Propagation of mathematical constraints in subdefinite models
In the real world we almost always deal only with objects that possess such properties as incompleteness, imprecision, inconsistency, subdefinitess, etc. For this reason, the study of these properties and the nontraditional methods of knowledge processing that are based on them is a very important direction of research.
This paper describes a novel approach to solving problems that is based on subdefinite calculations. The use of these methods makes it possible to solve overdetermined and underdetermined problems, as well as problems with uncertain, imprecise and incomplete data. Such problems can be expressed in terms of subdefinite models (SD-models). Propagation of mathematical constraints in all the SD-models is supported by a single data-driven inference algorithm. Several examples are given to show the capabilities of this approach for solving a wide class of constraint satisfaction problems.
KeywordsData Type Constraint Satisfaction Problem Constraint Propagation Knowledge Engineer USSR Acad
Unable to display preview. Download preview PDF.
- [Alef83]Alefeld, G., Herzberger, Ju.: Introduction in Interval Computations, Academic Press, New York, (1983).Google Scholar
- [UniC1]Babichev, A.B., et al.: UniCalc — an intelligent solver for mathematical problems, Proceedeings of East-West AI Conference: from theory to practice, Moscow, (1993), 257–260.Google Scholar
- [Borde]Borde, S.B., et al.: Subdefiniteness and Calendar Scheduling, Ibid, 315–318.Google Scholar
- [Kan84]Kandrashina, E.Yu.: Means for Representing Temporal Information in Knowledge Bases, Trans. USSR Acad. Sci., Technical Cybernetics, 5, Moscow, (1984), 15–22 (in Russian).Google Scholar
- [Kan86]Kandrashina, E.Yu.: Means for Representing Temporal Information in Knowledge Bases. Event Sequences, Trans. USSR Acad. Sci., Technical Cybernetics, 5, Moscow, (1986), 211–231 (in Russian).Google Scholar
- [Nar80a]Narin'yani, A.S.: Subdefinite Set — a Formal Model of Uncompletely Specified Aggregate, Proc. of the Symp. on Fuzzy Sets and Possibility Theory, Acapulco, Mexico, (1980).Google Scholar
- [Nar80b]Narin'yani, A.S.: Subdefinite Sets — New Data Type for Knowledge Representation, Preprint USSR Acad. Sci., Siberian Division, Computer Center, 232, Novosibirsk, (1980) (in Russian).Google Scholar
- [Nar82]Narin'yani, A.S.: Active Data Types for Representing and Processing of Subdefinite Information, In: Actual Problems of the Computer Architecture Development and Computer and Computer System Software, Novosibirsk, (1983), 128–141 (In Russian).Google Scholar
- [Nar86a]Narin'yani, A.S.: Subdefiniteness in Knowledge Representation and Processing, Trans. USSR Acad. Sci., Technical cybernetics, 5, Moscow, (1986), 3–28 (in Russian).Google Scholar
- [Nar86b]Narin'yani, A.S.: Representation of Subdefiniteness, Over-definiteness and Absurdity in Knowledge Bases (Some Formal Aspects), Computers and Artificial Intelligence, (1986), 5, N 6, 479–487.Google Scholar
- [Nar87]Narin'yani, A.S., Telerman, V.V., Dmitriev, V.E.: Virtual Data-Flow Machine as Vehicle of Inference/Computations in Knowledge Bases, In: Ph. Jorrand, V. Sgurev (Eds.) Artificial Intelligence II: Methodology, Systems, Application, North-Holland, (1987), 149–154.Google Scholar
- [UniC2]Semenov, A.L., Babichev, A.B., Leshchenko A.S.: Subdefinite computations and symbolic transformations in the UniCalc solver, This volume.Google Scholar
- [Tel88]Telerman, V.V.: Active Data Types,-Preprint, USSR Acad. Sci., Siberian Division, Computer Center, 792, Novosibirsk, (1988) (In Russian).Google Scholar
- [Tel93a]Telerman, V.V.: Constraint propagation in sub-definite models, In: B. Mayoh, J. Penjam, E. Tyugu (Eds.) NATO Advanced Study Institute, CONSTRAINT PROGRAMMING, Tallinn, (1993), 33–45.Google Scholar
- [Tel93b]Telerman, V.V.: Technological environment for construction and processing sub-definite models, Proc. East-West AI Conference: from theory to practice, Moscow, (1993), 356–360.Google Scholar
- [Waltz]Waltz, D.L.: Understanding line drawings of scenes with shadows, In: P. Winston (Ed.) The Psychology of computer Vision, McGraw-Hill, New York, (1975).Google Scholar