the European Conference on Machine Learning
Generalization under Implication by using Or-Introduction
ECML '93 Proceedings of the European Conference on Machine Learning
A completeness theorem and a computer program for finding theorems derivable from given axioms
A completeness theorem and a computer program for finding theorems derivable from given axioms
Undecidability of the Horn-clause implication problem
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Pac-learning recursive logic programs: efficient algorithms
Journal of Artificial Intelligence Research
Pac-learning recursive logic programs: negative results
Journal of Artificial Intelligence Research
Generalization of Clauses Relative to a Theory
Machine Learning - special issue on inductive logic programming
Learning in Clausal Logic: A Perspective on Inductive Logic Programming
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part I
Minimal Generalizations under OI-Implication
ISMIS '02 Proceedings of the 13th International Symposium on Foundations of Intelligent Systems
Intelligent data analysis
Compile the Hypothesis Space: Do it Once, Use it Often
Fundamenta Informaticae - Progress on Multi-Relational Data Mining
Least generalizations and greatest specializations of sets of clauses
Journal of Artificial Intelligence Research
OI-implication: soundness and refutation completeness
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
iSeM: approximated reasoning for adaptive hybrid selection of semantic services
ESWC'10 Proceedings of the 7th international conference on The Semantic Web: research and Applications - Volume Part II
Compile the Hypothesis Space: Do it Once, Use it Often
Fundamenta Informaticae - Progress on Multi-Relational Data Mining
The iSeM matchmaker: A flexible approach for adaptive hybrid semantic service selection
Web Semantics: Science, Services and Agents on the World Wide Web
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In the area of inductive learning, generalization is a main operation, and the usual definition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine learning. Almost all inductive learning systems that perform generalization of clauses use the relation θ-subsumption instead of implication. The main reason is that there is a well-known and simple technique to compute least general generalizations under θ-subsumption, but not under implication. However generalization under θ-subsumption is inappropriate for learning recursive clauses, which is a crucial problem since recursion is the basic program structure of logic programs. We note that implication between clauses is undecidable, and we therefore introduce a stronger form of implication, called T-implication, which is decidable between clauses. We show that for every finite set of clauses there exists a least general generalization under T-implication. We describe a technique to reduce generalizations under implication of a clause to generalizations under θ-subsumption of what we call an expansion of the original clause. Moreover we show that for every non-tautological clause there exists a T-complete expansion, which means that every generalization under T-implication of the clause is reduced to a generalization under θ-subsumption of the expansion.