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Hybrid Knowledge Bases
October 1996 (vol. 8 no. 5)
pp. 773-785

Abstract—Deductive databases that interact with, and are accessed by, reasoning agents in the real world (such as logic controllers in automated manufacturing, weapons guidance systems, aircraft landing systems, land-vehicle maneuvering systems, and air-traffic control systems) must have the ability to deal with multiple modes of reasoning. Specifically, the types of reasoning we are concerned with include, among others, reasoning about time, reasoning about quantitative relationships that may be expressed in the form of differential equations or optimization problems, and reasoning about numeric modes of uncertainty about the domain which the database seeks to describe. Such databases may need to handle diverse forms of data structures, and frequently they may require use of the assumption-based nonmonotonic representation of knowledge.

A hybrid knowledge base is a theoretical framework capturing all the above modes of reasoning. The theory tightly unifies the Constraint Logic Programming Scheme of Jaffar and Lassez [12], the Generalized Annotated Logic Programming Theory of Kifer and Subrahmanian [17], and the Stable Model semantics of Gelfond and Lifschitz [7]. New techniques are introduced which extend both the work on Annotated Logic Programming and the Stable Model semantics. (Proofs are omitted from the paper to ensure readability. Complete details of all results may be found in [24].)

[1] K. Apt, "Logic Programming," Handbook of Theoretical Computer Science, vol. B, J. van Leeuven, ed., pp. 493-574.Cambridge, Mass.: MIT Press, 1990.
[2] K. Apt, H.A. Blair, and A. Walker, "Towards a Theory of Declarative Knowledge," Foundations of Deductive Databases and Logic Programming, J. Minker, ed., pp. 89-148. Morgan Kaufmann, 1988.
[3] S. Adali and, V.S. Subrahmanian, "Amalgamating Knowledge Bases II: Algorithms, Data Structures and Query Processing," Technical Report CS-TR-3124, Computer Science Dept., Univ. of Maryland, 1993.
[4] J. Benton and V.S. Subrahmanian, "Hybrid Knowledge Bases for Missile Siting Problems," Proc. IEEE Conf. Applications of Artificial Intelligence, 1994.
[5] C. Bell, A. Nerode, R. Ng, and V.S. Subrahmanian, "Implementing Deductive Databases by Linear Programming," Proc. ACM SIGACT/SIGART/SIGMOD Symp. Principles of Database Systems, pp. 283-292, 1992. Available as Univ. of Maryland Technical Report CS-TR-2747, 1991.
[6] A. Frisch, "The Substitutional Framework for Sorted Deduction," Artificial Intelligence, vol. 49, pp. 161-198, 1991.
[7] M. Gelfond and V. Lifschitz, "The Stable Model Semantics for Logic Programming," Proc. Fifth Int'l Conf. and Symp. Logic Programming, R.A. Kowalski and K.A. Bowen, eds., pp. 1,070-1,080. MIT Press, 1988.
[8] J. Grant, W. Litwin, N. Roussopoulos, and T. Sellis, "An Algebra and Calculus for Relational Multidatabase Systems," Proc. First Int'l Workshop Interoperability in Multidatabase Systems, pp. 118-124. IEEE CS Press, 1991.
[9] R. Hähnle, "Towards an Efficient Tableau Rules for Multiple-valued Logics," Proc. Workshop Computer Science Logic, pp. 248-260. Springer, 1990.
[10] R. Hähnle, "Uniform Notation Tableau Rules for Multiple-Valued Logics," Proc. Int'l Symp. Multiple-Valued Logic, pp. 26-29, 1991.
[11] J. Horst, E.W. Kent, H. Rifky, and V.S. Subrahmanian, "Intelligent, Real-Time Robotic Reasoning with Hybrid Knowledge Bases," Proc. Fourth Int'l Workshop Pattern Recognition in Practice. North-HollandElsevier, 1994.
[12] J. Jaffar and J.L. Lassez, "Constraint Logic Programming," Proc. ACM Principles of Programming Languages, pp. 111-119, 1987.
[13] J. Jaffar, S. Michaylov, P. Stuckey, and R. Yap, "The${\rm CLP}(\Re)$Language and System," ACM Trans. Programming Languages and Systems, 1992.
[14] M. Kifer and E. Lozinskii, "RI: A Logic for Reasoning with Inconsistency," Proc. Fourth Symp. Logic in Computer Science, pp. 253-262,Asilomar, Calif., 1989.
