Labelled tableaux for nonmonotonic reasoning: Cumulative consequence relations

Journal of Logic and Computation

Volumn 12, Issue 6, 2002, Pages 1027-1060

  Artosi, Alberto ^a   Governatori, Guido ^b   Rotolo, Antonino ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Conditional logic; Labelled tableaux; Nonmonotonic reasoning

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; MODAL ANALYSIS; SEMANTICS; THEOREM PROVING;

CONDITIONAL LOGICS;

FORMAL LOGIC;

EID: 0037217004     PISSN: 0955792X     EISSN: None     Source Type: Journal    
DOI: 10.1093/logcom/12.6.1027     Document Type: Article

References (40)

1. A. Artosi, P. Benassi, G. Govematori, and A. Rotolo. Shakespearian modal logic: A labelled treatment of modal identity. In Advances in Modal Logic. Volume 1, M. Kracht, M. de Rijke, H. Wansing, and M. Zakharyaschev, eds, pp. 1-20. CSLI Publications, Stanford, 1998.
2. A. Artosi and G. Governatori. A tableau methodology for deontic conditional logic. In Deon'98. Fourth International Workshop on Deontic Logic in Computer Science, pp. 75-91, Bologna, 1998. CIRFID. http://arXiv.org/abs/cs.L0/0003050.
3. A. Artosi, G. Governatori, and A. Rotolo. A labelled tableau calculus for nonmonotonic (cumulative) consequence relations. In Automated Reasoning with Analytic Tableaux and Related Methods, R. Dyckhoff, ed., pp. 82-97. Springer-Verlag, Berlin, 2000.
4. A. Artosi, G. Govematori, and G. Sartor. Towards a computational treatment of deontic defeasibility. In Deontic Logic, Agency and Normative Systems, M.A. Brown and J. Carmo, eds, pp. 27-46. Springer-Verlag, Berlin, 1996.
5. M. Baldoni. Normal multimodal logic with interaction axioms. In Labelled Deduction, D. Basin, M. D'Agostino, D. Gabbay, S. Matthews, and L. Viganò, eds, pp. 33-58. Kluwer, Dordrecht, 2000.
6. B. Beckert and R. Goré. Free-variable tableaux for propositional modal logic. Studia Logica, forthcoming.
7. D. Billington. Defeasible logic is stable. Journal of Logic and Computation, 3, 370-400, 1993.
8. C. Boutilier. Conditional logics of normality: a modal approach. Artificial Intelligence, 68, 87-154, 1994.
9. J.P. Burgess. Quick completeness proofs for some logic of conditionals. Notre Dame Journal of Formal Logic, 22, 76-84, 1981.
10. B. Chellas. Basic conditional logic. Journal of Philosophical Logic, 4, 133-153, 1975.
11. G. Crocco and L. Fariñas del Cerro. Structure, consequence relation and logic. In What is a Logical System, D. Gabbay, ed., pp. 375-393. Oxford University Press, Oxford, 1994.
12. G. Crocco and P. Lamarre. On the connections between non-monotonic reference systems and conditional logics. In Principles of Knowledge Representation and Reasoning (KR '92), B. Nebel, C. Rich, and W. Swartout, eds, pp. 565-571. Morgan Kaufman Publishers, San Mateo, CA, 1992.
13. M. D'Agostino and M. Mondadori. The taming of the cut. Journal of Logic and Computation, 4, 285-319, 1994.
14. H. de Swart. A Gentzen- or Beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactuals logics VC and VCS. Journal of Symbolic Logic, 48, 1-20, 1983.
15. J.P. Delgrande. A first-order conditional logic for prototypical properties. Artificial Intelligence, 33, 105-139, 1987.
16. L. Fariñas del Cerro, A. Herzig, and J. Lange. From ordering-based nonmonotonic reasoning to conditional logics. Artificial Intelligence, 66, 375-393, 1994.
17. M. Fitting. Proof Methods for Modal and Intuitionistic Logic. Reidel, Dordmcht, 1983.
