A sequent calculus and a theorem prover for standard conditional logics

ACM Transactions on Computational Logic

Volumn 8, Issue 4, 2007, Pages

  Olivetti, Nicola ^a   Pozzato, Gian Luca ^b   Schwind, Camilla B ^a,c  

^a AIX MARSEILLE UNIVERSITY   (France)

^b UNIVERSITY OF TURIN   (Italy)

^c MAP CNRS   (France)

Author keywords

Analytic sequent calculi; Automated deduction; Conditional logics; Labeled deductive systems; Logic programming; Proof theory

Indexed keywords

AUTOMATION; COMPUTATIONAL COMPLEXITY; LOGIC PROGRAMMING; THEOREM PROVING;

PROOF SYSTEMS; SEQUENT CALCULUS; SPACE COMPLEXITY BOUNDS;

DIFFERENTIATION (CALCULUS);

EID: 34548383817     PISSN: 15293785     EISSN: 1557945X     Source Type: Journal    
DOI: 10.1145/1276920.1276924     Document Type: Article

References (52)

1. ARTOSI, A., GOVERNATORI, G., AND ROTOLO, A. 2002. Labelled tableaux for nonmonotonic reasoning: Cumulative consequence relations. J. Logic Comput. 12, 6, 1027-1060.
2. BECKERT, B. AND GORÉ, R. 1997. Free variable tableaux for propositional modal logics. In Proceedings of Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX' 97) Lecture Notes in Artificial Intelligence, vol. 1227, Springer-Verlag, 91-106.
3. BECKERT, B. AND POSEGGA, J. 1995. leantap: Lean tableau-based deduction. J Automat. Reason. 15, 3, 339-358.
4. BELL, J. 1990. The logic of nonmonotonicity. AI 41, 3, 365-374.
5. BOUTILIER, C. 1994. Conditional logics of normality: a modal approach. AI 68, 1, 87-154.
6. CHELLAS, B. F. 1975. Basic conditional logics. J Phil. Logic 4, 133-153.
7. COSTELLO, T AND MCCARTHY, J. 1999. Useful counterfactuals. Electron. Trans. AI 3, Section A.
8. CROCCO, G. AND DEL CERRO, L. F. 1995. Structure, consequence relation and logic, volume 4. In D. M. Gabbay, Ed., What is a Logical System, Oxford University Press, 239-259.
9. CROCCO, G., DEL CERRO, L. F., AND HERZIG, A. 1995. Conditionals: From philosophy to computer science. In Studies in Logic and Computation, Oxford University Press.
10. CROCCO, G. AND LAMARRE, P. 1992. On the connection between nonmonotonic inference systems and conditional logics. In Proceedings of the 3rd International Conference on Principles of Knowledge. Representation and Reasoning, B. Nebel and E. Sandewall Ed., 565-571.
11. DE SWART, H. C. M. 1983. A gentzen-or beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactual logics vc and vcs. J. Symb. Logic 48, 1, 1-20.
12. DELGRANDE, J. P. 1987. A first-order conditional logic for prototypical properties. AI 33, 1, 105-130.
13. DELGRANDE, J. P. 1988. An approach to default reasoning based on a first-order conditional logic: Revised report. AI 36, 1, 63-90.
14. DELGRANDE, J. P. AND GROENEBOER, C. 1990. A general approach for determining the validity of commonsense assertions using conditional logics. Int. J. Intel. Syst. 5, 5, 505-520.
15. FITTING, M. 1998. Leantap revisited. J. Logic Computa. 8,1, 33-47.
16. FRIEDMAN, N. AND HALPERN, J. 1994. On the complexity of conditional logics. In Proceedings of the 4th International Conference Principles of Knowledge Representation and Reasoning. 202-213.
17. FRIEDMAN, N. AND HALPERN, J. Y. 2001. Plausibility measures and default reasoning. J. ACM 48, 4, 648-685.
18. GABBAY, D. M. 1996. Labelled Deductive Systems. Oxford Logic Guides, vol i. Oxford University Press.
19. GABBAY, D. M., GIORDANO, L., MARTELLI, A., OLIVETTI, N., AND SAPINO, M. L. 2000. Conditional reasoning in logic programming. J. Logic Program. 44, 1-3, 37-74.
20. GABBAY, D. M. AND OLIVETTI, N. 2000. Goal-Directed Proof Theory. Kluwer Academic Publishers.
21. GARDENFORS, P. AND ROTT, H. 1995. Belief revision. In Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 4, D. M. Gabbay, C. J. Hogger, and J. A. Robinson Ed., Oxford. University of Press.
22. GENT, I. P. 1992. A sequent or tableaux-style system for lewis's counterfactual logic vc. Notre Dame J. Formal Logic 33, 3, 369-382.
23. GINSBERG, M. L. 1986. Counterfactuals. AI 30, 1, 35-79.
24. GIORDANO, L., GLIOZZI, V., AND OLIVETTI, N. 2002. Iterated belief revision and conditional logic. Studia Logica 70, 1, 23-47.
25. GIORDANO, L., GLIOZZI, V., AND OLIVETTI, N. 2005. Weak agm postulates and strong ramsey test: a logical formalization. AI 168, 1-2, 1-37.
