基于描述逻辑的定性空间推理研究
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摘要
定性空间推理结合了定性推理、空间推理与人工智能,它已经成为人工智能领域的一个研究热点。定性空间推理研究人类对几何空间中的空间对象及其关系定性认知常识的表示与处理。作为空间关系的重要组成部分,空间拓扑关系研究空间对象在拓扑变换下不变的性质,它是定性空间关系建立的基础。因此,空间拓扑关系的表示与推理非常重要。
目前,空间拓扑关系的研究取得了很大进展,但这些研究若直接使用一阶逻辑,而不附加任何约束,则一方面破坏了知识的结构特性,不便于用来驱动推理,另一方面,对获得可判定和有效性的推理问题来说,一阶逻辑表达能力太强。始于20世纪80年代的描述逻辑,是一阶谓词逻辑的一个可判定的子集,它能够提供可判定的推理服务,因此,描述逻辑在十多年来受到人们的特别关注,并且作为知识表示的工具,在越来越多的领域中得到较好的应用,但是目前在定性空间推理方面的应用的研究还较少。本论文将描述逻辑应用到空间推理中,充分利用描述逻辑较强的表达和推理能力,提高空间推理的准确性和可判定性。本文主要进行了以下几个方面的研究工作:
①定性空间具体域
分析了现有各种空间拓扑关系表示方法,然后结合描述逻辑,给出了定性空间具体域,该具体域包括空间对象的基元集合以及空间对象间拓扑关系集合。在此基础上,对具体域中表达的空间拓扑关系进行符号化表示,用描述逻辑的形式表
达空间关系。
②基于描述逻辑关系断言的空间拓扑关系推理规则
给出了基于描述逻辑关系断言的空间拓扑关系推理规则,并用实例说明了推理规则的运用。
③定性空间关系可满足性判定基于SI形式语言,给出了定性空间关系可满足性判定算法,并通过实例说明了算法的运用。
④基于描述逻辑的定性空间推理应用实例
通过实例,给出了基于描述逻辑的空间拓扑关系推理规则及可满足性判定算法和空间拓扑关系集的一致性检测在定性空间拓扑关系推理中的应用,对描述逻辑在定性空间推理中的应用进行了初步探索。
Qualitative spatial reasoning combines qualitative reasoning, spatial reasoning and artificial intelligence together. It has become a hot topic in the research of artificial intelligence. Qualitative spatial reasoning researches the expressing and processing of human cognition of geometry spatial objects and their relations. As an important component of spatial relations, spatial topology relations research the constant properties of space objects with topological transformation. The expressing and reasoning of spatial topology relationship is very important because it is the basis for the establishment of qualitative spatial relations.
At present, the research of spatial topology relationship has made great progress, but using first-order logic without any additional constraints, will result in many problems such as destroying the structure characteristics of the knowledge and inconvenient for reasoning, and so on. On the other hand, the first-order logic is too strong to handle determined and effective issues. The description logic proposed in 1980s is a decidable subset of first-order logic, and it can give decidable reasoning service. Therefore, the description logic has been paid special attention and been used in more and more fields as the knowledge representation tool. But, qualitative spatial reasoning is still a new field for the research of the description logic.This thesis fully uses the expressing and reasoning ability of description logic and applies it in the spatial reasoning to increase the accuracy and decidability of the reasoning. The main work is listed as following:
Firstly, this thesis put forward the qualitative spatial concrete domain.
This thesis has analyzed existed spatial topology expressing methods, and then gives the qualitative spatial concrete domain which based on the description logic and contains the set of basic spatial objects and the topological relationships between them. On this basis, the thesis put forward the symbolic expressing of the topological relationships which are in the concrete domain and use description logic to express the spatial relationships.
Secondly, this thesis gives the reasoning rules of spatial topological relationship which based on description logic.
This thesis put forward the reasoning rules of spatial topological relationships which based on description logic and then introduce it through an example.
Thirdly, this thesis put forward the qualitative spatial relationships satisfiability determination algorithm.
This thesis has researched the appropriate formal language which can be used in qualitative spatial reasoning, and then put forward the qualitative spatial relationships satisfiabiligy determination algorithm and illustrates the application of this algorithm through an example.
Fourthly, this thesis put forward the example of the application of qualitative spatial reasoning which based on description logic.