18. D.M. Gabbay. Theoretical foundations for nonmonotonic reasoning in expert systems. In Proceedings of the NATO Advanced Study Institute on Logics and Concurrent Systems, K.R. Apt, ed., pp. 439-457. Springer-Verlag, Berlin 1985.
19. D.M. Gabbay. Conditional implications and non-monotonic consequence. In Conditionals: From Philosophy to Computer Science, G. Crocco, L. Fariñas del Cerro, and A. Herzig, eds, pp. 337-360. Oxford University Press, Oxford, 1995.
20. D.M. Gabbay. Labelled Deductive Systems. Oxford University Press, Oxford, 1996.
21. D.M. Gabbay and Guido Governatori. Dealing with label dependent deontic modalities. In Norms, Logics and Information Systems, P. McNamara and H. Prakken, eds, pp. 311-330. IOS Press, Amsterdam, 1998.
22. D.M. Gabbay and G. Governatori. Fibred modal tableaux. In Labelled Deduction, D. Basin, M. D'Agostino, D. Gabbay, S. Matthewsm and L. Viganò, eds, pp. 163-194. Kluwer, Dordrecht, 2000.
23. I. Gent. A tableau- or sequent-style system for Lewis's counterfactual logic VC. Notre Dame Journal of Formal Logic, 33, 1992.
24. +: Beyond refutation, in KI-95 Activities: Workshops, Posters, Demos, L. Dreschler-Fischer and S. Pribbenow, eds, pp. 75-76. Gesellschaft für Informatik, Bonn, 1995.
25. G. Governatori. Un modello formale per il ragionamento giuridico. PhD thesis, CIRFID, University of Bologna, Bologna, 1997.
26. C. Groeneboer and J.P. Delgrande. Tableau-based theorem proving in normal conditional logics. In AAAI'88, volume 1, pp. 171-176, 1988.
27. G.E. Hughes and M.J. Cresswell. An Introduction to Modal Logic. Methuen, London, 1968.
28. H. Katsuno and K. Satoh. A unified view of consequence relation, belief revision, and conditional logic. In Conditionals: From Philosophy to Computer Science, G. Crocco, L. Fariñas del Cerro, and A. Herzig, eds, pp. 33-66. Oxford University Press, Oxford, 1995.
29. S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167-207, 1990.
30. P. Lamarre. A promenade from monotonicity to nonmonotonocity following a theorem prover. In Principles of Knowledge Representation and Reasoning (KR '92), B. Nebel C. Rich, and W. Swartout, eds, pp. 572-580. Morgan Kaufman Publishers, San Mateo, CA, 1992.
31. D. Lehmann. What does a conditional base entail? In Proceedings of Knowledge Representation and Reasoning (KR'89), R.J. Brachman, H.J. Levesque, and R. Reiter, eds, pp. 212-222. Morgan Kaufman Publishers, San Mateo, CA, 1989.
32. D. Lewis. Counterfactuals. Basil Blackwell, Oxford, 1986.
33. F. Massacci. Strongly analytic tableaux for normal modal logics. In Proceedings of the Twelvth International Conference on Automated Deduction (CADE), A. Bundy, ed., volume 814 of Lecture Notes in Computer Science, pp. 723-737. Springer-Verlag, Berlin, 1994.
34. D. Nute. Topics in Conditional Logic. Reidel, Dordmcht, 1980.
35. C. Pizzi. Decision procedures for logics of consequential implication. Notre Dame Journal of Formal Logic, 32, 618-636, 1993. And 1993 correction (same journal).
36. A. Rasso. Modal Logic as Labelled Deductive Systems. PhD thesis, Department of Computing, imperial College, London, 1996.
37. Y. Shoham. A semantical approach to nonmonotonic logics. In Proceedings of the Tenth International Joint Conference on Artificial Intelligence, J. McDermott, ed., pp. 388-392. Morgan Kaufman Publishers, Los Altos, CA, 1987.
38. R.M. Smuilyan. First-Order Logic. Springer-Verlag, Berlin, 1968.
39. R.H. Thomason. A Fitch-style formulation of conditional logic. Logique et Analyse, 52, 397-412, 1970.
40. L. Viganò. Labelled Non-Classical Logics. Kluwer, Boston, 2000.