Abstract
We consider a two-variable guarded fragment with number restrictions for binary relations and give a satisfiability preserving transformation of formulas in this fragment to the three-variable guarded fragment. The translation can be computed in polynomial time and produces a formula that is linear in the size of the initial formula even for the binary coding of number restrictions. This allows one to reduce reasoning problems for many description logics to the satisfiability problem for the guarded fragment.
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References
Andréka, H., van Benthem, J., Németi, I.: Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27, 217–274 (1998)
Ganzinger, H., de Nivelle, H.: A superposition decision procedure for the guarded fragment with equality. In: Proc. 14th IEEE Symposium on Logic in Computer Science, pp. 295–305. IEEE Computer Society Press, Los Alamitos (1999)
Grädel, E.: Decision procedures for guarded logics. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 31–51. Springer, Heidelberg (1999a)
Grädel, E.: On the restraining power of guards. Journal of Symbolic Logic 64(4), 1719–1742 (1999b)
Haarslev, V., Möller, R.: Optimizing reasoning in description logics with qualified number restrictions. In: Proceedings of the International Workshop on Description Logics (DL 2001), Stanford, USA, pp. 142–151 (2001)
Haarslev, V., Timmann, M., Möller, R.: Combining tableau and algebraic methods for reasoning with qualified number restrictions in description logics. In: Proceedings of the International Workshop on Methods for Modalities 2 (M4M-2), Amsterdam, Netherlands (2001)
Hladik, J.: Implementation and optimisation of a tableau algorithm for the guarded fragment. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, p. 145. Springer, Heidelberg (2002)
Hladik, J., Sattler, U.: A translation of looping alternating automata to description logics. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 90–105. Springer, Heidelberg (2003)
Tobies, S.: Complexity Results and Practical Algorithms for Logics in Knowledge Representation, PhD thesis, RWTH Aachen, Germany (2001)
Vardi, M.: Why is modal logic so robustly decidable? In: Immerman, N., Kolaitis, P.G. (eds.) Descriptive Complexity and Finite Models. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 31, pp. 149–184. American Mathematical Society, Princeton University (1996)
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Kazakov, Y. (2004). A Polynomial Translation from the Two-Variable Guarded Fragment with Number Restrictions to the Guarded Fragment. In: Alferes, J.J., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2004. Lecture Notes in Computer Science(), vol 3229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30227-8_32
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DOI: https://doi.org/10.1007/978-3-540-30227-8_32
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