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Volumn 177, Issue 4, 2007, Pages 1046-1062

Filter-based resolution principle for lattice-valued propositional logic LP(X)

Author keywords

Automated reasoning; Complex generalized clause; Filter; Lattice valued logic; Resolution principle; Simple generalized clause

Indexed keywords

ALGEBRA; NUMERICAL METHODS; OPTICAL FILTERS; OPTICAL RESOLVING POWER; THEOREM PROVING;

EID: 33751224166     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2006.07.027     Document Type: Article
Times cited : (25)

References (81)
  • 2
    • 38249011188 scopus 로고
    • Complexity of resolution proofs and function introduction
    • Baaz M., and Leitsch A. Complexity of resolution proofs and function introduction. Ann. Pure Appl. Logic 57 (1992) 181-215
    • (1992) Ann. Pure Appl. Logic , vol.57 , pp. 181-215
    • Baaz, M.1    Leitsch, A.2
  • 3
    • 0000970038 scopus 로고
    • Resolution-based theorem proving for many-valued logics
    • Baaz M., and Fermüller C.G. Resolution-based theorem proving for many-valued logics. J. Symbol. Comput. 19 (1995) 353-391
    • (1995) J. Symbol. Comput. , vol.19 , pp. 353-391
    • Baaz, M.1    Fermüller, C.G.2
  • 4
  • 5
    • 0343826093 scopus 로고    scopus 로고
    • Fuzzy temporal constraint logic: a valid resolution principle
    • Cárdenas Viedma I.N.S.M.A., and Marín Morales R. Fuzzy temporal constraint logic: a valid resolution principle. Fuzzy Sets Syst. 117 (2001) 231-250
    • (2001) Fuzzy Sets Syst. , vol.117 , pp. 231-250
    • Cárdenas Viedma, I.N.S.M.A.1    Marín Morales, R.2
  • 7
    • 0031109050 scopus 로고    scopus 로고
    • CLIN-S-A semantically guided first-order theorem prover
    • Chu H., and Plaisted D. CLIN-S-A semantically guided first-order theorem prover. J. Automat. Reason. 18 (1997) 183-188
    • (1997) J. Automat. Reason. , vol.18 , pp. 183-188
    • Chu, H.1    Plaisted, D.2
  • 8
    • 0031108705 scopus 로고    scopus 로고
    • DISCOUNT-A distributed and learning equational prover
    • Denzinger J., Kronenburg M., and Schulz S. DISCOUNT-A distributed and learning equational prover. J. Automat. Reason. 18 (1997) 189-198
    • (1997) J. Automat. Reason. , vol.18 , pp. 189-198
    • Denzinger, J.1    Kronenburg, M.2    Schulz, S.3
  • 9
    • 0032362014 scopus 로고    scopus 로고
    • Temporal resolution using a breadth-first search algorithm
    • Dixon C. Temporal resolution using a breadth-first search algorithm. Ann. Math. Artif. Intell. 22 (1998) 87-115
    • (1998) Ann. Math. Artif. Intell. , vol.22 , pp. 87-115
    • Dixon, C.1
  • 10
    • 33751207192 scopus 로고    scopus 로고
    • D. Dubois, J. Lang, H. Prade, Theorem proving under uncertainty-a possibility theory based approach, in: Proc. of the International Joint Conference on Artificial Intelligence (IJCAI'87), Mitano, Italy, 1987, pp. 984-986.
  • 11
    • 33751218358 scopus 로고    scopus 로고
    • D. Dubois, J. Lang, H. Prade, Automated reasoning using possibility logic semantics, belief revision and variable certainty weights, in: Proc. of the Fifth Workshop on Uncertainty in Artificial Intelligence, Windor, Ont., 1989, pp. 81-87.