This thesis put forward the synthesized application of reasoning rules of spatial topological relationships and satisfiability determination algorithm and consistency detecting through the example. It gives the preliminary exploration of how to apply the description logic to the qualitative spatial reasoning.
目前,空间拓扑关系的研究取得了很大进展,但这些研究若直接使用一阶逻辑,而不附加任何约束,则一方面破坏了知识的结构特性,不便于用来驱动推理,另一方面,对获得可判定和有效性的推理问题来说,一阶逻辑表达能力太强。始于20世纪80年代的描述逻辑,是一阶谓词逻辑的一个可判定的子集,它能够提供可判定的推理服务,因此,描述逻辑在十多年来受到人们的特别关注,并且作为知识表示的工具,在越来越多的领域中得到较好的应用,但是目前在定性空间推理方面的应用的研究还较少。本论文将描述逻辑应用到空间推理中,充分利用描述逻辑较强的表达和推理能力,提高空间推理的准确性和可判定性。本文主要进行了以下几个方面的研究工作:
①定性空间具体域
分析了现有各种空间拓扑关系表示方法,然后结合描述逻辑,给出了定性空间具体域,该具体域包括空间对象的基元集合以及空间对象间拓扑关系集合。在此基础上,对具体域中表达的空间拓扑关系进行符号化表示,用描述逻辑的形式表
达空间关系。
②基于描述逻辑关系断言的空间拓扑关系推理规则
给出了基于描述逻辑关系断言的空间拓扑关系推理规则,并用实例说明了推理规则的运用。
③定性空间关系可满足性判定基于SI形式语言,给出了定性空间关系可满足性判定算法,并通过实例说明了算法的运用。
④基于描述逻辑的定性空间推理应用实例
通过实例,给出了基于描述逻辑的空间拓扑关系推理规则及可满足性判定算法和空间拓扑关系集的一致性检测在定性空间拓扑关系推理中的应用,对描述逻辑在定性空间推理中的应用进行了初步探索。
Qualitative spatial reasoning combines qualitative reasoning, spatial reasoning and artificial intelligence together. It has become a hot topic in the research of artificial intelligence. Qualitative spatial reasoning researches the expressing and processing of human cognition of geometry spatial objects and their relations. As an important component of spatial relations, spatial topology relations research the constant properties of space objects with topological transformation. The expressing and reasoning of spatial topology relationship is very important because it is the basis for the establishment of qualitative spatial relations.
At present, the research of spatial topology relationship has made great progress, but using first-order logic without any additional constraints, will result in many problems such as destroying the structure characteristics of the knowledge and inconvenient for reasoning, and so on. On the other hand, the first-order logic is too strong to handle determined and effective issues. The description logic proposed in 1980s is a decidable subset of first-order logic, and it can give decidable reasoning service. Therefore, the description logic has been paid special attention and been used in more and more fields as the knowledge representation tool. But, qualitative spatial reasoning is still a new field for the research of the description logic.This thesis fully uses the expressing and reasoning ability of description logic and applies it in the spatial reasoning to increase the accuracy and decidability of the reasoning. The main work is listed as following:
Firstly, this thesis put forward the qualitative spatial concrete domain.
This thesis has analyzed existed spatial topology expressing methods, and then gives the qualitative spatial concrete domain which based on the description logic and contains the set of basic spatial objects and the topological relationships between them. On this basis, the thesis put forward the symbolic expressing of the topological relationships which are in the concrete domain and use description logic to express the spatial relationships.
Secondly, this thesis gives the reasoning rules of spatial topological relationship which based on description logic.
This thesis put forward the reasoning rules of spatial topological relationships which based on description logic and then introduce it through an example.
Thirdly, this thesis put forward the qualitative spatial relationships satisfiability determination algorithm.
This thesis has researched the appropriate formal language which can be used in qualitative spatial reasoning, and then put forward the qualitative spatial relationships satisfiabiligy determination algorithm and illustrates the application of this algorithm through an example.
Fourthly, this thesis put forward the example of the application of qualitative spatial reasoning which based on description logic.
This thesis put forward the synthesized application of reasoning rules of spatial topological relationships and satisfiability determination algorithm and consistency detecting through the example. It gives the preliminary exploration of how to apply the description logic to the qualitative spatial reasoning.