26. GIORDANO, L., GLIOZZI, V., OLIVETTI, N., AND POZZATO, G. L. 2005. Analytic tableaux for klm preferential and cumulative logics. In Proceedings of 12th Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR'05). Lecture Notes in Artificial Intelligence, vol. 3835, Springer-Verlag, 666-681.
27. GIORDANO, L., GLIOZZI, V., OLIVETTI, N., AND SCHWIND, C. 2003. Tableau calculi for preference-based conditional logics. In Proceedings of Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX' 03). Lecture Notes in Artificial Intelligence, vol. 2796, Springer, 81-101.
28. GIORDANO, L. AND SCHWIND, C. 2004. Conditional logic of actions and causation. AI 157, 1-2, 239-279.
29. GRAHNE, G. 1998. Updates and counterfactuals. J. Logic Comput. 8, 1, 87-117.
30. HUDELMAIER, J. 1993. An script O sign(n log n)-space decision procedure for intuitionistic propositional logic. J. Logic Comput. 3, 1, 63-75.
31. KRAUS, S., LEHMANN, D., AND MAGIDOR, M. 1990. Nonmonotonic reasoning, preferential models and cumulative logics. AI 44, 1-2, 167-207.
32. LAMARRE, P. 1992. Etude des raisonnements non-monotones: Apports des logiques des conditionnels et des logiques modales. PhD thesis, Université Paul Sabatier, Toulouse.
33. LAMARRE, P. 1993. A tableaux prover for conditional logics. In Proceedings of the 4th International Conference Principles of Knowledge Representation and Reasoning, 572-580.
34. LEHMANN, D. AND MAGIDOR, M. 1992. What does a conditional knowledge base entail? AI 55, 1, 1-60.
35. LEWIS, D. 1973. Counterfactuals. Basil Blackwell Ltd.
36. LINDSTROM, S. AND RABINOWICZ, W. 1992. Belief revision, epistemic conditionals and the ramsey test. Synthese 91, 195-237.
37. MILLER, D. AND HODAS, J. S. 1994. Logic programming in a fragment of intuitionistic linear logic. J. Inform. Computa. 110, 2, 327-365.
38. MILLER, D., NADATHUR, G., PFENNING, F., AND SCEDROV, A. 1991. Uniform proofs as a foundation for logic programming. Ann. Pure Appl. Logic 51, 1-2, 125-157.
39. NEGRI, S. 2005. Proof analysis in modal logic. J. Philos. Logic, To Appear.
40. NUTE, D. 1980. Topics in Conditional Logic. Reidel, Dordrecht.
41. OBEID, N. 2001. Model-based diagnosis and conditional logic. Appl. Intell. 14, 213-230.
42. OLIVETTI, N. AND POZZATO, G. L. 2003. Condlean: A theorem prover for conditional logics. In Proceedings of Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX'03). Lecture Notes in Artificial Intelligence, vol. 2796, Springer, 264-270.
43. OLIVETTI, N. AND POZZATO, G. L. 2005. Condlean 3.0: Improving condlean for stronger conditional logics. In Proceedings of Automated Reasoning with Analytic Tableaux and Related Methods, (TABLEAUX'05). Lecture Notes in Artificeal Intelligence, vol. 3702, Springer-Verlag, 338-332.
44. OLIVETTI, N., POZZATO, G. L., AND SCHWIND, C. B. 2005. A sequent calculus and a theorem prover for standard conditional logics: Extended version. Tech. rep. 87/05, Dip. di Informatica, Università degli Studi di Torino, http://www.di.unito.it/ ~argo/biblio/publications.php?author=Pozzato.
45. OLIVETTI, N. AND SCHWIND, C. B. 2000. Analytic tableaux for conditional logics. Tech. rep., University of Torino.
46. OLIVETTI, N. AND SCHWIND, C. B. 2001. A calculus and complexity bound for minimal conditional logic. In Proceedings of Italian Conference on Theoretical Computer Science (ICTCS'01). Lecture Notes in Computer Science, vol. 2202, Springer-Verlag, 384-404.
47. POZZATO, G. L. 2003. Deduzione automatica per logiche condizionali: Analisi e sviluppo di un theorem prover. Tesi di laurea, Informatica, Università di Torino. http://www.di.unito.it/~ pozzato/tesiPozzato.html.
48. PYM, D. J. AND HARLAND, J. 1994. A uniform proof-theoretic investigation of linear logic programming. J. Logic Comput. 4, 2, 175-207.
49. SCHWIND, C. B. 1999. Causality in action theories. Electr. Trans. AI 3, A, 27-50.
50. STALNAKER, R. 1968. A theory of conditionals. In N. Rescher, Ed., Studies in Logical Theory, American Philosophical Quarterly, Monograph Series no.2, Blackwell, Oxford, 98-112.
51. TROELSTRA, A. S. AND SCHWICHTENBERG, H. 2000. Basic Proof Theory. Cambridge University Press.
52. VIGANÒ, L. 2000. Labelled Nonclassical Logics. KIuwer Academic Publishers, Dordrecht.