  • 12
    • 45149137400 scopus 로고
    • Resolution principle in possibilistic logic
    • Dubois D., and Prade H. Resolution principle in possibilistic logic. Internat. J. Approx. Reason. 4 1 (1990) 1-21
    • (1990) Internat. J. Approx. Reason. , vol.4 , Issue.1 , pp. 1-21
    • Dubois, D.1    Prade, H.2
  • 13
    • 21144464260 scopus 로고
    • Model building by resolution
    • Proc. of 6th Workshop on Computer Science Logic (CSL'92), Springer, New York
    • Fermüller C., and Leitsch A. Model building by resolution. Proc. of 6th Workshop on Computer Science Logic (CSL'92). Lecture Notes in Computer Science vol. 702 (1993), Springer, New York 134-148
    • (1993) Lecture Notes in Computer Science , vol.702 , pp. 134-148
    • Fermüller, C.1    Leitsch, A.2
  • 14
    • 0033123385 scopus 로고    scopus 로고
    • T-resolution: Refinements and model elimination
    • Formisano A., and Polocriti A. T-resolution: Refinements and model elimination. J. Automat. Reason. 22 (1999) 433-483
    • (1999) J. Automat. Reason. , vol.22 , pp. 433-483
    • Formisano, A.1    Polocriti, A.2
  • 15
    • 0037289978 scopus 로고    scopus 로고
    • A perspective on certain polynomial-time solvable classes of satisfiability
    • Franco J., and Gelder A.V. A perspective on certain polynomial-time solvable classes of satisfiability. Discr. Appl. Math. 125 (2003) 177-214
    • (2003) Discr. Appl. Math. , vol.125 , pp. 177-214
    • Franco, J.1    Gelder, A.V.2
  • 16
    • 11144254815 scopus 로고    scopus 로고
    • Labelled resolution for classical and non-classical logics
    • Gabbay D.M., and Reyle U. Labelled resolution for classical and non-classical logics. Stud. Log. 59 (1997) 179-216
    • (1997) Stud. Log. , vol.59 , pp. 179-216
    • Gabbay, D.M.1    Reyle, U.2
  • 18
    • 0037380443 scopus 로고    scopus 로고
    • Back jumping for quantified Boolean logic satisfiability
    • Giunchiglia E., Narizzano M., and Tacchella A. Back jumping for quantified Boolean logic satisfiability. Artif. Intell. 145 (2003) 99-120
    • (2003) Artif. Intell. , vol.145 , pp. 99-120
    • Giunchiglia, E.1    Narizzano, M.2    Tacchella, A.3
  • 19
    • 0013337219 scopus 로고    scopus 로고
    • A treatise on many-valued logics
    • Research Studies Press, Baldock
    • Gottwald S. A treatise on many-valued logics. Studies in Logic and Computation vol. 9 (2001), Research Studies Press, Baldock
    • (2001) Studies in Logic and Computation , vol.9
    • Gottwald, S.1
  • 21
    • 54649083317 scopus 로고    scopus 로고
    • Commodious axiomatization of quantifiers in multiple-value logic
    • Hähnle R. Commodious axiomatization of quantifiers in multiple-value logic. Stud. Log. 61 1 (1998) 101-121
    • (1998) Stud. Log. , vol.61 , Issue.1 , pp. 101-121
    • Hähnle, R.1
  • 23
    • 0035389846 scopus 로고    scopus 로고
    • Strategies for solving the Boolean satisfiability problem using binary decision diagrams
    • Kalla P., Zeng Z., and Ciesielski M.J. Strategies for solving the Boolean satisfiability problem using binary decision diagrams. J. Syst. Architect. 47 (2001) 491-503
    • (2001) J. Syst. Architect. , vol.47 , pp. 491-503
    • Kalla, P.1    Zeng, Z.2    Ciesielski, M.J.3
  • 24
    • 33751212863 scopus 로고    scopus 로고
    • M. Kifer, On the expressive power of annotated logic program, in: Proc. of the 1989 North American Conference on Logic Programming, Cleveland, OH, 1989, pp. 1069-1089.
