α-resolution principle based on lattice-valued propositional logic LP(X)

Information sciences

Volumn 130, Issue 1-4, 2000, Pages 195-223

  Xu, Yang ^a   Ruan, Da ^b   Kerre, Etienne E ^c   Liu, Jun ^b  

^a SOUTHWEST JIAOTONG UNIVERSITY   (China)

^b BELGIAN NUCLEAR RESEARCH CENTRE   (Belgium)

^c GHENT UNIVERSITY   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; AUTOMATION; THEOREM PROVING;

LATTICE-VALUED LOGICS; MULTI-VALUED LOGICS;

FORMAL LOGIC;

EID: 0034497853     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0255(00)00069-4     Document Type: Article

References (90)

1. Birkhoff G. Lattice Theory. third ed. 1967;American Mathematical Society Providence, RL.
2. Borns D.W., Mack J.M. An Algebraic Introduction to Mathematical Logic. 1975;Springer, Berlin.
3. Bolc L., Borowik P. Many-Valued Logics. 1992;Springer, Berlin.
4. Rosser J.B., Turquette A.R. Many-Valued Logic. 1952;North-Holland, Amsterdam.
5. Rescher N. Many-Valued Logic. 1969;McGraw-Hill, New York.
6. Zadeh L.A. Fuzzy sets. Information and Control. 8(3):1965;338-353.
7. Goguen J.A. The logic of inexact concepts. Synthese. 19:1969;325-373.
8. J. Pavelka, On fuzzy logic I: Many-valued rules of inference, II: Enriched residuated lattices and semantics of propositional calculi, III: Semantical completeness of some many-valued propositional calculi, in: Zeitschr. F. Math. Logik und Grundlagend. Math, vol. 25, 1979, pp. 45-52, 119-134, 447-464.
9. Novak V. First-order fuzzy logic. Studia Logica. 46(1):1982;87-109.
10. D. Dubois, H. Prade, The generalized modus ponens under sup-min composition - A theoretical study, in: M.M. Gupta et al. (Eds.), Approximate Reasoning in Expert System, North-Holland, Amsterdam, 1985, pp. 217-232.
11. D. Dubois, J. Lang, H. Prade, Fuzzy sets in approximate reasoning, Part I: Inference with possibility distributions, Part II: Logical approaches, Fuzzy Sets and Systems 40 (1991) 143-202, 203-244.
12. Robinson J.P. A machine-oriented logic based on the resolution principle. J. ACM. 12:1965;23-41.
13. Loveland D.W. Automated Theorem Proving: A Logical Basis. 1978;North-Holland, Amsterdam.
14. Murray N.V. Completely non-clausal theorem proving. Artificial Intelligence. 18:1982;67-85.
15. X.H. Wang, X.H. Liu, Generalized resolution, J. Comput. (2) (1982) 81-92 (in Chinese).
16. Wos L. Automated Reasoning: Basic Research Problems. 1988;Prentice-Hall, Englewood Cliffs, NJ.
17. Lee R.C.T., Chang C.L. Some properties of fuzzy logic. Information and Control. 19:1971;417-431.
18. Lee R.C.T. Fuzzy logic and the resolution principle. J. ACM. 19:1972;109-119.
19. Chang C.L., Lee R.C.T. Symbolic Logic and Mechanical Theorem Proving. 1973;Academic Press, New York.
20. Mukaidono M. On some properties of fuzzy logic. Syst. Comput. Control. 6(2):1975;36-43.
21. Mukaidono M. Fuzzy inference of resolution style. Yager R.R. Fuzzy Sets and Possibility Theory. 1982;224-231 Pergamon Press, New York.
22. Yager R.R. Inference in a multiple-valued logic system. Int. J. Man Machine Stud. 23:1985;27-44.
23. X.H. Liu, H. Xiao, Operator fuzzy logic and fuzzy resolution, in: Proceedings of the Fifth IEEE International Symposium on Multiple-Valued Logic (ISMVL '85), Kingstion, Canada, 1985, pp. 68-75.
24. Weigert T.J., Tsai J.P., Liu X.H. Fuzzy operator logic and fuzzy resolution. J. Autom. Reasoning. 10:1993;59-78.
