Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-25T03:54:31.637Z Has data issue: false hasContentIssue false

On representation theorems for nonmonotonic consequence relations

Published online by Cambridge University Press:  12 March 2014

Ramón Pino Pérez*
Affiliation:
Lab. D'informatique Fondamentale de Lille, U.A. 369 du CNRS, Université de Lille I, 59655 Villeneuve D'ascq, France E-mail: pino@cril.univ-artois.fr Lab. D'informatique Fondamentale de Lille, U.A. 369 du CNRS, Université de Lille I, 59655 Villeneuve D'ascq, France E-mail: pino@lifl.fr
Carlos Uzcátegui
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, Venezuela E-mail: uzca@ciens.ula.ve
*
CRIL, Faculté des Sciences, Université d'Artois, 62307 Lens, France

Abstract

One of the main tools in the study of nonmonotonic consequence relations is the representation of such relations in terms of preferential models. In this paper we give an unified and simpler framework to obtain such representation theorems.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bezzazi, H., Makinson, D., and Pérez, R. Pino, Beyond rational monotony: some strong non-Horn rules for nonmonotonic inference relations, Journal of Logic and Computation, vol. 7 (1997), pp. 605–631.CrossRefGoogle Scholar
[2]Bezzazi, H. and Pérez, R. Pino, Rational transitivity and its models, Proceedings of the twenty-sixth international symposium on multiple-valued logic (Santiago de Compostela, Spain), IEEE Computer Society Press, May 1996, pp. 160–165.Google Scholar
[3]Freund, M., Injective models and disjunctive relations, Journal of Logic and Computation, vol. 3 (1993), pp. 231–247.CrossRefGoogle Scholar
[4]Freund, M., Lehmann, D., and Morris, P., Rationality, transitivity and contraposition, Artificial Intelligence, vol. 52 (1991), pp. 191–203.CrossRefGoogle Scholar
[5]Gärdenfors, P. and Makinson, D., Nonmonotonic inferences based on expectations, Artificial Intelligence, vol. 65 (1994), pp. 197–245.CrossRefGoogle Scholar
[6]Kraus, S., Lehmann, D., and Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, vol. 14 (1990), no. 1, pp. 167–207.Google Scholar
[7]Lehmann, D. and Magidor, M., What does a conditional knowledge base entail?, Artificial Intelligence, vol. 55 (1992), pp. 1–60.CrossRefGoogle Scholar
[8]Lobo, J. and Uzcátegui, C., Abductive consequence relations, Artificial Intelligence, vol. 89 (1997), pp. 149–171.CrossRefGoogle Scholar
[9]Makinson, D., General patterns in nonmonotonic reasoning, Handbook of Logic in Artificial Intelligence and Logic Programming (Hogger, C., Gabbay, D., and Robinson, J., editors), vol. 111, Nonmonotonic Reasoning and Uncertain Reasoning, Oxford University Press, 1994.Google Scholar
[10]Pérez, R. Pino and Uzcátegui, C., Jumping to explanations vs. jumping to conclusions, Artificial Intelligence, vol. 111 (1999), no. 2, pp. 131–169.Google Scholar
[11]Satoh, Ken, A probabilistic interpretation for lazy nonmonotonic reasoning, Proceedings of AAAI-90 (Boston), August 1990, pp. 659–664.Google Scholar