引文
[1]刘亚彬,刘大有.空间推理与地理信息系统综述[J].软件学报, 2000: 1598-1606.
[2] A.G.Chon, S.M.Hazarika, Qualitative Spatial representation and reasoning:an overview[J]. Fundament Information, May 2001, Volume 46 Issue 1-2(2001):2-32.
[3]郭平.定性空间推理技术及其应用[D].重庆:重庆大学计算机学院,博士论文. 2004.
[4] Egenhofer, M., Franzosa, R. Point-Set topological spatial relations[J]. International Journal of Geographical Information System, 1991, 5 (2 ):161- 174.
[5] Ping Guo, Tao Huang-Fu, Ya Luo, Research on the Relationship Between 4-intersection and Classifying Invariant Base on the Simple Regions[J].In Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, Xi an, China, 2003: 1642-1647.
[6] Egenhofer, M. J. and Herring, J., Categorizing topological spatial relationships between point, line and area objects, The 9-intersections: formalism and its use for natural language spatial predicates[R]. Technical Report 94-1., National Centre for Geographic Information and Analysis, Santa Barbara, 1994.
[7]史忠植.高级人工智能[M].科学出版社, 2006.9.
[8] Brachman R J. and Schmolze J G., An overview of the KL-ONE knowledge representation system[J], Cognitive Science, 1985, 9 (2):171-216.
[9] Baader F , Calvanese D , McGuinness D , et al . The Description Logic Handbook : Theory , Implementation and Applications [M] . 2nd ed. Cambridge : Cambridge Univer sity Press , 2007:47-100.
[10] Li Shuying , Li Mei , Jiang Yuncheng , et al . Fuzzy description logic L-ALCN [J] . Journal of Computer Research and Development , 2008 , 45 (4) : 619-625 (in Chinese) (李淑英,李梅,蒋运承,等.模糊描述逻辑L-ALCN [J] .计算机研究与发展, 2008, 45 (4) : 619-625).
[11] Jiang Yuncheng , Wang J u , Deng Peimin , et al . Semantics and reasoning of terminological cycles in description logic FL -[J] . Chinese Journal of Computers , 2008 , 31 (2) : 185-195 (in Chinese).
[12]邱剑锋,王申康,马勤勇,王玥,徐海长.描述逻辑在基于语义的服务消息交互中的应用[J].计算机应用研究.vol26 No.1, Jan 2009:289-293.
[13] Description Logic.home page http://dl.kr.org/[Z].2009.
[14] Liu Y. B., CHEN G., The Research of Spatial Reasoning in Description Logic[J]. Computer Science, 2004 Vol.31(8):110-112 (in Chinese)
[15] Brachman R J, Levesque H J, The tractability of subsumption in frame-based descriptionlanguages[J]. In: Proceedings of the 4th National Conference of the American Association for Artificial Intelligence (AAAI-84), Austin, TX, 1984:34-37.
[16] Baader F, Horrocks I, Sattler U, Description logics as ontology languages for the semantic web[R]. In: Hutter D, Stephan W, eds. Festschrift in honor of Jorg Siekmann, Lecture Notes in Artificial Intelligence, Springer, 2003:4-5.
[17] Mays E, Dionne R, Weida R. K-REP system overview[J]. SIGART Bulletin, 1991, 2(3):93-97.
[18] Peltason C. The BACK system-an overview[M]. SIGART Bulletin, 1991, 2(3):114-119.
[19] MacGregor R. The evolving technology of classification-based knowledge representation systems[J]. In: Sowa J F, ed. Principles of Semantic Networks, Morgan Kaufmann, Los Altos: 1991:385-400.
[20] Schmidt-SchauβM, Smolka G. Attributive concept descriptions with complements[J]. Artificial Intelligence Journal, 1991, 48(1):1-26.
[21] Donini F, Lenzerini M, Nardi D, et al.The complexity of concept languages[J]. In: Proc. of the 2nd Int Conf on the Principles of Knowledge Representation and Reasoning (KR-91), Boston, MA, USA, 1991.
[22] Hollunder B, Nutt W, Schmidt-Schauss M. Subsumption algorithms for concept description languages[M]. In:ECAI-90, Pitman Publishing, London, 1990.
[23] Donini F M, Lenzerini M, Nardi D, et al. Tractable concept languages[J]. In: Proc. of the 12th Int Joint Conf. on Artificial Intelligence(IJCAI-91), Sydney, 1991:458-463.
