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Fuzzy temporal constraint logic: A valid resolution principle. (English) Zbl 0984.03021

Summary: We propose a fuzzy temporal constraint logic. First of all, we provide the formal language which will allow the expression of well-formed formulas related to the temporal events by means of temporal constraints. Secondly, we introduce a valid resolution principle in order to solve the queries in this logic. Finally, we will show that this resolution principle is a generalization of the resolution principle proposed for a possibilistic logic with fuzzy predicates [D. Dubois and H. Prade, Int. J. Approximate Reasoning 4, 1-21 (1990; Zbl 0697.68083)]. All this will serve to reason within a context of the theoretical model of the temporal reasoning proposed by Marín and Barro (Fuzzy Temporal Constraint Network, FTCN) [see R. Marín, S. Barro, A. Bosch and J. Mira, Cybern. Syst. 25, 217-231 (1994; Zbl 0809.68111)]. This model underlies a module for the resolution of temporal queries. This module belongs to a diagnostic and intelligent monitoring system of patients, based on temporal reasoning. The system is applied to the patients admitted in the Intensive Care Units with severe ischemic cardiopathy, submitted to continuous monitoring of the electrical and mechanical signals of the heart. However, what is exposed here in this document is not limited to a field of application in particular, but instead, it is completely general.

MSC:

03B52 Fuzzy logic; logic of vagueness
68T37 Reasoning under uncertainty in the context of artificial intelligence
68N17 Logic programming
92C50 Medical applications (general)
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References:

[1] Allen, J. F., Maintaining knowledge about temporal intervals, Comm. ACM, 26, 832-843 (1983) · Zbl 0519.68079
[2] Allen, J. F., Towards a general theory of action and time, Artificial. Intelligence, 23, 2, 123-154 (1984) · Zbl 0567.68025
[3] Barro, S.; Marı́n, R.; Mira, J.; Patón, A. R., A model and a language for the fuzzy representation and handling of time, Fuzzy Sets and Systems, 61, 153-175 (1994)
[4] S. Barro, R. Marı́n, R.P. Otero, R. Ruı́z, J. Mira, On the handling of time in intelligent monitoring of CCU patients, Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1992, pp. 871-873.; S. Barro, R. Marı́n, R.P. Otero, R. Ruı́z, J. Mira, On the handling of time in intelligent monitoring of CCU patients, Proceedings of the 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 1992, pp. 871-873.
[5] Dechter, R.; Meiri, I.; Pearl, J., Temporal constraint networks, Artificial Intelligence, 49, 61-95 (1991) · Zbl 0737.68070
[6] Dubois, D.; Lang, J.; Prade, H., Timed possibilistic logic, Fund. Inf., XV, 211-234 (1991) · Zbl 0745.03019
[7] D. Dubois, J. Lang, H. Prade, Possibilistic logic, in: D.M. Gabbay, C.J. Hogger, J.A. Robinson (Eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, 1994, pp. 439-513.; D. Dubois, J. Lang, H. Prade, Possibilistic logic, in: D.M. Gabbay, C.J. Hogger, J.A. Robinson (Eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, 1994, pp. 439-513.
[8] Dubois, D.; Prade, H., Necessity measures and the resolution principle, IEEE Trans. Systems Man Cybernet., 17, 474-478 (1987) · Zbl 0643.94053
[9] Dubois, D.; Prade, H., Possibility Theory: An Approach to Computerized Processing of Uncertainty (1988), Plenum Press: Plenum Press New York
[10] Dubois, D.; Prade, H., Processing fuzzy temporal knowledge, IEEE Trans. Systems Man Cybernet., 19, 4, 729-744 (1989)
[11] Dubois, D.; Prade, H., Resolution principles in possibilistic logic, Internat. J. Approx. Reason., 4, 1-21 (1990) · Zbl 0697.68083
[12] Enderton, H. B., A Mathematical Introduction to Logic (1972), Academic Press: Academic Press New York · Zbl 0298.02002
[13] L. Godo, L. Vila, A temporal reasoning system based on fuzzy temporal constraints, Actas del Cuarto Congreso Español sobre Tecnologı́as y Lógica Fuzzy, Blanes, 1994, pp. 43-48.; L. Godo, L. Vila, A temporal reasoning system based on fuzzy temporal constraints, Actas del Cuarto Congreso Español sobre Tecnologı́as y Lógica Fuzzy, Blanes, 1994, pp. 43-48.
[14] Gupta, M. M.; Qi, J., Theory of T-norms and fuzzy inference methods, Fuzzy Sets and Systems, 40, 431-450 (1991) · Zbl 0726.03017
[15] Hrycej, T., Temporal prolog, Proceedings of the European Conference on Artificial Intelligence’88 (1988), Munich: Munich Germany
[16] Hrycej, T., A temporal extension of prolog, J. Logic Programming, 15, 113-145 (1993) · Zbl 0787.68094
[17] Kaufmann, A.; Gupta, M., Introduction to Fuzzy Arithmetic (1985), Van Nostrand Reinhold: Van Nostrand Reinhold New York · Zbl 0588.94023
[18] Marı́n, R.; Barro, S.; Bosch, A.; Mira, J., Modeling time representation from a fuzzy perspective, Cybernet. Systems, 25, 2, 207-215 (1994) · Zbl 0809.68111
[19] Marı́n, R.; Barro, S.; Palacios, P.; Ruı́z, R.; Martı́n, F., An approach to fuzzy temporal reasoning in medicine, Mathware and Soft Comput., 1, 3, 265-276 (1994)
[20] Marı́n, R.; Cárdenas, M. A.; Balsa, M.; Sánchez, J. L., Obtaining solutions in fuzzy constraint networks, Internat. J. Approx. Reason., 16, 3-4, 261-288 (1997) · Zbl 0939.68116
[21] J.M. Mendel, Fuzzy Logic Systems for Engineering: A Tutorial, IEEE, New York, 1995, pp. 345-377.; J.M. Mendel, Fuzzy Logic Systems for Engineering: A Tutorial, IEEE, New York, 1995, pp. 345-377.
[22] Tsang, Foundations of Constraint Satisfaction, Academic Press, New York, 1993.; Tsang, Foundations of Constraint Satisfaction, Academic Press, New York, 1993.
[23] Vila, L., L. Godo, On fuzzy temporal constraint networks, Mathware and Soft Comput., 1, 3, 315-334 (1994) · Zbl 0833.68012
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