Abstract
In this article we present a detailed, formal treatment of the linked inference principle, and we apply this principle to obtain the abstract formulations of various linked inference rules. Included among such rules are linked UR-resolution, linked hyperresolution, and linked binary resolution, each of which generalizes the corresponding standard and well-known inference rule. In addition to the formalism, we discuss the motivation and objectives for the formulation of linked inference rules. We also include experimental results and numerous examples. In particular, we show how and why the effectiveness of an automated reasoning program can be, and often is, markedly increased by relying on the linked version rather than the more familiar standard version of an inference rule.
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References
Andrews, P. (1968), ‘Resolution with merging’, Journal of the ACM 15, 367–381.
Andrews, P. (1976), ‘Refutations by matings’, IEEE Transactions on Computers C 25, 801–807.
Antoniou, G., and Ohlbach, H. (1983), ‘Terminator’, Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe West Germany, pp. 916–919.
Bibel, W. (1987), Automated Theorem Proving, 2nd edn., Vieweg Verlag, Braunschweig, West Germany.
Bledsoe, W., and Hines, L. (1980), ‘Variable elimination and chaining in a resolution-based prover for inequalities’, Proceedings of the Fifth International Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 87, W. Bibel and R. Kowalski (Eds.), Springer-Verlag, New York, pp. 70–87.
Boyer, R., and Moore, J (1988), A Computational Logic Handbook, Academic Press, San Diego.
Clocksin, W., and Mellish, C. (1984), Programming in Prolog, 2nd edn., Springer-Verlag, New York.
Davis, M. (1963), ‘Eliminating the irrelevant from mechanical proofs’, Experimental Arithmetic, High Speed Computing and Mathematics, Proceedings of Symposia in Applied Mathematics, Vol. 15, American Mathematical Society, Providence, R.I., pp. 15–30.
Dixon, J. (1973), ‘Z-resolution: Theorem proving with compiled axioms’, Journal of the ACM 20, 127–147.
Kirchner, C. (ed.) (1989), Special Issue on Unification, Journal of Symbolic Computation 7.
Kowalski, R. (1975), ‘A proof procedure based on connection graphs’, Journal of the ACM 22, 572–595.
Kowalski, R. (1979), Logic for Problem Solving, Elsevier North-Holland, New York.
Loveland, D. (1969), A simplified format for the model elimination procedure’, Journal of the ACM 16, 349–363.
Loveland, D. (1969), ‘Theorem-provers combining model elimination and resolution’, Machine Intelligence 4, B. Meltzer and D. Michie (Eds.) Edinburgh University Press, Edinburgh, pp. 73–82.
Lukasiewicz, J. (1970), ‘The equivalential calculus’, Jan Lukasiewicz: Selected Works, L. Borkowski (Ed.), North-Holland, Amsterdam, pp. 250–277.
McCharen, J., Overbeek, R., and Wos, L. (1976), ‘Complexity and related enhancements for automated theorem-proving programs’, Computers and Mathematics with Applications 2, 1–16.
McCune, W. (1990a), OTTER 2.0 Users Guide, Technical Report ANL-90/9, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill.
McCune, W. (1990b), ‘Experiments with discrimination tree indexing and path indexing for term retrieval’, Journal of Automated Reasoning (to appear).
Moore, J (1984), personal communication.
Overbeek, R. (1975), ‘An implementation of hyper-resolution’, Computational Mathematics with Applications 1, 201–214.
Robinson, G., and Wos, L. (1969), ‘Paramodulation and theorem-proving in first-order theories with equality’, Machine Intelligence 4, B. Meltzer and D. Michie (Eds.), Edinburgh University Press, Edinburgh, pp. 135–150.
Robinson, J. (1965), ‘A machine-oriented logic based on the resolution principle’, Journal of the ACM 12, 23–41.
Robinson, J. (1965), ‘Automatic deduction with hyper-resolution’, International Journal of Computer Mathematics 1, 227–234.
Shostak, R. E. (1976), ‘Refutation graphs’, Artificial Intelligence 7, 51–64.
Siekmann, J. (1989), ‘Unification theory’, p. 207 in [10].
Smith, B. (1988), Reference Manual for the Environmental Theorem Prover, An Incarnation of AURA, Technical Report ANL-88–2, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill.
Stickel, M. (1985), ‘Automated deduction by theory resolution’, Journal of Automated Reasoning 1, 333–355.
Stickel, M. (1988), ‘A Prolog technology theorem prover: Implementation by an extended Prolog compiler’, Journal of Automated Reasoning 4, 353–380.
Veroff, R., and Henschen, L. (1981), ‘Application of automatic transformations to program verification’, Proceedings of the Seventh International Joint Conference on Artificial Intelligence, Vol. 1, A. Drinan (Ed.), Vancouver, British Columbia, pp. 472–479.
Wos, L., Carson, D., and Robinson, G. (1964), ‘The unit preference strategy in theorem proving’, Proceedings of the AFIPS Conference 26, Spartan Books, Washington, D.C., pp. 615–621.
Wos, L., Robinson, G., and Carson, D. (1965), ‘Efficiency and completeness of the set of support strategy in theorem proving’, Journal of the ACM 12, 536–541.
Wos, L., Overbeek, R., and Henschen, L. (1980), ‘Hyperparamodulation: A refinement of paramodulation’, Proceedings of the Fifth International Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 87, W. Bibel and R. Kowalski (Eds.), Springer-Verlag, New York, pp. 208–219.
Wos, L., Overbeek, R., Lusk, E., and Boyle, J. (1984), Automated Reasoning: Introduction and Applications, Prentice-Hall, Englewood Cliffs, N.J.; 2nd edn., McGraw-Hill 1992.
Wos, L., Veroff, R., Smith, B., and McCune, W. (1984), ‘The linked inference principle, II: The user's viewpoint’, Proceedings of the Seventh International Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 170, R. Shostak (Ed.), springer-Verlag, New York, pp. 316–332.
Wos, L., and McCune, W. (1986), ‘Negative paramodulation’, Proceedings of the Eighth International Conference on Automated Deduction, Springer-Verlag Lecture Notes in Computer Science, Vol. 230, J. Siekmann (Ed.), Springer-Verlag, New York, pp. 229–239.
Wos, L. (1987), Automated Reasoning: 33 Basic Research Problems, Prentice-Hall, Englewood Cliffs, N.J.
Wos, L., and McCune, W. (1990), ‘Automated theorem proving and logic programming: A natural symbiosis, Journal of Logic Programming (to appear).
Yates, R., Raphael, B., and Hart, T. (1970), ‘Resolution graphs’, Artificial Intelligence 1, 257–289.
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This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.
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Veroff, R., Wos, L. The linked inference principle, I: The formal treatment. J Autom Reasoning 8, 213–274 (1992). https://doi.org/10.1007/BF00244283
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DOI: https://doi.org/10.1007/BF00244283