[24] Donini F M, Hollunder B, Lenzerini M, et al. The complexity of existential quantification in concept languages[J]. Artificial Intelligence Journal, 1992(2-3):309-327.
[25] Schild K. A correspondence theory for terminological logics: Preliminary report[R]. In: Proc. of the 12th Int Joint Conf. on Artificial Intelligence(IJCAI-91), 1991:466-471.
[26] Horrocks I. Using an expressive description logic: FaCT or Fiction?[J] In: Proc. of the 6th Int Conf. on the Principles of Knowledge Representation and Reasoning(KR-98), 1998:636-647.
[27] Haarslev V, Moller R. RACE system description[J]. In: Lambrix P, Borgida A, Lenzerini M, et al. Proceedings of the International Workshop on Description Logics, Linkoping, Sweden, 1999
[28] Patel-Schneider P F. DLP[J]. In: Proc. of the 1999 Description Logic Workshop(DL’99), CEUR Electronic Workshop Proceedings. http://ceurws.org/vol-22/, 1999:9-13.
[29] De Giacomo G, Lenzerini M.Boosting the correspondence between description logics and propositional dynamic logics[J]. In: Proc. of the 12th Nat Conf. on Aritificial Intelligence(AAAI-94) AAAI Press/The MIT Press, 1994:205-212 .
[30] Schild K.Querying Knowledge and Data Bases by a Universal Description Logic with Recursion[D]: [PhD thesis]. University at des Saarlandes, Germany, 1995.
[31] Borgida A. On the relative expressive power of Description Logics and Predicate Calculus[J]. To appear in Artificial Intelligence, 1996.
[32] Pacholski L, Szwast W, Tendera L. Complexity of two-variable logic with counting[J]. In: Proc. of the 12th Ann IEEE Symp on Logic in Computer Science(LICS-97), IEEE Computer Society Press, 1997.318-327 .
[33] Gradel E, Kolaitis P G, Vardi M Y. On the decision problem for two-variable first-order logic[J]. Bulletin of Symbolic Logic, 1997, 3(1):53-69.
[34] Gradel E. Guarded fragments of first-order logic: A perspective for new description logics?[J] In: Proc. of the 1998 Description Logic Workshop(DL’98). CEUR Electronic Workshop Proceedings, http://ceur-ws.org/vol-11/, 1998.
[35] Gradel E. On the restraining power of guards[J]. Journal of Symbolic Logic, 1999, 64: 1719-1742.
[36] The IEA/AIE-2000 Workshop on Applications of Spatio-Temporal Reasoning Workshop Report[R], 1999.
[37]陈科.空间方位知识库与推理组件的研究与开发[D].重庆:重庆大学计算机学院,硕士论文. 2009.
[38] Leung, Y. Intelligent spatial decision support systems[J]. Berlin: Springer-Verlag. 1997, 1998. http://nsdi.Usgs.gov/nsdi/.
[39] Randell D A, Witkowski M, Shanahan M. From images to bodis: Modelling and exploiting spatial occlusion and motion parallax[J]. In: Nebel B, ed. Proceedings of IJCAI’01. Seattle: Morgna Kaufmann Publishers Inc. 2001:57-63.
[40] Bailey-Kellogg C, Ramakreshnan N.Ambiguity-directed sampling for qualitative analysis of sparse data from spatially-distributed physical systems[J].In:Nebel B, ed.Proceedings of IJCAI’01.Seattle:Morgna Kaufmann Publishers Inc.2001:43-50.
[41] D. Randell, Z. Cui, and A. Cohn, A spatial logic based on regions and connection[J], in Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning, Morgan Kaufmann, 1992:165–176.
[42] Cohn, A. G., Randell, D. A. and Cui, Z. Taxonomies of Logically Defined Qualitative Spatial Relations[J].International Journal of Human-Computer Studies: Special issue on Formal Ontology in Conceptual Analysis and Knowledge Representation, 43(5{6), 1995:831-846.
[43] Egenhofer, M., Franzosa, R. Point-Set topological spatial relations[J]. International Journal of Geographical Information System, 1991, 5(2):161- 174.
[44]邹景华.基于语义万维网的智能信息检索技术研究[D].重庆:重庆大学计算机学院,硕士论文. 2005.