25. Liu X.H. Resolution-based Automated Reasoning. 1994;Academic Press, China. (in Chinese).
26. Orlowska E., Wierzchon S. Mechanical reasoning in fuzzy logics. Logique et Analyses. 110-111:1985;193-207.
27. X.H. Liu, Fuzzy Logic and Fuzzy Reasoning, Press of Ji Lin University, 1989 (in Chinese).
28. D. Dubois, J. Lang, H. Prade, Theorem proving under uncertainty - A possibility theory based approach, in: Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI '87), Mitano, Italy, 1987, pp. 984-986.
29. D. Dubois, J. Lang, H. Prade, Automated reasoning using possibility logic semantics, belief revision and variable certainty weights, in: Proceedings of the Fifth Workshop on Uncertainty in Artificial Intelligence, Windor, Ontario, 1989, pp. 81-87.
30. Dubois D., Prade H. Resolution principle in possibilistic logic. Int. J. Approx. Reasoning. 4(1):1990;1-21.
31. Morgan C.G. Resolution for many-valued logics. Logique et Analyses. 19(74-76):1976;311-339.
32. + -valued logic Fundamenta Informaticae. II(1):1978;1-15.
33. Orlowska E. Resolution system and their application II. Fundamenta Informaticae. III(3):1980;333-362.
34. Orlowska E. Mechanical proof methods for Post logics. Logique et Analyses. 28(110):1985;173-192.
35. Schmitt P.H. Computational aspects of three-valued logic. Siekmann J.H. Proceedings of the Eighth International Conference on Automated Deduction. 1986;190-198 Springer, Berlin.
36. R. Hahnle, Uniform notation tableau rules for multiple-valued logics, in: Proceedings of the International Symposium on Multiple-Valued Logic, Victoria, BC, 1991, pp. 238-245.
37. R. Hahnle, Towards an efficient tableau proof procedure for multiple-valued logics, in: Proceedings of the Workshop on Computer Science Logic, Lecture Notes in Computer Science, vol. 533, Springer, Berlin, 1990, pp. 248-260.
38. Hahnle R. Automated Deduction in Multiple-Valued Logics. 1993;Oxford University Press, Oxford.
39. R. Hahnle, Short CNF in finitely-valued logics, in: J. Komorowski, Z.W. Ras (Eds.), in: Proceedings of the Seventh International Symposium on Methodologies for Intelligent Systems, 1993, pp. 49-58.
40. N.V. Murray, E. Rosenthal, Resolution and path dissolution in multiple-valued logics, in: Proceedings of the Sixth International Symposium on Methodologies for Intelligent Systems, Charlotte, Lecture Notes in Artificial Intelligence, vol. 542, 1991, pp. 570-579.
41. N.V. Murray, E. Rosenthal, Improving tableau proof in multiple-valued logic, in: Proceedings of the 21st International Symposium on Multiple-valued Logic, Victoria, BC, Canada, 1991, pp. 230-237.
42. Blair H.A., Subrahamnian V.S. Paraconsistent logic programming. Theoret. Comput. Sci. 68:1989;135-154.
43. N.C.A. da Costa et al., Automated theorem proving in paraconsistent logics: theory and implementation, in: W. Kaiseralsutern (Ed.), Proceedings of the 10th International Conference on Automated Deduction, Lecture Notes in Artificial Intelligence, vol. 449, Springer, Berlin, 1990, pp. 72-86.
44. M. Kifer et al., On the expressive power of annotated logic program. in: Proceedings of the North American Conference on Logic Programming, Cleveland, OH, 1989, pp. 1069-1089.
45. Subrahamnian V.S. Paraconsistent disjunctive databases. Theoret. Comput. Sci. 93:1992;115-141.
