Abstract
We present a sound and complete calculus for an expressive sorted first-order logic. Sorts are extended to the semantic and pragmatic use of unary predicates. A sort may denote an empty set and the sort structure can be created by making use of the full first-order language. Technically spoken, we allow sort declarations to be used in the same way than ordinary atoms. Therefore we can compile every first-order logic formula into our logic.
The extended expressivity implies an extended sorted inference machine. We present a new unification algorithm and show that the declarations the unification algorithm is built on have to be changed dynamically during the deduction process. Deductions in the resulting resolution calculus are very efficient compared to deductions in the unsorted resolution calculus. The approach is a conservative extension of the known sorted approaches, as it simplifies to the known sorted calculi if we apply the calculus to the much more restricted input formulas of these calculi.
This research was supported by the ESPRIT project MEDLAR (3125) of the European Community
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References
C. Beierle, U. Hedstück, U. Pletat, and J. Siekmann. An order-sorted logic for knowledge representation systems. Artificial Intelligence, 55:149–191, 1992.
H.J. Bürckert. Constraint resolution. Lecture Notes in Artificial Intelligence. Springer Verlag, 1991.
A.G. Cohn. A more expressive formulation of many sorted logic. Journal of Automated Reasoning, 3(2):113–200, 1987.
A.M. Frisch. A general framework for sorted deduction: Fundamental results on hybrid reasoning. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 126–136, May 1989.
W. McCune. Otter 2.0. In 10th International Conference on Automated Deduction, pages 663–664. Springer Verlag, 1990.
W. McCune and L. Wos. Experiments in automated deduction with condensed detachment. In 11th International Conference on Automated Deduction, pages 209–223. Springer Verlag, 1992.
D. Meredith. In memoriam carew arthur meredith (1904–1976). Notre Dame Journal of Formal Logic, 18(513–516), 1977.
M. Schmidt-Schauß. Computational aspects of an order sorted logic with term declarations. Lecture Notes in Artificial Intelligence. Springer Verlag, 1989.
J. Siekmann. Unification theory. Journal of Symbolic Computation, Special Issue on Unification, 7:207–274, 1989.
M. Stickel. Theory resolution. Journal of Automated Reasoning, 1(4):333–355, 1985.
C. Walther. A Many-sorted Calculus based on Resolution and Paramodulation. Research Notes in Artificial Intelligence. Pitman Ltd., 1987.
C. Weidenbach. A sorted logic using dynamic sorts. MPI-Report MPI-I-91-218, Max-Planck-Institut für Informatik, Saarbrücken, December 1991.
C. Weidenbach and H.J. Ohlbach. A resolution calculus with dynamic sort structures and partial functions. In Proceedings of the 9th European Conference on Artificial Intelligence, pages 688–693. Pitman Publishing, London, August 1990.
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© 1993 Springer-Verlag Berlin Heidelberg
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Weidenbach, C. (1993). A new sorted logic. In: Jürgen Ohlbach, H. (eds) GWAI-92: Advances in Artificial Intelligence. Lecture Notes in Computer Science, vol 671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018991
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DOI: https://doi.org/10.1007/BFb0018991
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