[45]林玉莲,胡正凡.环境心理学[M].北京,中国建筑工业出版社,2000.12.
[46] Clementini, E., Di Felice, P. and Oosterom, P., A small set of formal topological relationships suitable for end-user interatction[J], D. Abel and B. C. Ooi (eds.) Advances in Spatial Databases:Proc. 3rd Intl. Symposium on Spatial Databases (SSD'93), LNCS No. 692, Springer-Verlag, 1993:277-295.
[47] Liu G, Zhu G, Wu W, Hu Z, Liu Y.An Effective Call Admission Policy for Multi-Services Wireless Networks Using Stochastic Control[J].In:Proc.IEEE Vehicular Technology Conf., 2004.
[48]梅婧,林作铨.从ALC到SHOQ(D):描述逻辑及其Tableau算法[J].北京,计算机科学2005vol.32.No.3:1-11.
[49] Schild K.A correspondence theory for terminological logic[J]:Preliminary report.In:Proc.of UCAI'91, Sydney, 1991:466-471.
[50] Sattler U.A concept language extended with different kinds of transitive roles[J].In 20.Deutsche Jahrestagung for KI, LNAI1137.Springer-Verlag, 1996.
[51] Horrocks I, Gough G.Description logics with transitive roles[J].In:M.-C.Rousset, R. Brachmann, F.Donini, E-Franconi, I.Horrocks, and A.Levy, eds, Proc.of DL'97, 1997:25-28.
[52] F.Baader and P.Hanschke.A scheme for integrating concrete domains into concept languages[J].In Twelfth International Joint Conference on Artificial Intelligence, 1991.8:452-457.
[53] Horrocks I, Sattler U, Tobies S.A description logic with transitive and converse roles, role hierarchies and qualifying number restrictions[J]:[LTCS-Report 99-08].LuFg Theoretical Computer Science, RWTH Aachen, Germany, 1999.
[54] Ping Guo, Ruixia-Zhang. Spatial topology relationships concrete domain and consistency determination[J]. 2009 WASE International Conference on Information Engineering (ICIE), Taiyuan, Chanxi China, july, 2009:611-614.
[2] A.G.Chon, S.M.Hazarika, Qualitative Spatial representation and reasoning:an overview[J]. Fundament Information, May 2001, Volume 46 Issue 1-2(2001):2-32.
[3]郭平.定性空间推理技术及其应用[D].重庆:重庆大学计算机学院,博士论文. 2004.
[4] Egenhofer, M., Franzosa, R. Point-Set topological spatial relations[J]. International Journal of Geographical Information System, 1991, 5 (2 ):161- 174.
[5] Ping Guo, Tao Huang-Fu, Ya Luo, Research on the Relationship Between 4-intersection and Classifying Invariant Base on the Simple Regions[J].In Proceedings of the 2003 International Conference on Machine Learning and Cybernetics, Xi an, China, 2003: 1642-1647.
[6] Egenhofer, M. J. and Herring, J., Categorizing topological spatial relationships between point, line and area objects, The 9-intersections: formalism and its use for natural language spatial predicates[R]. Technical Report 94-1., National Centre for Geographic Information and Analysis, Santa Barbara, 1994.
[7]史忠植.高级人工智能[M].科学出版社, 2006.9.
[8] Brachman R J. and Schmolze J G., An overview of the KL-ONE knowledge representation system[J], Cognitive Science, 1985, 9 (2):171-216.
[9] Baader F , Calvanese D , McGuinness D , et al . The Description Logic Handbook : Theory , Implementation and Applications [M] . 2nd ed. Cambridge : Cambridge Univer sity Press , 2007:47-100.
[10] Li Shuying , Li Mei , Jiang Yuncheng , et al . Fuzzy description logic L-ALCN [J] . Journal of Computer Research and Development , 2008 , 45 (4) : 619-625 (in Chinese) (李淑英,李梅,蒋运承,等.模糊描述逻辑L-ALCN [J] .计算机研究与发展, 2008, 45 (4) : 619-625).
[11] Jiang Yuncheng , Wang J u , Deng Peimin , et al . Semantics and reasoning of terminological cycles in description logic FL -[J] . Chinese Journal of Computers , 2008 , 31 (2) : 185-195 (in Chinese).