46. M. Kifer, E. Lozinskii, RI: a logic for reasoning with inconsistency, in: Proceedings of the 21st International Symposium on Multiple-Valued Logic, 1991, pp. 253-262.
47. Kifer M., Subrahamnian V.S. Theory of generalized annotated logic programming and its application. J. Logic Programming. 12:1992;335-367.
48. Lu J.J., Henschen L.J. The completeness of gp-resolution for annotated logic. Inform. Process. Lett. 44:1992;135-140.
49. J.J. Lu, N.V. Murray, E. Rosenthal, Signed formulas and annotated logics, in: Proceedings of the 23th International Symposium on Multiple-Valued Logic, 1993, pp. 48-53.
50. J.J. Lu, N.V. Murray, E. Rosenthal, Signed formulas and fuzzy operator logics, in: J. Komorowski, Z.W. Ras, Proceedings of the Seventh International Symposium on Methodologies for Intelligent Systems, 1993, pp. 75-84.
51. Manna Z., Waldinger R. Special relations in automated deduction. J. ACM. 33(1):1986;1-59.
52. Z. Stachniak, The resolution rule: an algebraic perspective, in: Proceedings of Algebraic Logic and Universal Algebra in Computer Science Conference, Lecture Notes in Computer Science, vol. 425, Springer, Heidelberg, 1988, pp. 227-242.
53. P. O'hearn and Z. Stachniak, Note on theorem proving strategies for resolution counterparts of non-classical logics, in: Proceedings of the International Symposium on Symbolic and Algebraic Computation, Poreland, Oregon, 1989, pp. 364-372.
54. Z. Stachniak, Resolution rule: algebraic perspective, in: Proceedings of the European Workshop on Logics in AI, Amsterdam, Lecture Notes in Computer Science, vol. 425, Springer, Berlin, 1990, pp. 227-242.
55. Z. Stachniak, Resolution Proof Systems: An Algebraic Theory, Kluwer Academic Publishers, Netherlands, 1996.
56. M. Baaz, C.G. Fermuller, Resolution for many valued logics, in: A. Voronkv (Ed.), Proceedings of Logic Programming and Automated Reasoning (LPAR'92), Lecture Notes in Artificial Intelligence, vol. 624, Springer, Berlin, 1992, pp. 107-118.
57. Xu Y. Lattice implication algebras. J. Southwest Jiaotong University. 89(1):1993;20-27. (in Chinese).
58. Y. Xu, Homomorphisms in latttice implication algebras, in: Proceedings of the Fifth Many-Valued Logical Congress of China, Nanjing, vol. 11, 1992, pp. 206-211 (in Chinese).
59. Xu Y., Qin K.Y. Lattice H implication algebras and class of lattice implication algebras. J. Hebei Mining Civil Eng. College. 9(2):1992;139-143. (in Chinese).
60. Y. Xu, K.Y. Qin, On lattice properties of lattice implication algebras, in: Collection Works on Applied Mathematics, Press of Chengdu University of Science and Technology, Chengdu, vol. 11, 1992, pp. 54-58 (in Chinese).
61. Xu Y., Qin K.Y. On filters of lattice implication algebras. J. Fuzzy Math. (Los Angeles). 1(2):1993;251-260.
62. K.Y. Qin, Y. Xu, Lukasiewicz implication algebra on [0,1], in: Proceedings of the Fifth IFSA, Seoul, vol. 7, 1993, pp. 410-412.
63. Y. Xu, K.Y. Qin, On the category of lattice implication algebras, in: Proceedings of the First Asian Fuzzy Systems Symposium, Singapore, vol. 11, 1993, pp. 1098-1101.
64. Xu Y., Qin K.Y. Characteristics of proper lattice implication algebras. Chinese Quart. J. Math. 10(4):1994;14-17.
65. Liu J., Xu Y. On filters and structure of lattice implication algebras. Chinese Sci. Bull. 42(18):1997;1517-1520.
