Abstract
This article describes an original resolution strategy (RCD: "Résolution CAT-correcte Dirigée") which is defined in propositionnal logic. This strategy represents a restriction of the application of "resolution principle" [12] and is specially designed to infer particular Horn clauses called CATCL ("Clauses à Antécédents Typés et Conséquents Limités").
We show that all significant clauses for an ATMS (Assumption-based Truth Maintenance System [4, 5, 6]) can be considered CATCL clauses under certain conditions and thus define an ATMS based on this resolution strategy, named ARC ("ATMS basé sur la Résolution CAT-correcte dirigée").
The ARC system retains all the advantages of conventional ATMS, allows the manipulation of general clauses (not only Horn clauses or disjunctions of assumptions), and integrates the new concept of "required label" which permits an improvement in performances.
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References
Cayrol and Tayrac, Les résolutions CAT-correcte et CCT-correcte, la résolution CAT-correcte dans l'ATMS, "Colloque international sur l'informatique cognitive des organisations", Québec 89.
Cayrol et Tayrac, CAT-correct and CCT-correct resolution, CAT-correct resolution in ATMS, submited to Artificial Intelligence.
Chang and Lee, Symbolic Logic and Mechanical Theorem Proving, Computer Science and Applied Mathematics (1973).
de Kleer, An Assumption-based TMS, Artificial Intelligence 28 (1986) 127–162.
de Kleer, Extending the ATMS, Artificial Intelligence 28 (1986) 163–196.
de Kleer, Problem Solving with the ATMS, Artificial Intelligence 28 (1986) 197–224.
de Kleer, A general labeling algorithm for assumption-based truth maintenance, Proceedings of the National Conference on Artificial Intelligence, Saint Paul, MN (August 1988), 188–192.
Kean and Tsiknis, An incremental method for generating prime implicants/implicates, University of British Columbia Technical Report TR-88-16 (1988).
Kowalski, Studies in the completeness and efficiency of theorem proving by resolution, Ph.D. Thesis Univ. of Edinburgh, Scotland (1970).
Maier D. and Warren D. S., Computing with Logic. The Benjamin/Cummings Publishing Company, Inc. (1988).
Reiter and de Kleer, Foundations of assumption-based truth maintenance system. Preliminary report. Proc. of Amer. Assoc. for Artificial Intelligence Conf. (AAAI-87), Seatle, 183–188.
Robinson, Automatic deduction with Hyper-resolution. Intern. J. Comput. Math. 1 (227–234).
Tayrac, Etude de nouvelles stratégies de résolution, Application à l'ATMS, Ph.D. Thesis Univ. Paul Sabatier of Toulouse, France, June 1990.
Tison, Generalized Consensus Theory and Application to the Minimisation of Boolean Functions, IEEE Transaction on Electronic Computers, EC-16, 4, August 67, pp 446–456.
Tsiknis and Kean, Clause Management Systems, University of British Columbia, Technical report TR-88-21 (1988).
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© 1991 Springer-Verlag Berlin Heidelberg
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Tayrac, P. (1991). ARC: An extended ATMS based on directed CAT-correct resolution. In: Martins, J.P., Reinfrank, M. (eds) Truth Maintenance Systems. TMW 1990. Lecture Notes in Computer Science, vol 515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0037032
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DOI: https://doi.org/10.1007/BFb0037032
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