[12]邱剑锋,王申康,马勤勇,王玥,徐海长.描述逻辑在基于语义的服务消息交互中的应用[J].计算机应用研究.vol26 No.1, Jan 2009:289-293.
[13] Description Logic.home page http://dl.kr.org/[Z].2009.
[14] Liu Y. B., CHEN G., The Research of Spatial Reasoning in Description Logic[J]. Computer Science, 2004 Vol.31(8):110-112 (in Chinese)
[15] Brachman R J, Levesque H J, The tractability of subsumption in frame-based descriptionlanguages[J]. In: Proceedings of the 4th National Conference of the American Association for Artificial Intelligence (AAAI-84), Austin, TX, 1984:34-37.
[16] Baader F, Horrocks I, Sattler U, Description logics as ontology languages for the semantic web[R]. In: Hutter D, Stephan W, eds. Festschrift in honor of Jorg Siekmann, Lecture Notes in Artificial Intelligence, Springer, 2003:4-5.
[17] Mays E, Dionne R, Weida R. K-REP system overview[J]. SIGART Bulletin, 1991, 2(3):93-97.
[18] Peltason C. The BACK system-an overview[M]. SIGART Bulletin, 1991, 2(3):114-119.
[19] MacGregor R. The evolving technology of classification-based knowledge representation systems[J]. In: Sowa J F, ed. Principles of Semantic Networks, Morgan Kaufmann, Los Altos: 1991:385-400.
[20] Schmidt-SchauβM, Smolka G. Attributive concept descriptions with complements[J]. Artificial Intelligence Journal, 1991, 48(1):1-26.
[21] Donini F, Lenzerini M, Nardi D, et al.The complexity of concept languages[J]. In: Proc. of the 2nd Int Conf on the Principles of Knowledge Representation and Reasoning (KR-91), Boston, MA, USA, 1991.
[22] Hollunder B, Nutt W, Schmidt-Schauss M. Subsumption algorithms for concept description languages[M]. In:ECAI-90, Pitman Publishing, London, 1990.
[23] Donini F M, Lenzerini M, Nardi D, et al. Tractable concept languages[J]. In: Proc. of the 12th Int Joint Conf. on Artificial Intelligence(IJCAI-91), Sydney, 1991:458-463.
[24] Donini F M, Hollunder B, Lenzerini M, et al. The complexity of existential quantification in concept languages[J]. Artificial Intelligence Journal, 1992(2-3):309-327.
[25] Schild K. A correspondence theory for terminological logics: Preliminary report[R]. In: Proc. of the 12th Int Joint Conf. on Artificial Intelligence(IJCAI-91), 1991:466-471.
[26] Horrocks I. Using an expressive description logic: FaCT or Fiction?[J] In: Proc. of the 6th Int Conf. on the Principles of Knowledge Representation and Reasoning(KR-98), 1998:636-647.
[27] Haarslev V, Moller R. RACE system description[J]. In: Lambrix P, Borgida A, Lenzerini M, et al. Proceedings of the International Workshop on Description Logics, Linkoping, Sweden, 1999
[28] Patel-Schneider P F. DLP[J]. In: Proc. of the 1999 Description Logic Workshop(DL’99), CEUR Electronic Workshop Proceedings. http://ceurws.org/vol-22/, 1999:9-13.
[29] De Giacomo G, Lenzerini M.Boosting the correspondence between description logics and propositional dynamic logics[J]. In: Proc. of the 12th Nat Conf. on Aritificial Intelligence(AAAI-94) AAAI Press/The MIT Press, 1994:205-212 .
[30] Schild K.Querying Knowledge and Data Bases by a Universal Description Logic with Recursion[D]: [PhD thesis]. University at des Saarlandes, Germany, 1995.
[31] Borgida A. On the relative expressive power of Description Logics and Predicate Calculus[J]. To appear in Artificial Intelligence, 1996.
[32] Pacholski L, Szwast W, Tendera L. Complexity of two-variable logic with counting[J]. In: Proc. of the 12th Ann IEEE Symp on Logic in Computer Science(LICS-97), IEEE Computer Society Press, 1997.318-327 .
[33] Gradel E, Kolaitis P G, Vardi M Y. On the decision problem for two-variable first-order logic[J]. Bulletin of Symbolic Logic, 1997, 3(1):53-69.