  • 25
    • 0024876283 scopus 로고    scopus 로고
    • M. Kifer, E. Lozinskii, RI: A logic for reasoning with inconsistency, in: Proc. of the 21st International Symposium on Multiple-Valued Logics (ISMVL'91), Victoria, BC, Canada, 1991, pp. 253-262.
  • 26
    • 0012228090 scopus 로고    scopus 로고
    • A new fuzzy resolution principle based on the antonym
    • Kim C.S., Kim D.S., and Park J.S. A new fuzzy resolution principle based on the antonym. Fuzzy Sets and Syst. 113 (2000) 299-307
    • (2000) Fuzzy Sets and Syst. , vol.113 , pp. 299-307
    • Kim, C.S.1    Kim, D.S.2    Park, J.S.3
  • 27
    • 0344550359 scopus 로고    scopus 로고
    • The complexity of minimal satisfiability problems
    • Kirousis L.M., and Kolaitis P.G. The complexity of minimal satisfiability problems. Inform. Comput. 187 (2003) 20-39
    • (2003) Inform. Comput. , vol.187 , pp. 20-39
    • Kirousis, L.M.1    Kolaitis, P.G.2
  • 28
    • 0003019709 scopus 로고
    • Eliminating duplication with the hyper-linking strategy
    • Lee S.J., and Plaisted D.A. Eliminating duplication with the hyper-linking strategy. J. Automat. Reason. 9 (1992) 25-42
    • (1992) J. Automat. Reason. , vol.9 , pp. 25-42
    • Lee, S.J.1    Plaisted, D.A.2
  • 29
    • 0031108707 scopus 로고    scopus 로고
    • LINUS-A link instantiation prover with unit support
    • Letz R. LINUS-A link instantiation prover with unit support. J. Automat. Reason. 18 (1997) 205-210
    • (1997) J. Automat. Reason. , vol.18 , pp. 205-210
    • Letz, R.1
  • 30
    • 33751227293 scopus 로고    scopus 로고
    • Filter and structure of lattice implication algebra
    • Liu J., and Xu Y. Filter and structure of lattice implication algebra. Chin. Sci. Bull. 10 (1997) 1049-1052
    • (1997) Chin. Sci. Bull. , vol.10 , pp. 1049-1052
    • Liu, J.1    Xu, Y.2
  • 31
    • 33751249715 scopus 로고    scopus 로고
    • J. Liu, Study on lattice-valued logic system and lattice-valued resolution principle, Ph.D. thesis, Southwest Jiaotong University, Chengdu, China, 1999.
  • 33
    • 84945709685 scopus 로고
    • Mechanical theorem proving by model elimination
    • Loveland D.W. Mechanical theorem proving by model elimination. ACM Trans. Math. Software 15 2 (1968) 236-251
    • (1968) ACM Trans. Math. Software , vol.15 , Issue.2 , pp. 236-251
    • Loveland, D.W.1
  • 34
    • 0027191746 scopus 로고    scopus 로고
    • J.J. Lu, N.V. Murray, E. Rosenthal, Signed formulas and annotated logics, in: Proc. of the 23rd International Symposium on Multiple-Valued Logics (ISMVL'93), 1993, pp. 48-53.
  • 35
    • 84947752975 scopus 로고    scopus 로고
    • J.J. Lu, N.V. Murray, E. Rosenthal, Signed formulas and fuzzy operator logics, in: J. Komorowski, Z.W. Ras (Eds.), Proc. of the Seventh International Symposium on Mathodologies for Intelligent Systems (ISMIS'93), 1993, pp. 75-84.
