Abstract
Soft constraints based on semirings are a generalization of classical constraints, where tuples of variables’ values in each soft constraint are uniquely associated to elements from an algebraic structure called semiring. This framework is able to express, for example, fuzzy, classical, weighted, valued and over-constrained constraint problems. Classical constraint propagation has been extended and adapted to soft constraints by defining a schema for soft local consistency [BMR97]. On the other hand, in [Apt99a,Apt99b] it has been proved that most of the well known constraint propagation algorithms for classical constraints can be cast within a single schema.
In this paper we combine these two schema and we show how the framework of [Apt99a,Apt99b] can be used for soft constraints. In doing so, we generalize the concept of soft local consistency, and we prove some convenient properties about its termination.
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References
K. R. Apt, The Essence of Constraint Propagation, Theoretical Computer Science, 221(1–2), pp. 179–210, 1999.
K. R. Apt, The Rough Guide to Constraint Propagation, Proc. of the 5th International Conference on Principles and Practice of Constraint Programming (CP’99), (invited lecture), Springer-Verlag Lecture Notes in Computer Science 1713, pp. 1–23.
C. Bessière. Arc-consistency and Arc-consistency again. Artificial Intelligence, 65(1), 1994.
S. Bistarelli, P. Codognet, Y. Georget and F. Rossi Labeling and Partial Local Consistency for Soft Constraint Programming Proc. of the 2nd International Workshop on Practical Aspects of Declarative Languages (PADL’ 00), Springer-Verlag Lecture Notes in Computer Science 1753, 2000.
S. Bistarelli, U. Montanari and F. Rossi. Constraint Solving over Semirings. Proceedings of IJCAI’95, Morgan Kaufman, 1995.
S. Bistarelli, U. Montanari and F. Rossi. Semiring-based Constraint Solving and Optimization. Journal of ACM, vol. 44, no. 2, March 1997.
D. Dubois, H. Fargier and H. Prade. The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction. Proc. IEEE International Conference on Fuzzy Systems, IEEE, pp. 1131–1136, 1993.
H. Fargier and J. Lang Uncertainty in Constraint Satisfaction Problems: a Probabilistic Approach Proc. European Conference on Symbolic and Qualitative Approaches to Reasoning and Uncertainty (ECSQARU), Springer-Verlag, LNCS 747, pp. 97–104, 1993.
E. C. Freuder and R. J. Wallace. Partial Constraint Satisfaction. AI Journal, 1992, 58.
P. Van Hentenryck, Y. Deville and C-M. Teng. A generic arc-consistency algorithm and its specializations. Artificial Intelligence 57 (1992), pp 291–321.
K. Marriott and P. Stuckey. Programming with Constraints. MIT Press, 1998.
T. Schiex and H. Fargier and G. Verfaille. Valued Constraint Satisfaction Problems: Hard and Easy Problems. Proc. IJCAI95, Morgan Kaufmann, pp. 631–637, 1995
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Bistarelli, S., Gennari, R., Rossi, F. (2000). Constraint Propagation for Soft Constraints: Generalization and Termination Conditions. In: Dechter, R. (eds) Principles and Practice of Constraint Programming – CP 2000. CP 2000. Lecture Notes in Computer Science, vol 1894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45349-0_8
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DOI: https://doi.org/10.1007/3-540-45349-0_8
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