Automated reasoning in some local extensions of ordered structures

Proceedings of The International Symposium on Multiple-Valued Logic

Volumn , Issue , 2007, Pages

  Sofronie Stokkermans, Viorica ^a   Ihlemann, Carsten ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN ALGEBRA; DATA STRUCTURES; HIERARCHICAL SYSTEMS;

ALGEBRAIC STRUCTURES; LOCAL EXTENSIONS; MONOTONICITY AXIOMS;

LOGIC PROGRAMMING;

EID: 34548234891     PISSN: 0195623X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISMVL.2007.10     Document Type: Conference Paper

References (24)

1. R Baader. Terminological cycles in a description logic with existential restrictions. In G. Gottlob and T. Walsh, editors, Proc. 18th International Joint Conference on Artificial Intelligence, pages 325-330. Morgan Kaufmann, 2003.
2. S. Burris. Polynomial time uniform word problems. Mathematical Logic Quarterly, 41:173-182, 1995.
3. B. Davey and H. Priestley. Introduction to Lattices and Order. Cambridge University Press, 1990.
4. J. Farley. Priestley duality for order-preserving maps into distributive lattices. Order, 13:65-98, 1996.
5. H. Ganzinger. Relating semantic and proof-theoretic concepts for polynomial time decidability of uniform word problems. In Proc. 16th IEEE Symp. on Logic in Computer Science (LICS'01), pages 81-92. IEEE Comp. Soc. Press, 2001.
6. H. Ganzinger, G. Hagen, R. Nieuwenhuis, A. Oliveras, and C. Tinelli. DPLL(T): Fast decision procedures. In R. Alur and D. Peled, editors, Proc. 16th International Conference on Computer Aided Verification (CAV'04), LNCS 3114, pages 175-188. Springer, 2004.
7. J. Gispert and D. Mundici. MV-algebras: A variety for magnitudes with archimedean units. Algebra Universalis, 53:7-43, 2005.
8. R. Goldblatt. Varieties of complex algebras. Annals of Pure and Applied Logic, 44(3):153-301, 1989.
9. R. Hähnle. Many-valued logic and mixed integer programming. Annals of Mathematics and Artificial Intelligence, 12(3,4):231-264, Dec. 1994.
10. R. Hähnle. Proof theory of many-valued logic - linear optimization - logic design. Soft Computing - A Fusion of Foundations, Methodologies and Applications, 1(3):107-119, 1997.
11. R. Hähnle. Complexity of many-valued logics. In M. Fitting and E. Orlowska, editors, Beyond Two: Theory and Applications of Multiple Valued Logic, volume 114 of Studies in Fuzziness and Soft Computing, chapter 3, pages 211-233. Springer, Berlin, 2003.
12. P. Hájek. Metamathematics of Fuzzy Logic. Trends in Logic, Volume 4. Kluwer Academic Publishers, Dordrecht, 1998.
13. C. Hartonas and J. Dunn. Stone duality for lattices. Algebra Universalis, 37(3):391-401, 1997.
14. E. Marchioni and F. Montagna. Complexity and definability issues in LΠ1/2. Journal of Logic and Computation, to appear.
15. D. Mundici. Satisfiability of many-valued sentential logics is NP-complete. Theoretical Computer Science, 52:145-153, 1987.
16. H. Priestley. Representation of distributive lattices by means of ordered Stone spaces. Bull. London Math. Soc., 2:186-190, 1970.
17. V. Sofronie-Stokkermans. Duality and canonical extensions of bounded distributive lattices with operators, and applications to the semantics of non-classical logics I. Studia Logica, 64(1):93-132, 2000.
18. V. Sofronie-Stokkermans. On uniform word problems involving bridging operators on distributive lattices. In U. Egly and C. Fermüller, editors, Proceedings of TABLEAUX 2002. LNAI 2381, pages 235-250. Springer, 2002.
19. V. Sofronie-Stokkermans. Resolution-based decision procedures for the universal theory of some classes of distributive lattices with operators. Journal of Symbolic Computation, 36(6):891-924, 2003.
20. V. Sofronie-Stokkermans. Hierarchic reasoning in local theory extensions. In R. Nieuwenhuis, editor, 20th International Conference on Automated Deduction (CADE-20), LNAI 3632, pages 219-234. Springer, 2005.
21. V. Sofronie-Stokkermans. Interpolation in local theory extensions. In U. Furbach and N. Shankar, editors, Proc. 3rd International Joint Conference on Automated Reasoning (IJCAR 2006), LNAI 4130, pages 235-250. Springer, 2006.
22. E. Sontag. Real addition and the polynomial hierarchy. Information Processing Letters, 20(3): 115-120, 1985.
23. H. Stone. The representation of boolean algebras. Bull. Amer. Math. Soc, 44:807-816, 1938.
24. A. Urquhart. A topological representation theory for lattices. Algebra Universalis, 8:45-58, 1978.