  • 36
    • 0032143854 scopus 로고    scopus 로고
    • A framework for reasoning in multiple-valued logics
    • Lu J.J., Murray N.V., and Rosenthal E. A framework for reasoning in multiple-valued logics. J. Automat. Reason. 21 1 (1998) 39-67
    • (1998) J. Automat. Reason. , vol.21 , Issue.1 , pp. 39-67
    • Lu, J.J.1    Murray, N.V.2    Rosenthal, E.3
  • 38
    • 33751233652 scopus 로고    scopus 로고
    • J. Ma, Study on lattice implication algebra and lattice-valued propositional logic LP(X), Master's thesis, Southwest Jiaotong University, Chengdu, China, 1999.
  • 39
    • 33751207509 scopus 로고    scopus 로고
    • J. Ma, Lattice-valued logical system and automated reasoning based on lattice implication algebra, Ph.D. thesis, Southwest Jiaotong University, Chengdu, China, 2002.
  • 40
    • 33751246555 scopus 로고    scopus 로고
    • W. McCune, OTTER 3.0 reference manual and guide, Tech. Rep. Tech. Rep. ANL-94/6, Argonne National Laboratory, 1994. Available from: .
  • 41
    • 84895918869 scopus 로고
    • Resolution for many-valued logics
    • Morgan C. Resolution for many-valued logics. Logique et Anal. (N.S.) 19 (1976) 311-339
    • (1976) Logique et Anal. (N.S.) , vol.19 , pp. 311-339
    • Morgan, C.1
  • 42
    • 0016480006 scopus 로고
    • On some properties of fuzzy logic
    • Mukaidono M. On some properties of fuzzy logic. Systems Comput. Controls 6 2 (1975) 36-43
    • (1975) Systems Comput. Controls , vol.6 , Issue.2 , pp. 36-43
    • Mukaidono, M.1
  • 43
    • 0001934371 scopus 로고
    • Fuzzy inference of resolution style
    • Yager R.R. (Ed), Pergamon Press, New York
    • Mukaidono M. Fuzzy inference of resolution style. In: Yager R.R. (Ed). Fuzzy Sets and Possibility Theory (1982), Pergamon Press, New York 224-231
    • (1982) Fuzzy Sets and Possibility Theory , pp. 224-231
    • Mukaidono, M.1
  • 44
    • 0019937295 scopus 로고
    • Completely nonclausal resolution theorem proving
    • Murray N.V. Completely nonclausal resolution theorem proving. Artif. Intell. 18 1 (1982) 67-85
    • (1982) Artif. Intell. , vol.18 , Issue.1 , pp. 67-85
    • Murray, N.V.1
  • 45
    • 0026151854 scopus 로고    scopus 로고
    • N.V. Murray, E. Rosenthal, Improving tableau proof in multiple valued logics, in: Proc. of 21st International Symposium of Multiple-Valued Logics (ISMVL'91), Victoria, BC, Canada, 1991, pp. 230-237.
  • 49
    • 0005277759 scopus 로고
    • +-valued logic
    • +-valued logic. Fund. Inform. 2 1 (1978) 1-15
    • (1978) Fund. Inform. , vol.2 , Issue.1 , pp. 1-15
    • Orlowska, E.1
  • 50
    • 0005279092 scopus 로고
    • Resolution system and their application II
    • Orlowska E. Resolution system and their application II. Fund. Inform. 3 3 (1980) 333-362
    • (1980) Fund. Inform. , vol.3 , Issue.3 , pp. 333-362
    • Orlowska, E.1
  • 51
    • 0005315856 scopus 로고
    • Mechanical proof methods for post logics
    • Orlowska E. Mechanical proof methods for post logics. Logique et Anal. (N.S.) 28 110 (1985) 173-192
    • (1985) Logique et Anal. (N.S.) , vol.28 , Issue.110 , pp. 173-192
    • Orlowska, E.1
  • 52
    • 84982606937 scopus 로고
    • 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 119-134, 447-464
    • Pavelka J. 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. Z. Math. Logik Grundlagen Math. 25 (1979) 45-52 119-134, 447-464
    • (1979) Z. Math. Logik Grundlagen Math. , vol.25 , pp. 45-52
    • Pavelka, J.1
  • 54
    • 0001037786 scopus 로고
    • Introduction to a general theory of elementary propositions
    • Post E.L. Introduction to a general theory of elementary propositions. Amer. J. Math. 43 (1921) 163-185
    • (1921) Amer. J. Math. , vol.43 , pp. 163-185
    • Post, E.L.1
  • 55
    • 33751216262 scopus 로고    scopus 로고
    • K. Qin, Study of lattice-valued logic system and its application based on lattice implication algebra, Ph.D. thesis, Southwest Jiaotong University, Chengdu, China, 1996.
