A PSpace Algorithm for Graded Modal Logic
- Stephan Tobies
- … show all 1 hide
Purchase on Springer.com
$29.95 / €24.95 / £19.95*
* Final gross prices may vary according to local VAT.
We present a PSpace algorithm that decides satisfiability of the graded modal logic Gr(K R)—a natural extension of propositional modal logic K R by counting expressions—which plays an important role in the area of knowledge representation. The algorithm employs a tableaux approach and is the first known algorithm which meets the lower bound for the complexity of the problem. Thus, we exactly fix the complexity of the problem and refute a ExpTime-hardness conjecture. This establishes a kind of “theoretical benchmark” that all algorithmic approaches can be measured with.
- Y. André, J. van Benthem, and I. Németi. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic, 27(3):217–274, 1998. CrossRef
- F. Baader, M. Buchheit, and B. Hollunder. Cardinality restrictions on concepts. Artificial Intelligence, 88(1-2):195–213, 1996. CrossRef
- D. Calvanese, M. Lenzerini, and D. Nardi. A Unified Framework for Class Based Representation Formalisms. Proc. of KR-94, 1994.
- W. Van der Hoek, and M. De Rijke. Counting objects. Journal of Logic and Computation, 5(3):325–345, June 1995.
- F. M. Donini, M. Lenzerini, D. Nardi, and W. Nutt. The complexity of concept languages.. Information and Computation, 134(1):1–58, 10 April 1997.
- K. Fine. In so many possible worlds. Notre Dame Journal of Formal Logic, 13:516–520, 1972. CrossRef
- F. Giunchiglia and R. Sebastiani. Building decision procedures for modallogics from propositional decision procedures—the case study of modal K.. Proc. of CADE-13, LNCS 1104. Springer, 1996.
- B. Hollunder and F. Baader. Qualifying number restrictions in concept languages. In Proc. of KR-91, pages 335–346, Boston (USA) 1991.
- J. Y. Halpern and Y. Moses. A guide to completeness and complexity for model logics of knowledge and belief. Artificial Intelligence 54(3):319–379, April 1992.
- U. Hustadt and R. A. Schmidt. On evaluating decision procedures for modal logic. In Proc. of IJCAI-97, volume 1, pages 202–207, 1997.
- R. E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing,, 6(3):467–480, September 1977.
- H. J. Ohlbach and R. A. Schmidt. Functional translation and second-order frame properties of modal logics. Journal of Logic and Computation, 7(5):581–603, October 1997.
- H. J. Ohlbach, R. A. Schmidt, and U. Hustadt. Translating graded modalities into predicate logic.. In H. Wansing, editor, Proof Theory of Modal Logic volume 2 of Applied Logic Series, pages 253–291. Kluwer, 1996.
- W. J. Savitch. Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4(2):177–192, April 1970.
- K. Schild. A correspondence theory for terminological logics: Preliminary report. In Proc. of IJCAI-91,, pages 466–471, 1991.
- R. A. Schmidt. Resolution is a decision procedure for many propositional modal logics: Extended abstract. In M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, editors, Advances in Modal Logic ’96. CLSI Publications, 1997.
- M. Schmidt-Schauß and G. Smolka. Attributive concept descriptions with complements. Artificial Intelligence, 48:1–26, 1991. CrossRef
- A PSpace Algorithm for Graded Modal Logic
- Book Title
- Automated Deduction — CADE-16
- Book Subtitle
- 16th International Conference on Automated Deduction Trento, Italy, July 7–10, 1999 Proceedings
- pp 52-66
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- eBook Packages
- Stephan Tobies (4)
- Author Affiliations
- 4. LuFg Theoretical Computer Science, RWTH Aachen, Germany
To view the rest of this content please follow the download PDF link above.