Abstract
Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ajili, F., Kirchner, C.: A modular framework for the combination of symbolic and built-in constraints. In: Proceedings of Fourteenth International Conference on Logic Programming, Leuven, Belgium, pp. 331–345. The MIT Press, Cambridge (1997)
Baader, F., Ghilardi, S.: Connecting many-sorted theories. LTCS-Report LTCS-05-04, TU Dresden, Germany, See (2005), http://lat.inf.tu-dresden.de/research/reports.html
Baader, F., Ghilardi, S., Tinelli, C.: A new combination procedure for the word problem that generalizes fusion decidability results in modal logics. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 183–197. Springer, Heidelberg (2004)
Baader, F., Lutz, C., Sturm, H., Wolter, F.: Fusions of description logics and abstract description systems. Journal of Artificial Intelligence Research 16, 1–58 (2002)
Baader, F., Tinelli, C.: A new approach for combining decision procedures for the word problem, and its connection to the Nelson-Oppen combination method. In: Proceedings of the 14th International Conference on Automated Deduction, Townsville (Australia). LNCS (LNAI), vol. 1249, pp. 19–33. Springer, Heidelberg (1997)
Baader, F., Tinelli, C.: Deciding the word problem in the union of equational theories. Information and Computation 178(2), 346–390 (2002)
Chang, C.-C., Keisler, H.J.: Model Theory, 3rd edn. North-Holland, Amsterdam (1990)
Domenjoud, E., Klay, F., Ringeissen, C.: Combination techniques for non-disjoint equational theories. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 267–281. Springer, Heidelberg (1994)
Fiorentini, C., Ghilardi, S.: Combining word problems through rewriting in categories with products. Theoretical Computer Science 294, 103–149 (2003)
Gallier, J.H.: Logic for Computer Science: Foundations of Automatic Theorem Proving. Harper & Row, New York (1986)
Ghilardi, S.: Model-theoretic methods in combined constraint satisfiability. Journal of Automated Reasoning 33(3–4), 221–249 (2004)
Kracht, M., Wolter, F.: Properties of independently axiomatizable bimodal logics. The Journal of Symbolic Logic 56(4), 1469–1485 (1991)
Kutz, O., Lutz, C., Wolter, F., Zakharyaschev, M.: \(\mathcal{E}\)-connections of abstract description systems. Artificial Intelligence 156, 1–73 (2004)
Makkai, M., Reyes, G.E.: First-Order Categorical Logic. Lecture Notes in Mathematics, vol. 611. Springer, Berlin (1977)
Nelson, G.: Combining satisfiability procedures by equality-sharing. In: Bledsoe, W.W., Loveland, D.W. (eds.) Automated Theorem Proving: After 25 Years. Contemporary Mathematics, vol. 29, pp. 201–211. American Mathematical Society, Providence (1984)
Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. on Programming Languages and Systems 1(2), 245–257 (1979)
Nipkow, T.: Combining matching algorithms: The regular case. Journal of Symbolic Computation 12, 633–653 (1991)
Oppen, D.C.: Complexity, convexity and combinations of theories. Theoretical Computer Science 12, 291–302 (1980)
Pigozzi, D.: The join of equational theories. Colloquium Mathematicum 30(1), 15–25 (1974)
Spaan, E.: Complexity of Modal Logics. PhD thesis, Department of Mathematics and Computer Science, University of Amsterdam, The Netherlands (1993)
Tinelli, C.: Cooperation of background reasoners in theory reasoning by residue sharing. Journal of Automated Reasoning 30(1), 1–31 (2003)
Tinelli, C., Ringeissen, C.: Unions of non-disjoint theories and combinations of satisfiability procedures. Theoretical Computer Science 290(1), 291–353 (2003)
Wolter, F.: Fusions of modal logics revisited. In: Advances in Modal Logic. CSLI, Stanford, CA (1998)
Zarba, C.: Combining multisets with integers. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 363–376. Springer, Heidelberg (2002)
Zawadowski, M.W.: Descent and duality. Ann. Pure Appl. Logic 71(2), 131–188 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Baader, F., Ghilardi, S. (2005). Connecting Many-Sorted Theories. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_21
Download citation
DOI: https://doi.org/10.1007/11532231_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28005-7
Online ISBN: 978-3-540-31864-4
eBook Packages: Computer ScienceComputer Science (R0)