  • 56
    • 84918983692 scopus 로고
    • A machine-oriented logic based on the resolution principle
    • Robinson J.A. A machine-oriented logic based on the resolution principle. J. ACM 12 (1965) 23-41
    • (1965) J. ACM , vol.12 , pp. 23-41
    • Robinson, J.A.1
  • 58
    • 84957677624 scopus 로고    scopus 로고
    • Optimal axiomatizations for multiple-valued operators and quantifiers based on semilattices
    • Proc. 13th Conference on Automated Deduction. McRobbie M., and Slaney J. (Eds), Springer, New Brunswick, NJ
    • Salzer G. Optimal axiomatizations for multiple-valued operators and quantifiers based on semilattices. In: McRobbie M., and Slaney J. (Eds). Proc. 13th Conference on Automated Deduction. Lecture Notes in Computer Science vol. 1104 (1996), Springer, New Brunswick, NJ 688-702
    • (1996) Lecture Notes in Computer Science , vol.1104 , pp. 688-702
    • Salzer, G.1
  • 59
    • 0033123386 scopus 로고    scopus 로고
    • Decidability by resolution for propositional model logics
    • Schmidt R. Decidability by resolution for propositional model logics. J. Automat. Reason. 22 (1999) 376-396
    • (1999) J. Automat. Reason. , vol.22 , pp. 376-396
    • Schmidt, R.1
  • 61
    • 1342264163 scopus 로고    scopus 로고
    • Graded many-valued resolution with aggregation
    • Smutná-Hliněná D., and Vojtáš P. Graded many-valued resolution with aggregation. Fuzzy Sets Syst. 143 (2004) 157-168
    • (2004) Fuzzy Sets Syst. , vol.143 , pp. 157-168
    • Smutná-Hliněná, D.1    Vojtáš, P.2
  • 62
    • 33751247720 scopus 로고    scopus 로고
    • Z. Song, Study of uncertainty reasoning based on lattice implication algebra in intelligent control, Ph.D. thesis, Southwest Jiaotong University, Chengdu, China, 1998.
  • 64
    • 0345441123 scopus 로고    scopus 로고
    • Automated theorem proving by resolution for finitely-valued logics based on distributive lattices with operators
    • Sofronie-Stokkermans V. Automated theorem proving by resolution for finitely-valued logics based on distributive lattices with operators. Mult.-Valued Log. 6 3/4 (2001) 289-344
    • (2001) Mult.-Valued Log. , vol.6 , Issue.3-4 , pp. 289-344
    • Sofronie-Stokkermans, V.1
  • 66
    • 8844274310 scopus 로고    scopus 로고
    • 0-algebras, and multiple-valued logic
    • 0-algebras, and multiple-valued logic. Fuzzy Syst. Math. 16 2 (2002) 1-15
    • (2002) Fuzzy Syst. Math. , vol.16 , Issue.2 , pp. 1-15
    • Wang, G.1
  • 67
    • 33751210188 scopus 로고    scopus 로고
    • X. Wang, Study on lattice-valued logic based on lattice implication algebra and its model theory, Ph.D. thesis, Southwest Jiaotong University, Chengdu, China, 2004.
