Annotation theories over finite graphs

Studia Logica

Volumn 93, Issue 2, 2009, Pages 147-180

  Gabbay, Dov M ^a,b,c   Szałas, Andrzej ^d,e  

^a KING'S COLLEGE LONDON   (United Kingdom)

^b BAR ILAN UNIVERSITY   (Israel)

^c UNIVERSITY OF LUXEMBOURG   (Luxembourg)

^d UNIVERSITY OF WARSAW   (Poland)

^e LINKÖPING UNIVERSITY   (Sweden)

Author keywords

Annotations; Argumentation theory; Labeled graphs; Second order quantifier elimination; Semantics of logic programs

Indexed keywords

EID: 71149108256     PISSN: 00393215     EISSN: 15728730     Source Type: Journal    
DOI: 10.1007/s11225-009-9220-3     Document Type: Article

References (36)

1. Abiteboul, S., R. Hull, and V. Vianu, Foundations of Databases, Addison-Wesley Pub. Co., 1996.
2. Ackermann W.: 'Untersuchungen über das eliminationsproblem der mathematischen logik'. Mathematische Annalen 110, 390-413 (1935).
3. Baader, F., D. Calvanese, D. L. McGuinness, D. Nardi, and P. F. Patel- Schneider, (eds.) Description Logic Handbook, Cambridge University Press, 2002.
4. Blackburn P., Seligman J.: 'Hybrid languages'. Journal of Logic, Language and Information 4, 41-62 (1995).
5. Cadoli, M., Tractable Reasoning in Artificial Intelligence, vol. 941 of LNCS, Springer-Verlag, 1995.
6. Cadoli M, Donini F. M.: 'A survey on knowledge compilation'. AI Communications 10(3-4), 137-150 (1997).
7. Caminada, M., and D. M. Gabbay, 'A logical account of formal argumentation', Studia Logica, 93 (2009), 2-3, 109-145, this issue.
8. Darwiche A., Marquis P.: 'A knowledge compilation map'. Journal of Artificial Intelligence Research 17, 229-264 (2002).
9. Doherty, P., W. Łukaszewicz, A. Skowron, and A. Szałas, Knowledge representation techniques. A rough set approach, vol. 202 of Studies in Fuziness and Soft Computing, Springer-Verlag, 2006.
10. Doherty P., Łukaszewicz W., Szałas A.: 'A reduction result for circumscribed semi-Horn formulas'. Fundamenta Informaticae 28(3-4), 261-271 (1996).
11. Doherty P., Łukaszewicz W., Szałas A.: 'Computing circumscription revisited'. Journal of Automated Reasoning 18(3), 297-336 (1997).
12. Doherty, P., and A. Szałas, 'On the correspondence between approximations and similarity', in S. Tsumoto, R. Slowinski, J. Komorowski, and J. W. Grzymala-Busse, (eds.), Proc. RSCTC'2004, vol. 3066 of LNAI, 2004, pp. 143-152.
13. Ebbinghaus H-D., Flum J.: Finite Model Theory. Springer-Verlag, Heidelberg (1995).
14. Gabbay D. M., Ohlbach H. J.: 'Quantifier elimination in second-order predicate logic'. South African Computer Journal 7, 35-43 (1992).
15. Gabbay, D. M., R. Schmidt, and A. Szałas, Second-Order Quantifier Elimination. Foundations, Computational Aspects and Applications, vol. 12 of Studies in Logic, College Publications, 2008.
16. Gabbay D. M., Szałas A.: 'Second-order quantifier elimination in higher-order contexts with applications to the semantical analysis of conditionals'. Studia Logica 87, 37-50 (2007).
17. Gelfond, M., and V. Lifschitz, 'The stable model semantics for logic programming', in Proceedings of the Fifth International Conference on Logic Programming (ICLP), 1988, pp. 1070-1080.
18. Goranko V.: 'Temporal logics with reference pointers and computation tree logics'. Journal of Applied Non-Classical Logics 10, 3-4 (2000).
19. Horrocks, I., and U. Sattler, 'Ontology reasoning in the shoq(d) description logic', in In Proc. of the 17th Int. Joint Conf. on Artificial Intelligence (IJCAI 2001, 2001, pp. 199-204.
20. Immerman, N., Descriptive Complexity, Springer-Verlag, New York, Berlin, 1998.
21. Kachniarz, J., and A. Szałas, 'On some extensions of second-order quantifier techniques', Unpublished manuscript, (2001).
22. Kirousis, L. M., and P. G. Kolaitis, 'A dichotomy in the complexity of propositional circumscription', in In Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science - LICS'01, 2001, pp. 71-80.
23. Kolaitis, P. G., and C. H. Papadimitriou, 'Some computational aspects of circumscription', Journal of the ACM, 37 (1990), 1, 1-14.
24. Lifschitz, V., 'Computing circumscription', in Readings in Nonmonotonic Reasoning, Morgan Kaufmann, 1985, pp. 121-127.
25. Lifschitz V.: 'On the satisfiability of circumscription'. Artificial Intelligence J. 28, 17-27 (1986).
26. Lifschitz, V., 'Circumscription', in D. M. Gabbay, C. J. Hogger, and J. A. Robinson, (eds.), Handbook of Artificial Intelligence and Logic Programming, vol. 3, Oxford University Press, 1991, pp. 297-352.
27. McCarthy J.: 'Circumscription: A form of non-monotonic reasoning'. Artificial Intelligence J. 13, 27-39 (1980).
28. Nonnengart, A., and A. Szałas, 'A fixpoint approach to second-order quantifier elimination with applications to correspondence theory', in E. Orłowska, (ed.), Logic at Work: Essays Dedicated to the Memory of Helena Rasiowa, vol. 24 of Studies in Fuzziness and Soft Computing, Springer Physica-Verlag, 1998, pp. 307-328.
29. Pawlak, Z., Rough Sets. Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Dordrecht, 1991.
30. Phan M. D.: 'On the acceptability of arguments and its fundamental role in nonmonotonic reasoning. logic programming and n-person games'. Artificial Intelligence 77, 321-357 (1995).
31. Schaefer, T. J., 'The complexity of satisfiability problems', in STOC '78: Proceedings of the 10th Annual ACM symposium on Theory of Computing, 1978, pp. 216-226.
32. Selman, B., and H. Kautz, 'Knowledge compilation using horn approximations', in In Proceedings of AAAI-91, 1991, pp. 904-909.
33. Selman B., Kautz H.: 'Knowledge compilation and theory approximation'. Journal of the ACM 43, 193-224 (1996).
34. Szałas A.: 'On the correspondence between modal and classical logic: An automated approach'. Journal of Logic and Computation 3, 605-620 (1993).
35. van Benthem J.: 'Minimal predicates, fixed-points, and definability'. Journal of Symbolic Logic 70(3), 696-712 (2005).
36. Wu, Yining, M. Caminada, and D. M. Gabbay, 'Complete extensions in argumentation coincide with 3-valued stable models in logic programming', Studia Logica, 93 (2009), 2-3, 383-403, this issue.