66. Liu J., Xu Y. On prime filters and decomposition theorem of lattice implication algebras. J. Fuzzy Math. (Los Angeles). 6(4):1998;1001-1008.
67. Liu J., Xu Y. On the representation of lattice implication algebras. J. Fuzzy Math. (Los Angeles). 7(1):1999;251-258.
68. Jun Y.B., Xu Y., Qin K.Y. Implicative filters of lattice implication algebras. Bull. Korean Math. Soc. 34(2):1997;193-198.
69. Jun Y.B., Xu Y., Qin K.Y. Positive implicative and associative filters of lattice implication algebras. Bull. Korean Math. Soc. 35(1):1998;53-61.
70. Jun Y.B., Roh E.H., Xu Y. LI-ideals in lattice implication algebras. Bull. Korean Math. Soc. 35(1):1998;13-24.
71. Jun Y.B., Xu Y. On right regular maps of lattice implication algebras. J. Inst. Math. Comp. Sci. (Math. Ser.) India. 10(1):1997;53-58.
72. Jun Y.B., Xu Y. Fuzzy LI-ideals in lattice implication algebras. J. Fuzzy Math. (Los Angeles). 7(4):1999;997-1003.
73. Jun Y.B., Xu Y., Liu J. Quotient lattice implication algebras induced by fuzzy LI-ideals. J. Fuzzy Math. (Los Angeles). 7(4):1999;1013-1020.
74. Xu Y., Qin K.Y. Lattice-valued propositional logic (I). J. Southwest Jiaotong Univ. 1(2):1993;123-128. (in English).
75. Qin K.Y., Xu Y. Lattice-valued propositional logic (II). J. Southwest Jiaoong Univ. 2(1):1994;22-27. (in English).
76. Xu Y., Qin K.Y., Song Z.M. On syntax of first-order lattice-valued logic system FM. Chinese Sci. Bull. 42(17):1997;1052-1055.
77. Qin K.Y., Xu Y., Song Z.M. Compactness and Lowenheim-Skolem property of first-order lattice-valued logic system FM. Chinese Sci. Bull. 43(4):1998;371-375. (in Chinese).
78. Qin K.Y., Xu Y.Y. Fuzzy propositional logic system. FP(X) (I) J. Fuzzy Math. (Los Angeles). 3:1994;152-157.
79. *(X) (II), in: Proceedings of China Association for Science and Technology Second Academic Annual Meeting of Youths (Sichuan), Press of Southwest Jiaotong University, vol. 8, 1995, pp. 253-257.
80. K.Y. Qin, Study on lattice-valued logic system based on lattice implication algebras and their applications, Ph.D. Thesis, Southwest Jiaotong University, 1996 (in Chinese).
81. Qin K.Y., Xu Y., Song Z.M. Lattice-valued propositional logic. LP(X) (I) Fuzzy Sys. Math. 11(4):1997;5-10. (in Chinese).
82. Qin K.Y., Xu Y., Song Z.M. Lattice-valued propositional logic. LP(X) (II) Fuzzy Sys. Math. 12(1):1998;10-19. (in Chinese).
83. vpl Inf. Sci. 114(1-4):1999;205-235.
84. vfl Int. J. General Sys. 29(1):2000;53-79.
85. vfl , Int. J. Multiple-Valued Logic, in press.
86. Qin K.Y., Xu Y., Song Z.M. Some kinds of approximate reasoning based on system. LP(X) Fuzzy Sys. Math. 12(2):1998;55-60. (in Chinese).
87. vpl Ruan D., Kerre E.E. Fuzzy IF-THEN Rule in Computational Intelligence: Theory and Application. 2000;81-106 Kluwer Academic Publishers, Dordrecht.
88. Y. Xu, D. Ruan, J. Liu, Uncertainty automated reasoning in intelligent learning of soft knowledge, in: Proceedings of the ICST Whorkshop: Information and Communication Technology for Teaching and Training, 9-10 September 1999, pp. 29-45.
89. J. Liu, Study on lattice-valued logic system and lattice-valued resolution principle, Ph.D. Thesis, Southwest Jiaotong University, 1999 (in Chinese).
90. J. Liu, Z.M. Song, K.Y. Qin, A resolution procedure based on a fuzzy logic, in: Proceedings of the Ninth IEEE International Conference on Fuzzy System (FUZZ-IEEE 2000), San Antonio, Texas, 2000.