[15] M. Kifer and E. Lozinskii, "A Logic for Reasoning with Inconsistency," J. Automated Reasoning, vol. 9, pp. 179-215, 1992.
[16] M. Kifer, G. Lausen, and J. Wu, "Logical Foundations of Object-Oriented and Frame-Based Languages," Technical Report 90/14, State Univ. of New York at Stonybrook, 1990.
[17] M. Kifer and V.S. Subrahmanian, "Theory of Generalized Annotated Logic Programming and its Applications," Proc. North Am. Conf. Logic Programming. MIT Press, 1989.
[18] M. Kifer and V.S. Subrahmanian, "Theory of Generalized Annotated Logic Programming and its Applications," J. Logic Programming, vol. 12, no. 4, pp. 335-368, 1992.
[19] W. Kim and J. Seo, "Classifying Schematic and Data Heterogeneity in Multidatabase Systems," Computer, Dec. 1991.
[20] S. Kraus and D. Lehmann, "Decision Procedures for Time and Chance," Proc. IEEE Symp. Foundation of Computer Science, pp. 202-209, 1983.
[21] R. Krishnamurthy, W. Litwin, and W. Kent, "Language Features for Interoperability of Databases with Schematic Discrepancies," Proc. ACM SIGMOD, 1991.
[22] S. Leach and J. Lu, "Computing Annotated Logic Programs," Proc. Int'l Conf. Logic Programming. MIT Press, 1994.
[23] A. Lefebvre, P. Bernus, and R. Topor, "Querying Heterogeneous Databases: A Case Study," draft manuscript, 1992.
[24] D. Lehmann and S. Shelah, "Reasoning with Time and Chance," Information and Control, vol. 53, no. 3, pp. 165-198, 1982.
[25] J.W. Lloyd, Foundations of Logic Programming, Springer Series in Symbolic Computation, second ed. New York: Springer-Verlag, 1987.
[26] J. Lu, A. Nerode, J. Remmel, and V.S. Subrahmanian, "Towards a Theory of Hybrid Knowledge Bases," TR93-14, Mathematical Sciences Inst., Cornell Univ., 1993.
[27] N.V. Murray and E. Rosenthal, "Signed Formulas: A Liftable Meta-Logic for Multiple-Valued Logics," Proc. ISMIS. Springer, 1993.
[28] R. Ng and V.S. Subrahmanian, "Probabilistic Logic Programming," Information and Computation, vol. 101, no. 2, pp. 150-201, 1992.
[29] H. Samet, The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
[30] A.P. Seth and J.A. Larson,“Federated database systems for managing distributed, heterogeneous andautonomous databases,” ACM Computing Surveys, vol. 22, no. 3, pp. 184-236, September 1990.
[31] M. Stickel, "Automated Deduction by Theory Resolution," J. Automated Reasoning, vol. 1, pp. 333-355, 1985.
[32] V.S. Subrahmanian, "Amalgamating Knowledge Bases," ACM Trans. Database Systems, 1994.
[33] A. van Gelder, K. Ross, and J. Schlipf, "Unfounded Sets and Well-founded Semantics for General Logic Programs," Proc. Symp. Principles of Database Systems, pp. 221-230, 1988.
[34] A. van Gelder, "The Alternating Fixpoint of Logic Programs with Negation," Proc. ACM Symp. Principles of Database Systems, pp. 1-10, 1989.
[35] T.J. Weigert, J-P. Tsai, and X. Liu, "Fuzzy Operator Logic and Fuzzy Resolution," J. Automated Reasoning, vol. 10, pp. 59-78, 1993.
[36] G. Wiederhold, "Mediators in the Architecture of Future Information Systems," Computer, pp. 38-49, Mar. 1992.
[37] G. Wiederhold, "Intelligent Integration of Information," Proc. ACM SIGMOD Conf. Management of Data, pp. 434-437, 1993.
[38] G. Wiederhold, S. Jajodia, and W. Litwin, "Dealing with Granularity of Time in Temporal Databases," Proc. Nordic Conf. Advanced Information Systems Eng., R. Anderson et al., eds., pp. 124-140. Springer, 1991,
[39] G Wiederhold, S. Jajodia, and W. Litwin, "Integrating Temporal Data in a Heterogeneous Environment," Temporal Databases. Benjamin Cummings, 1993.

Index Terms:
Annotated logic, constraint logic programming, heterogeneous system, mediator, stable model.
James J. Lu, Anil Nerode, V.s. Subrahmanian, "Hybrid Knowledge Bases," IEEE Transactions on Knowledge and Data Engineering, vol. 8, no. 5, pp. 773-785, Oct. 1996, doi:10.1109/69.542029
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