  • 68
    • 0032178308 scopus 로고    scopus 로고
    • A two-phase algorithm for solving a class of hard satisfiability problems 1
    • Warners J.P., and van Maaren H. A two-phase algorithm for solving a class of hard satisfiability problems 1. Oper. Res. Lett. 23 (1998) 81-88
    • (1998) Oper. Res. Lett. , vol.23 , pp. 81-88
    • Warners, J.P.1    van Maaren, H.2
  • 69
    • 85035790828 scopus 로고    scopus 로고
    • L. Wos, D. Carson, G. Robinson, The unit preference strategy in theorem proving, in: Proc. of the Fall Joint Computer Conference, 1964, pp. 615-621.
  • 70
    • 0001457667 scopus 로고
    • Efficiency and completeness of the set-of-support strategy in theorem proving
    • Wos L., Carson D., and Robinson G. Efficiency and completeness of the set-of-support strategy in theorem proving. ACM Trans. Math. Software 12 (1965) 536-541
    • (1965) ACM Trans. Math. Software , vol.12 , pp. 536-541
    • Wos, L.1    Carson, D.2    Robinson, G.3
  • 71
    • 0003165003 scopus 로고
    • Lattice implication algebra
    • Xu Y. Lattice implication algebra. J. Southwest Jiaotong Univ. 28 1 (1993) 20-27
    • (1993) J. Southwest Jiaotong Univ. , vol.28 , Issue.1 , pp. 20-27
    • Xu, Y.1
  • 72
    • 0012841872 scopus 로고
    • Lattice-valued propositional logic (I)
    • (English version)
    • Xu Y., and Qin K. Lattice-valued propositional logic (I). J. Southwest Jiaotong Univ. 2 (1993) 123-128 (English version)
    • (1993) J. Southwest Jiaotong Univ. , vol.2 , pp. 123-128
    • Xu, Y.1    Qin, K.2
  • 73
    • 0002324488 scopus 로고
    • Lattice-valued propositional logic (II)
    • (English version)
    • Xu Y., and Qin K. Lattice-valued propositional logic (II). J. Southwest Jiaotong Univ. 1 (1994) 22-27 (English version)
    • (1994) J. Southwest Jiaotong Univ. , vol.1 , pp. 22-27
    • Xu, Y.1    Qin, K.2
  • 74
    • 0005301269 scopus 로고    scopus 로고
    • Syntax of lattice-valued first-order logic FM
    • Xu Y., Qin K., and Song Z. Syntax of lattice-valued first-order logic FM. Chin. Sci. Bull. 10 (1997) 1052-1055
    • (1997) Chin. Sci. Bull. , vol.10 , pp. 1052-1055
    • Xu, Y.1    Qin, K.2    Song, Z.3
  • 77
    • 0034497853 scopus 로고    scopus 로고
    • α-Resolution principle based on lattice-valued propositional logic LP(X)
    • Xu Y., Ruan D., Kerre E.E., and Liu J. α-Resolution principle based on lattice-valued propositional logic LP(X). Inform. Sci. 130 (2000) 1-29
    • (2000) Inform. Sci. , vol.130 , pp. 1-29
    • Xu, Y.1    Ruan, D.2    Kerre, E.E.3    Liu, J.4
  • 79
    • 0035248015 scopus 로고    scopus 로고
    • α-Resolution principle based on first-order lattice-valued logic LF(X)
    • Xu Y., Ruan D., Kerre E.E., and Liu J. α-Resolution principle based on first-order lattice-valued logic LF(X). Inform. Sci. 132 (2001) 221-239
    • (2001) Inform. Sci. , vol.132 , pp. 221-239
    • Xu, Y.1    Ruan, D.2    Kerre, E.E.3    Liu, J.4
  • 81
    • 0022098330 scopus 로고
    • Inference in a multiple-valued logic system
    • Yager R.R. Inference in a multiple-valued logic system. Internat. J. Man-Machine Studies 23 (1985) 27-44
    • (1985) Internat. J. Man-Machine Studies , vol.23 , pp. 27-44
    • Yager, R.R.1


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