[34] Gradel E. Guarded fragments of first-order logic: A perspective for new description logics?[J] In: Proc. of the 1998 Description Logic Workshop(DL’98). CEUR Electronic Workshop Proceedings, http://ceur-ws.org/vol-11/, 1998.
[35] Gradel E. On the restraining power of guards[J]. Journal of Symbolic Logic, 1999, 64: 1719-1742.
[36] The IEA/AIE-2000 Workshop on Applications of Spatio-Temporal Reasoning Workshop Report[R], 1999.
[37]陈科.空间方位知识库与推理组件的研究与开发[D].重庆:重庆大学计算机学院,硕士论文. 2009.
[38] Leung, Y. Intelligent spatial decision support systems[J]. Berlin: Springer-Verlag. 1997, 1998. http://nsdi.Usgs.gov/nsdi/.
[39] Randell D A, Witkowski M, Shanahan M. From images to bodis: Modelling and exploiting spatial occlusion and motion parallax[J]. In: Nebel B, ed. Proceedings of IJCAI’01. Seattle: Morgna Kaufmann Publishers Inc. 2001:57-63.
[40] Bailey-Kellogg C, Ramakreshnan N.Ambiguity-directed sampling for qualitative analysis of sparse data from spatially-distributed physical systems[J].In:Nebel B, ed.Proceedings of IJCAI’01.Seattle:Morgna Kaufmann Publishers Inc.2001:43-50.
[41] D. Randell, Z. Cui, and A. Cohn, A spatial logic based on regions and connection[J], in Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning, Morgan Kaufmann, 1992:165–176.
[42] Cohn, A. G., Randell, D. A. and Cui, Z. Taxonomies of Logically Defined Qualitative Spatial Relations[J].International Journal of Human-Computer Studies: Special issue on Formal Ontology in Conceptual Analysis and Knowledge Representation, 43(5{6), 1995:831-846.
[43] Egenhofer, M., Franzosa, R. Point-Set topological spatial relations[J]. International Journal of Geographical Information System, 1991, 5(2):161- 174.
[44]邹景华.基于语义万维网的智能信息检索技术研究[D].重庆:重庆大学计算机学院,硕士论文. 2005.
[45]林玉莲,胡正凡.环境心理学[M].北京,中国建筑工业出版社,2000.12.
[46] Clementini, E., Di Felice, P. and Oosterom, P., A small set of formal topological relationships suitable for end-user interatction[J], D. Abel and B. C. Ooi (eds.) Advances in Spatial Databases:Proc. 3rd Intl. Symposium on Spatial Databases (SSD'93), LNCS No. 692, Springer-Verlag, 1993:277-295.
[47] Liu G, Zhu G, Wu W, Hu Z, Liu Y.An Effective Call Admission Policy for Multi-Services Wireless Networks Using Stochastic Control[J].In:Proc.IEEE Vehicular Technology Conf., 2004.
[48]梅婧,林作铨.从ALC到SHOQ(D):描述逻辑及其Tableau算法[J].北京,计算机科学2005vol.32.No.3:1-11.
[49] Schild K.A correspondence theory for terminological logic[J]:Preliminary report.In:Proc.of UCAI'91, Sydney, 1991:466-471.
[50] Sattler U.A concept language extended with different kinds of transitive roles[J].In 20.Deutsche Jahrestagung for KI, LNAI1137.Springer-Verlag, 1996.
[51] Horrocks I, Gough G.Description logics with transitive roles[J].In:M.-C.Rousset, R. Brachmann, F.Donini, E-Franconi, I.Horrocks, and A.Levy, eds, Proc.of DL'97, 1997:25-28.
[52] F.Baader and P.Hanschke.A scheme for integrating concrete domains into concept languages[J].In Twelfth International Joint Conference on Artificial Intelligence, 1991.8:452-457.
[53] Horrocks I, Sattler U, Tobies S.A description logic with transitive and converse roles, role hierarchies and qualifying number restrictions[J]:[LTCS-Report 99-08].LuFg Theoretical Computer Science, RWTH Aachen, Germany, 1999.
[54] Ping Guo, Ruixia-Zhang. Spatial topology relationships concrete domain and consistency determination[J]. 2009 WASE International Conference on Information Engineering (ICIE), Taiyuan, Chanxi China, july, 2009:611-614.
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