Abstract
Hypothesis finding constitutes a basic technique for fields of inference related to Discovery Science, like inductive inference and abductive inference. In this paper we explain that various hypothesis finding methods in clausal logic can be put on one general ground by using the combination of the upward refinement and residue hypotheses. Their combination also gives a natural extension of the relative subsumption relation. We also explain that definite bottom clauses, a special type of residue hypotheses, can be found by extending SLD-resolution.
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References
D. Angluin, M. Frazier, and L. Pitt. Learning Conjunctions of Horn Clauses. Machine Learning, 9:147–164, 1992.
H. Arimura. Learning Acyclic First-order Horn Sentences From Implication. In Proceedings of the 8th International Workshop on Algorithmic Learning Theory (LNAI 1316), pages 432–445, 1997.
H. Arimura and A. Yamamoto. Inductive Logic Programming: From Logic of Discovery to Machine Learning. IEICE Transactions on Information and Systems, E83-D(1):10–18, 2000.
W. Bibel. Deduction: Automated Logic. Academic Press, 1993.
W. Buntine. Generalized Subsumption and its Applications to Induction and Redundancy. Artificial Intelligence, 36:149–176, 1988.
C.-L. Chang and R. C.-T. Lee. Symbolic Logic and Mechanical Theorm Proving. Academic Press, 1973.
B. Fronhöfer and A. Yamamoto. Relevant Hypotheses as a Generalization of the Bottom Method. In Proceedings of the Joint Workshop of SIG-FAI and SIG-KBS, SIG-FAI/KBS-9902, pages 89–96. JSAI, 1999.
B. Fronhöfer and A. Yamamoto. Hypothesis Finding with Proof Theoretical Appropriateness Criteria. Submitted to the AI journal, 2000.
K. Inoue. Linear Resolution for Consequence Finding. Artificial Intelligence, 56:301–353, 1992.
K. Ito and A. Yamamoto. Finding Hypotheses from Examples by Computing the Least Generalization of Bottom Clauses. In Proceedings of the First International Conference on Discovery Science (Lecture Notes in Artificial Intelligence 1532), pages 303–314. Springer, 1998.
B. Jung. On Inverting Generality Relations. In Proceedings of the 3rd International Workshop on Inductive Logic Programming, pages 87–101, 1993.
P. D. Laird. Learning from Good and Bad Data. Kluwer Academic Publishers, 1988.
R.C.T. Lee. A Completeness Theorem and Computer Program for Finding Theorems Derivable from Given Axioms. PhD thesis, University of California, Berkeley, 1967.
A. Leitsch. The Resolution Calculus. Springer, 1997.
S. Muggleton. Inverse Entailment and Progol. New Generation Computing, 13:245–286, 1995.
C. H. Papadimitriou. Computational Complexity. Addison Wesley, 1993.
G. D. Plotkin. A Further Note on Inductive Generalization. In Machine Intelligence 6, pages 101–124. Edinburgh University Press, 1971.
D. Poole, R. Goebel, and R. Aleliunas. Theorist: A Logical Reasoning System for Defaults and Diagnosis. In N. Cercone and G. McCalla, editors, The Knowledge Frontier: Essays in the Representation of Knowledge, pages 331–352. Springer-Verlag, 1987.
C. Rouveirol. Extentions of Inversion of Resolution Applied to Theory Completion. In S. Muggleton, editor, Inductive Logic Programming, pages 63–92. Academic Press, 1992.
E. Y. Shapiro. Inductive Inference of Theories From Facts, 1981. Also in: Computational Logic (Lassez, J.-L. and Plotkin, G. eds.), The MIT Press, Cambridge, MA, pp.199–254, 1991.
A. Yamamoto. Representing Inductive Inference with SOLD-Resolution. In Proceedings of the IJCAI’97 Workshop on Abduction and Induction in AI, pages 59–63, 1997.
A. Yamamoto. Which Hypotheses Can Be Found with Inverse Entailment? In Proceedings of the Seventh International Workshop on Inductive Logic Programming (LNAI 1297), pages 296–308, 1997. The extended abstract is in Proceedings of the IJCAI’97 Workshop on Frontiers of Inductive Logic Programming, pp.19–23 (1997).
A. Yamamoto. Logical Aspects of Several Bottom-up Fittings. To appear in Proceedings of the 9th International Workshop on Algorithmic LEarning Theory, 1998.
A. Yamamoto. An Inference Method for the Complete Inverse of Relative Subsumption. New Generation Computing, 17(1):99–117, 1999.
A. Yamamoto. Using abduction for induction based on bottom generalization. In A. Kakas and P. Flach, editor, Abductive and Inductive Reasoning: Essays on their Relation and Integration, pages 267–280. Kluwer-Academic Press, 2000.
A. Yamamoto and B. Fronhöfer. Hypothesis Finding via Residue Hypotheses with the Resolution Principle. In Proceedings of the the 11th International Workshop on Algorithmic Learning Theory (LNAI 1968), pages 156–165, 2000.
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Yamamoto, A., Fronhöfer, B. (2002). A Theory of Hypothesis Finding in Clausal Logic. In: Arikawa, S., Shinohara, A. (eds) Progress in Discovery Science. Lecture Notes in Computer Science(), vol 2281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45884-0_16
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DOI: https://doi.org/10.1007/3-540-45884-0_16
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